# Prop-01 E1 live backends — `full`

**Started (UTC):** 2026-09-05T20:44:48.963148+00:00
**Finished (UTC):** 2026-09-05T22:59:49.986566+00:00
**Local (America/New_York):** 2026-09-05 18:59:49 EDT
**Total wall (s):** 8100.995902377999
**Protocol:** LAX-PROP-2026-09-04-01

## prop01_support_claim: **false**

STLS 20-seed tables (`prop01_results.md` / `prop01_stls_20seed_results.*`) were **not**
overwritten. This artifact is live PySR(A0)/PhySO(A4) only. Claim stays false until
Prop-01 §5 success criteria are met on the **full** live grid (not pilot).

## Locked metrics

- τ = 0.2, R\* = 0.25, C\* = 0.5 (from `sr_ladder/evaluate.py`)
- train_frac = 0.7

## Grid

- Mode: `full`
- Laws: ['linear_decay', 'harmonic_oscillator', 'damped_oscillator', 'lotka_volterra', 'diffusion_1d', 'burgers_1d', 'gravity_toy', 'dim_violating']
- Seeds: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
- N: [50, 100, 400]
- σ_rel: [0.0, 0.05]
- Arms: A0_pysr, A4_physo

## Pre-registered budgets (caps logged)

```json
{
  "A0_pysr": {
    "niterations": 55,
    "populations": 15,
    "population_size": 40,
    "tournament_selection_n": 10,
    "maxsize": 22,
    "timeout_in_seconds": 100,
    "wall_cap_s": 120,
    "target_mean_wall_s": 0
  },
  "A4_physo": {
    "epochs": 8,
    "stop_after_n_epochs": 8,
    "max_n_evaluations": 2500,
    "batch_size": 32,
    "parallel_mode": false,
    "device": "cpu",
    "wall_cap_s": 120,
    "zero_eq_retry": 2
  },
  "matched_wall_band_rel": 0.2
}
```

## Matched wall-clock band

```json
{
  "band_rel": 0.2,
  "n_paired_cells": 960,
  "n_within_band": 780,
  "frac_paired_within_band": 0.8125,
  "mean_ratio_a4_over_a0": 0.9672110478460156,
  "mean_wall_A0_pysr": 13.474185765066517,
  "mean_wall_A4_physo": 12.808137697489066,
  "arm_means_rel_gap": 0.049431414943399594,
  "arm_means_within_band": true,
  "soft_pad_documented": true,
  "mean_soft_pad_s": 0.0,
  "n_a4_zero_eq_cells": 0,
  "a4_zero_eq_examples": [],
  "caps_logged": true
}
```

- arm_means_within_band (±0.2): **True**
- mean wall A0=13.474185765066517 A4=12.808137697489066 rel_gap=0.049431414943399594
- soft_pad documented: mean_pad_s=0.0
- A4 zero-eq cells (not hidden): 0

## A4 zero-expression fails (explicit; counted in tables)

| seed | law | N | σ | equations | blockers |
| ---: | --- | ---: | ---: | --- | --- |
| — | — | — | — | none | — |

## Aggregate (mean ± Wilson CI over seeds)

| Law | σ | N | arm | n_seeds | recovery [CI] | accept [CI] | clean-fail [CI] | mean R | mean wall_s |
| --- | ---: | ---: | --- | ---: | --- | --- | --- | ---: | ---: |
| `burgers_1d` | 0.0 | 50 | `A0_pysr` | 20 | 0.450 [0.26,0.66] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 4.039e-11 | 9.62 |
| `burgers_1d` | 0.0 | 50 | `A4_physo` | 20 | 0.550 [0.34,0.74] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.01728 | 8.55 |
| `burgers_1d` | 0.0 | 100 | `A0_pysr` | 20 | 0.250 [0.11,0.47] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 2.419e-11 | 8.61 |
| `burgers_1d` | 0.0 | 100 | `A4_physo` | 20 | 0.550 [0.34,0.74] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.01495 | 8.67 |
| `burgers_1d` | 0.0 | 400 | `A0_pysr` | 20 | 0.050 [0.01,0.24] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 3.603e-12 | 11.4 |
| `burgers_1d` | 0.0 | 400 | `A4_physo` | 20 | 0.550 [0.34,0.74] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.01322 | 8.93 |
| `burgers_1d` | 0.05 | 50 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.007541 | 9.01 |
| `burgers_1d` | 0.05 | 50 | `A4_physo` | 20 | 0.500 [0.30,0.70] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.02098 | 9.32 |
| `burgers_1d` | 0.05 | 100 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005804 | 9.3 |
| `burgers_1d` | 0.05 | 100 | `A4_physo` | 20 | 0.550 [0.34,0.74] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.02246 | 8.64 |
| `burgers_1d` | 0.05 | 400 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005771 | 9.91 |
| `burgers_1d` | 0.05 | 400 | `A4_physo` | 20 | 0.550 [0.34,0.74] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.01931 | 9.01 |
| `damped_oscillator` | 0.0 | 50 | `A0_pysr` | 20 | 0.950 [0.76,0.99] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 1.083e-16 | 18 |
| `damped_oscillator` | 0.0 | 50 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.350 [0.18,0.57] | 0.650 [0.43,0.82] | 0.02669 | 16.9 |
| `damped_oscillator` | 0.0 | 100 | `A0_pysr` | 20 | 0.950 [0.76,0.99] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 1.442e-16 | 17 |
| `damped_oscillator` | 0.0 | 100 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.450 [0.26,0.66] | 0.550 [0.34,0.74] | 0.02786 | 30.5 |
| `damped_oscillator` | 0.0 | 400 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 3.692e-17 | 19.6 |
| `damped_oscillator` | 0.0 | 400 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.450 [0.26,0.66] | 0.550 [0.34,0.74] | 0.02765 | 15.2 |
| `damped_oscillator` | 0.05 | 50 | `A0_pysr` | 20 | 0.650 [0.43,0.82] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.006545 | 16.3 |
| `damped_oscillator` | 0.05 | 50 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.350 [0.18,0.57] | 0.650 [0.43,0.82] | 0.04374 | 15.6 |
| `damped_oscillator` | 0.05 | 100 | `A0_pysr` | 20 | 0.700 [0.48,0.85] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.006113 | 17.5 |
| `damped_oscillator` | 0.05 | 100 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.350 [0.18,0.57] | 0.650 [0.43,0.82] | 0.03366 | 16.1 |
| `damped_oscillator` | 0.05 | 400 | `A0_pysr` | 20 | 0.850 [0.64,0.95] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005225 | 18.7 |
| `damped_oscillator` | 0.05 | 400 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.350 [0.18,0.57] | 0.650 [0.43,0.82] | 0.03228 | 16.5 |
| `diffusion_1d` | 0.0 | 50 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 3.749e-14 | 9.67 |
| `diffusion_1d` | 0.0 | 50 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 5.957e-13 | 8.39 |
| `diffusion_1d` | 0.0 | 100 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 2.918e-14 | 8.78 |
| `diffusion_1d` | 0.0 | 100 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 4.923e-13 | 8.44 |
| `diffusion_1d` | 0.0 | 400 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 9.809e-13 | 9.28 |
| `diffusion_1d` | 0.0 | 400 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 1.428e-12 | 8.42 |
| `diffusion_1d` | 0.05 | 50 | `A0_pysr` | 20 | 0.250 [0.11,0.47] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.0072 | 8.79 |
| `diffusion_1d` | 0.05 | 50 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.007598 | 8.87 |
| `diffusion_1d` | 0.05 | 100 | `A0_pysr` | 20 | 0.550 [0.34,0.74] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.006658 | 8.85 |
| `diffusion_1d` | 0.05 | 100 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.006722 | 9.01 |
| `diffusion_1d` | 0.05 | 400 | `A0_pysr` | 20 | 0.600 [0.39,0.78] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005481 | 9.46 |
| `diffusion_1d` | 0.05 | 400 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005253 | 9.55 |
| `dim_violating` | 0.0 | 50 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 3.253e-15 | 8.29 |
| `dim_violating` | 0.0 | 50 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.250 [0.11,0.47] | 0.750 [0.53,0.89] | 94.06 | 8.31 |
| `dim_violating` | 0.0 | 100 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 6.408e-16 | 8.42 |
| `dim_violating` | 0.0 | 100 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.200 [0.08,0.42] | 0.800 [0.58,0.92] | 19.37 | 8.03 |
| `dim_violating` | 0.0 | 400 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 2.848e-32 | 9.07 |
| `dim_violating` | 0.0 | 400 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.250 [0.11,0.47] | 0.750 [0.53,0.89] | 8.485 | 8.11 |
| `dim_violating` | 0.05 | 50 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.006005 | 8.44 |
| `dim_violating` | 0.05 | 50 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.200 [0.08,0.42] | 0.800 [0.58,0.92] | 11.26 | 8.07 |
| `dim_violating` | 0.05 | 100 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005742 | 8.57 |
| `dim_violating` | 0.05 | 100 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.250 [0.11,0.47] | 0.750 [0.53,0.89] | 20.36 | 9.3 |
| `dim_violating` | 0.05 | 400 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.004638 | 9.27 |
| `dim_violating` | 0.05 | 400 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.150 [0.05,0.36] | 0.850 [0.64,0.95] | 10.91 | 9.78 |
| `gravity_toy` | 0.0 | 50 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0 | 20 |
| `gravity_toy` | 0.0 | 50 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.0623 | 15.4 |
| `gravity_toy` | 0.0 | 100 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0 | 19.6 |
| `gravity_toy` | 0.0 | 100 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.05843 | 15.2 |
| `gravity_toy` | 0.0 | 400 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0 | 20.8 |
| `gravity_toy` | 0.0 | 400 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.05971 | 15.3 |
| `gravity_toy` | 0.05 | 50 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 0.200 [0.08,0.42] | 0.800 [0.58,0.92] | 2.972 | 17.1 |
| `gravity_toy` | 0.05 | 50 | `A4_physo` | 20 | 0.250 [0.11,0.47] | 0.250 [0.11,0.47] | 0.750 [0.53,0.89] | 0.7511 | 15.2 |
| `gravity_toy` | 0.05 | 100 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 0.550 [0.34,0.74] | 0.450 [0.26,0.66] | 0.2417 | 17.4 |
| `gravity_toy` | 0.05 | 100 | `A4_physo` | 20 | 0.250 [0.11,0.47] | 0.400 [0.22,0.61] | 0.600 [0.39,0.78] | 0.4522 | 15.7 |
| `gravity_toy` | 0.05 | 400 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.0507 | 17.9 |
| `gravity_toy` | 0.05 | 400 | `A4_physo` | 20 | 0.500 [0.30,0.70] | 0.500 [0.30,0.70] | 0.500 [0.30,0.70] | 0.0886 | 15.6 |
| `harmonic_oscillator` | 0.0 | 50 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0 | 16.7 |
| `harmonic_oscillator` | 0.0 | 50 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.02844 | 18.8 |
| `harmonic_oscillator` | 0.0 | 100 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0 | 18.3 |
| `harmonic_oscillator` | 0.0 | 100 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.02546 | 16.8 |
| `harmonic_oscillator` | 0.0 | 400 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0 | 18.2 |
| `harmonic_oscillator` | 0.0 | 400 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.02519 | 20.2 |
| `harmonic_oscillator` | 0.05 | 50 | `A0_pysr` | 20 | 0.700 [0.48,0.85] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.006026 | 17.8 |
| `harmonic_oscillator` | 0.05 | 50 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.03592 | 15.8 |
| `harmonic_oscillator` | 0.05 | 100 | `A0_pysr` | 20 | 0.750 [0.53,0.89] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005273 | 17.2 |
| `harmonic_oscillator` | 0.05 | 100 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.03154 | 16 |
| `harmonic_oscillator` | 0.05 | 400 | `A0_pysr` | 20 | 0.700 [0.48,0.85] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.004687 | 17.5 |
| `harmonic_oscillator` | 0.05 | 400 | `A4_physo` | 20 | 0.950 [0.76,0.99] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.03101 | 16.3 |
| `linear_decay` | 0.0 | 50 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 6.08e-16 | 9.58 |
| `linear_decay` | 0.0 | 50 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 2.746e-15 | 7.3 |
| `linear_decay` | 0.0 | 100 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 4.912e-16 | 7.6 |
| `linear_decay` | 0.0 | 100 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 2.979e-15 | 7.5 |
| `linear_decay` | 0.0 | 400 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 3.023e-16 | 8.31 |
| `linear_decay` | 0.0 | 400 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 2.608e-15 | 7.69 |
| `linear_decay` | 0.05 | 50 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.007932 | 7.82 |
| `linear_decay` | 0.05 | 50 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.007932 | 7.91 |
| `linear_decay` | 0.05 | 100 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005211 | 7.98 |
| `linear_decay` | 0.05 | 100 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005211 | 7.53 |
| `linear_decay` | 0.05 | 400 | `A0_pysr` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.00495 | 8.52 |
| `linear_decay` | 0.05 | 400 | `A4_physo` | 20 | 1.000 [0.84,1.00] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.00495 | 7.47 |
| `lotka_volterra` | 0.0 | 50 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 1.555e-15 | 17 |
| `lotka_volterra` | 0.0 | 50 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.04938 | 16.9 |
| `lotka_volterra` | 0.0 | 100 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 1.843e-16 | 18.7 |
| `lotka_volterra` | 0.0 | 100 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.03841 | 17.6 |
| `lotka_volterra` | 0.0 | 400 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 1.879e-32 | 18.6 |
| `lotka_volterra` | 0.0 | 400 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.05457 | 18.2 |
| `lotka_volterra` | 0.05 | 50 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.006437 | 16.6 |
| `lotka_volterra` | 0.05 | 50 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 0.950 [0.76,0.99] | 0.050 [0.01,0.24] | 0.05561 | 17 |
| `lotka_volterra` | 0.05 | 100 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005259 | 17.7 |
| `lotka_volterra` | 0.05 | 100 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.04584 | 17.4 |
| `lotka_volterra` | 0.05 | 400 | `A0_pysr` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.005856 | 18.2 |
| `lotka_volterra` | 0.05 | 400 | `A4_physo` | 20 | 0.000 [0.00,0.16] | 1.000 [0.84,1.00] | 0.000 [0.00,0.16] | 0.04772 | 18 |

## Per-cell detail (measured)

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=2.607356165685503e-19 cons=0.0 wall_s=28.497 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.607356165685503e-19,
  "conservation_residual": 0.0,
  "equations": [
    "(y + y + y + y + (y + y + y)*0.6837316)*(-0.24788493)"
  ],
  "wall_s_total": 28.497015360975638,
  "wall_s_per_eq": [
    28.497015360975638
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y + y + y + y + (y + y + y)*0.6837316)*(-0.24788493)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.607356165685503e-19,
      "pred_coeffs": {
        "y": -1.499999999414364
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 28.497015360975638,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=7.415 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 7.414554096059874,
  "wall_s_per_eq": [
    7.414554096059874
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.414554096059874,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=5.765632170678522e-16 cons=0.0 wall_s=7.616 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.765632170678522e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(y*(-0.043130003) + y - 1*5.432162e-9)*(-1.5676111) - 8.148243e-9"
  ],
  "wall_s_total": 7.616284311981872,
  "wall_s_per_eq": [
    7.616284311981872
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*(-0.043130003) + y - 1*5.432162e-9)*(-1.5676111) - 8.148243e-9",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 5.765632170678522e-16,
      "pred_coeffs": {
        "1": 3.6727444819820033e-10,
        "y": -1.5000000285541666
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.616284311981872,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=5.768333147128499e-16 cons=0.0 wall_s=7.591 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.768333147128499e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.6102211) + y*0.11022113"
  ],
  "wall_s_total": 7.591417461051606,
  "wall_s_per_eq": [
    7.591417461051606
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.6102211) + y*0.11022113",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 5.768333147128499e-16,
      "pred_coeffs": {
        "y": -1.49999997
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.591417461051606,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=2.038430545251106e-16 cons=0.0 wall_s=7.355 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.038430545251106e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.9307592) + y*0.43075922 + y - (-y + y + y - 3.6100165e-9) - 5.648925e-9"
  ],
  "wall_s_total": 7.354589354014024,
  "wall_s_per_eq": [
    7.354589354014024
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.9307592) + y*0.43075922 + y - (-y + y + y - 3.6100165e-9) - 5.648925e-9",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 2.038430545251106e-16,
      "pred_coeffs": {
        "1": -2.0389085e-09,
        "y": -1.4999999800000001
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.354589354014024,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=3.297445219081388e-16 cons=0.0 wall_s=7.238 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.297445219081388e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.3356553) + y*(-0.16434468) - 1.5736706e-8 + 1.7177298e-8"
  ],
  "wall_s_total": 7.238058872055262,
  "wall_s_per_eq": [
    7.238058872055262
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.3356553) + y*(-0.16434468) - 1.5736706e-8 + 1.7177298e-8",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.297445219081388e-16,
      "pred_coeffs": {
        "1": 1.4405920000000018e-09,
        "y": -1.49999998
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.238058872055262,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=8.994521110327164e-16 cons=0.0 wall_s=7.386 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 8.994521110327164e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.3064286) + y*(-0.19357143)"
  ],
  "wall_s_total": 7.385760440025479,
  "wall_s_per_eq": [
    7.385760440025479
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.3064286) + y*(-0.19357143)",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 8.994521110327164e-16,
      "pred_coeffs": {
        "y": -1.50000003
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.385760440025479,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=3.252142293263022e-17 cons=0.0 wall_s=7.157 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.252142293263022e-17,
  "conservation_residual": 0.0,
  "equations": [
    "-y - 1*y*0.47413072 - 1*y*0.025869273"
  ],
  "wall_s_total": 7.156749545014463,
  "wall_s_per_eq": [
    7.156749545014463
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-y - 1*y*0.47413072 - 1*y*0.025869273",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.252142293263022e-17,
      "pred_coeffs": {
        "y": -1.499999993
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.156749545014463,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=1.0336115113788438e-15 cons=0.0 wall_s=7.565 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.0336115113788438e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-y - y - y + y*(-0.19580136) + y*1.6958014"
  ],
  "wall_s_total": 7.564930862979963,
  "wall_s_per_eq": [
    7.564930862979963
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-y - y - y + y*(-0.19580136) + y*1.6958014",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 1.0336115113788438e-15,
      "pred_coeffs": {
        "y": -1.49999996
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.564930862979963,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=1.6371632103263352e-34 cons=0.0 wall_s=7.648 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.6371632103263352e-34,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.34523106) - (y*0.15476894 + y + 1.6028123e-9) + 1.6028123e-9"
  ],
  "wall_s_total": 7.6480849960353225,
  "wall_s_per_eq": [
    7.6480849960353225
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.34523106) - (y*0.15476894 + y + 1.6028123e-9) + 1.6028123e-9",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.6371632103263352e-34,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.6480849960353225,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=3.080167472521629e-17 cons=0.0 wall_s=28.284 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.080167472521629e-17,
  "conservation_residual": 0.0,
  "equations": [
    "(-0.75979435*y + y*0.11965932 + y + y)*(-1.1030507)"
  ],
  "wall_s_total": 28.28390112204943,
  "wall_s_per_eq": [
    28.28390112204943
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-0.75979435*y + y*0.11965932 + y + y)*(-1.1030507)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.080167472521629e-17,
      "pred_coeffs": {
        "y": -1.5000000070639792
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 28.28390112204943,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=5.810322494404896e-15 cons=0.0 wall_s=7.711 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.810322494404896e-15,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4190406) + y*(-0.08095948)"
  ],
  "wall_s_total": 7.711225950042717,
  "wall_s_per_eq": [
    7.711225950042717
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4190406) + y*(-0.08095948)",
      "r2_train": 0.9999999999999958,
      "reward": null,
      "residual_heldout": 5.810322494404896e-15,
      "pred_coeffs": {
        "y": -1.50000008
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.711225950042717,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=7.254 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 7.253542075050063,
  "wall_s_per_eq": [
    7.253542075050063
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.253542075050063,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=7.520428044086061e-17 cons=0.0 wall_s=7.689 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.520428044086061e-17,
  "conservation_residual": 0.0,
  "equations": [
    "-0.9874653*y + y*(-0.25626737) + y*(-0.25626734)"
  ],
  "wall_s_total": 7.689011915004812,
  "wall_s_per_eq": [
    7.689011915004812
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-0.9874653*y + y*(-0.25626737) + y*(-0.25626734)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 7.520428044086061e-17,
      "pred_coeffs": {
        "y": -1.50000001
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.689011915004812,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=7.414 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-y + y - 1.5)"
  ],
  "wall_s_total": 7.414224055013619,
  "wall_s_per_eq": [
    7.414224055013619
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-y + y - 1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.414224055013619,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=6.209102093403555e-17 cons=0.0 wall_s=7.456 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.209102093403555e-17,
  "conservation_residual": 0.0,
  "equations": [
    "-1.3027085*y + y*(-0.19729151)"
  ],
  "wall_s_total": 7.455990388058126,
  "wall_s_per_eq": [
    7.455990388058126
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-1.3027085*y + y*(-0.19729151)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 6.209102093403555e-17,
      "pred_coeffs": {
        "y": -1.50000001
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.455990388058126,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=5.820281443969457e-16 cons=0.0 wall_s=7.413 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.820281443969457e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(y*(-0.74374044) + y*0.28474978 + y*0.45899072 - 0.148634) + y*(-1.351366)"
  ],
  "wall_s_total": 7.413009393028915,
  "wall_s_per_eq": [
    7.413009393028915
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(y*(-0.74374044) + y*0.28474978 + y*0.45899072 - 0.148634) + y*(-1.351366)",
      "r2_train": 0.9999999999999953,
      "reward": null,
      "residual_heldout": 5.820281443969457e-16,
      "pred_coeffs": {
        "y^2": 6.000000007944095e-08,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.413009393028915,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=7.840322800689251e-16 cons=0.0 wall_s=7.845 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.840322800689251e-16,
  "conservation_residual": 0.0,
  "equations": [
    "1.4999998*(-y + y*(-1.5646039e-7))"
  ],
  "wall_s_total": 7.845174674061127,
  "wall_s_per_eq": [
    7.845174674061127
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "1.4999998*(-y + y*(-1.5646039e-7))",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 7.840322800689251e-16,
      "pred_coeffs": {
        "y": -1.5000000346905538
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.845174674061127,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=1.160225090134709e-15 cons=0.0 wall_s=7.656 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.160225090134709e-15,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.19851254) + (-(-0.15673283)*y + y*0.17262284 + y)*(-0.97903633)"
  ],
  "wall_s_total": 7.655513157020323,
  "wall_s_per_eq": [
    7.655513157020323
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.19851254) + (-(-0.15673283)*y + y*0.17262284 + y)*(-0.97903633)",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 1.160225090134709e-15,
      "pred_coeffs": {
        "y": -1.5000000364214912
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.655513157020323,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=2.2529927344189274e-18 cons=0.0 wall_s=7.439 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.2529927344189274e-18,
  "conservation_residual": 0.0,
  "equations": [
    "(-y - y + y*2.6915114e-7)*0.7500001"
  ],
  "wall_s_total": 7.438538281014189,
  "wall_s_per_eq": [
    7.438538281014189
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-y - y + y*2.6915114e-7)*0.7500001",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.2529927344189274e-18,
      "pred_coeffs": {
        "y": -1.4999999981366179
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.438538281014189,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=2.596130541471392e-15 cons=0.0 wall_s=8.143 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.596130541471392e-15,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 8.143032099003904,
  "wall_s_per_eq": [
    8.143032099003904
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 2.596130541471392e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.143032099003904,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.143032099003904,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=2.449016597162232e-15 cons=0.0 wall_s=7.186 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.449016597162232e-15,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.186261446098797,
  "wall_s_per_eq": [
    7.186261446098797
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 2.449016597162232e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.186261446098797,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.186261446098797,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=1.951367568466373e-15 cons=0.0 wall_s=7.101 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.951367568466373e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 7.101085148053244,
  "wall_s_per_eq": [
    7.101085148053244
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.999999999999996,
      "reward": null,
      "residual_heldout": 1.951367568466373e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.101085148053244,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.101085148053244,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.75
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=1.5533592705639263e-15 cons=0.0 wall_s=7.179 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.5533592705639263e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.178689458989538,
  "wall_s_per_eq": [
    7.178689458989538
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999976,
      "reward": null,
      "residual_heldout": 1.5533592705639263e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.178689458989538,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.178689458989538,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=1.038901056928494e-15 cons=0.0 wall_s=7.134 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.038901056928494e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.1338974519167095,
  "wall_s_per_eq": [
    7.1338974519167095
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999968,
      "reward": null,
      "residual_heldout": 1.038901056928494e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.1338974519167095,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.1338974519167095,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=4.060463802808635e-15 cons=0.0 wall_s=7.064 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.060463802808635e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.064114664099179,
  "wall_s_per_eq": [
    7.064114664099179
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999976,
      "reward": null,
      "residual_heldout": 4.060463802808635e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.064114664099179,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.064114664099179,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=1.7124649998033665e-15 cons=0.0 wall_s=7.148 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.7124649998033665e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.148115358082578,
  "wall_s_per_eq": [
    7.148115358082578
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999966,
      "reward": null,
      "residual_heldout": 1.7124649998033665e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.148115358082578,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.148115358082578,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=7.609336356091748e-15 cons=0.0 wall_s=6.880 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.609336356091748e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.880442397086881,
  "wall_s_per_eq": [
    6.880442397086881
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 7.609336356091748e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.880442397086881,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.880442397086881,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=2.7756496753641856e-15 cons=0.0 wall_s=7.130 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.7756496753641856e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 7.129876377992332,
  "wall_s_per_eq": [
    7.129876377992332
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 2.7756496753641856e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.129876377992332,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.129876377992332,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.75
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=2.6729128300655636e-15 cons=0.0 wall_s=7.643 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.6729128300655636e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 7.642773660947569,
  "wall_s_per_eq": [
    7.642773660947569
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 2.6729128300655636e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.642773660947569,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.642773660947569,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.75
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=1.0688550123501702e-15 cons=0.0 wall_s=7.328 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.0688550123501702e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.327665801974945,
  "wall_s_per_eq": [
    7.327665801974945
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999981,
      "reward": null,
      "residual_heldout": 1.0688550123501702e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.327665801974945,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.327665801974945,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=1.9855183804940816e-15 cons=0.0 wall_s=7.190 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.9855183804940816e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.1897319190902635,
  "wall_s_per_eq": [
    7.1897319190902635
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 1.9855183804940816e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.1897319190902635,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.1897319190902635,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=6.055970416524149e-15 cons=0.0 wall_s=7.233 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.055970416524149e-15,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.233327207970433,
  "wall_s_per_eq": [
    7.233327207970433
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999967,
      "reward": null,
      "residual_heldout": 6.055970416524149e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.233327207970433,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.233327207970433,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=7.452743046564342e-16 cons=0.0 wall_s=7.486 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.452743046564342e-16,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 7.485825109062716,
  "wall_s_per_eq": [
    7.485825109062716
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.9999999999999961,
      "reward": null,
      "residual_heldout": 7.452743046564342e-16,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.485825109062716,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.485825109062716,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.75
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=1.1583596439302632e-15 cons=0.0 wall_s=7.295 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.1583596439302632e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.295152427977882,
  "wall_s_per_eq": [
    7.295152427977882
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999981,
      "reward": null,
      "residual_heldout": 1.1583596439302632e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.295152427977882,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.295152427977882,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=2.1464899226708053e-15 cons=0.0 wall_s=7.461 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.1464899226708053e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.461464382940903,
  "wall_s_per_eq": [
    7.461464382940903
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999949,
      "reward": null,
      "residual_heldout": 2.1464899226708053e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.461464382940903,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.461464382940903,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=9.7030450874686e-16 cons=0.0 wall_s=7.773 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 9.7030450874686e-16,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.772533981013112,
  "wall_s_per_eq": [
    7.772533981013112
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999971,
      "reward": null,
      "residual_heldout": 9.7030450874686e-16,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.772533981013112,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.772533981013112,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=4.713481742560366e-15 cons=0.0 wall_s=6.587 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.713481742560366e-15,
  "conservation_residual": 0.0,
  "equations": [
    "4*k*y"
  ],
  "wall_s_total": 6.586538447998464,
  "wall_s_per_eq": [
    6.586538447998464
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "4*k*y",
      "r2_train": 0.9999999999999952,
      "reward": null,
      "residual_heldout": 4.713481742560366e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.586538447998464,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.586538447998464,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.375
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=1.3976337495004608e-15 cons=0.0 wall_s=7.437 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.3976337495004608e-15,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.436547807068564,
  "wall_s_per_eq": [
    7.436547807068564
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 1.3976337495004608e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.436547807068564,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.436547807068564,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=6.249948814482736e-15 cons=0.0 wall_s=7.516 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.249948814482736e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.516036728047766,
  "wall_s_per_eq": [
    7.516036728047766
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999967,
      "reward": null,
      "residual_heldout": 6.249948814482736e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.516036728047766,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.516036728047766,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=2.2876041855163246e-16 cons=0.0 wall_s=7.573 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.2876041855163246e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-y + y - 0.032126218) + y*(-1.4678738)"
  ],
  "wall_s_total": 7.572805537958629,
  "wall_s_per_eq": [
    7.572805537958629
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-y + y - 0.032126218) + y*(-1.4678738)",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 2.2876041855163246e-16,
      "pred_coeffs": {
        "y": -1.500000018
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.572805537958629,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=8.088803402486515e-16 cons=0.0 wall_s=7.726 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 8.088803402486515e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.0043289666) + (y + y)*(-0.7478355)"
  ],
  "wall_s_total": 7.726146517088637,
  "wall_s_per_eq": [
    7.726146517088637
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.0043289666) + (y + y)*(-0.7478355)",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 8.088803402486515e-16,
      "pred_coeffs": {
        "y": -1.4999999666
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.726146517088637,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=5.220760898525916e-17 cons=0.0 wall_s=7.471 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.220760898525916e-17,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4994017) + y*(-0.00059830886)"
  ],
  "wall_s_total": 7.470603836001828,
  "wall_s_per_eq": [
    7.470603836001828
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4994017) + y*(-0.00059830886)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 5.220760898525916e-17,
      "pred_coeffs": {
        "y": -1.5000000088599998
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.470603836001828,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=5.786202257262396e-17 cons=0.0 wall_s=7.471 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.786202257262396e-17,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4514089) - 0.04859109*y - 7.515246e-9"
  ],
  "wall_s_total": 7.470996947959065,
  "wall_s_per_eq": [
    7.470996947959065
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4514089) - 0.04859109*y - 7.515246e-9",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 5.786202257262396e-17,
      "pred_coeffs": {
        "1": -7.515246e-09,
        "y": -1.4999999899999998
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.470996947959065,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=7.390469094081919e-17 cons=0.0 wall_s=7.532 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.390469094081919e-17,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5499661) + y*0.04996609"
  ],
  "wall_s_total": 7.531988280941732,
  "wall_s_per_eq": [
    7.531988280941732
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5499661) + y*0.04996609",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 7.390469094081919e-17,
      "pred_coeffs": {
        "y": -1.50000001
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.531988280941732,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=2.9651421579866964e-16 cons=0.0 wall_s=7.404 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.9651421579866964e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4496305) + y*(-0.050369523) - 1*(-3.6403822e-9)"
  ],
  "wall_s_total": 7.403653235989623,
  "wall_s_per_eq": [
    7.403653235989623
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4496305) + y*(-0.050369523) - 1*(-3.6403822e-9)",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 2.9651421579866964e-16,
      "pred_coeffs": {
        "1": 3.6403822e-09,
        "y": -1.5000000230000001
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.403653235989623,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=1.0074700957423265e-17 cons=0.0 wall_s=7.483 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.0074700957423265e-17,
  "conservation_residual": 0.0,
  "equations": [
    "(-y + y*0.07637464)*1.6240351"
  ],
  "wall_s_total": 7.483127427054569,
  "wall_s_per_eq": [
    7.483127427054569
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-y + y*0.07637464)*1.6240351",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.0074700957423265e-17,
      "pred_coeffs": {
        "y": -1.5000000038901358
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.483127427054569,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=5.399437150507483e-16 cons=0.0 wall_s=7.526 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.399437150507483e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(y*0.20008163 + y)*(-1.249915)"
  ],
  "wall_s_total": 7.5264468810055405,
  "wall_s_per_eq": [
    7.5264468810055405
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*0.20008163 + y)*(-1.249915)",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 5.399437150507483e-16,
      "pred_coeffs": {
        "y": -1.5000000305614503
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.5264468810055405,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=1.7012482901608431e-15 cons=0.0 wall_s=7.540 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.7012482901608431e-15,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.0270221) + y*(-0.47297785)"
  ],
  "wall_s_total": 7.540386418928392,
  "wall_s_per_eq": [
    7.540386418928392
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.0270221) + y*(-0.47297785)",
      "r2_train": 0.9999999999999983,
      "reward": null,
      "residual_heldout": 1.7012482901608431e-15,
      "pred_coeffs": {
        "y": -1.4999999499999999
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.540386418928392,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=9.490011761105641e-16 cons=0.0 wall_s=7.812 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 9.490011761105641e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.3921384) - 0.10786164*y"
  ],
  "wall_s_total": 7.811657481011935,
  "wall_s_per_eq": [
    7.811657481011935
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.3921384) - 0.10786164*y",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 9.490011761105641e-16,
      "pred_coeffs": {
        "y": -1.5000000400000002
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.811657481011935,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=3.169120640547295e-16 cons=0.0 wall_s=7.504 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.169120640547295e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(y*0.2339504 + y)*(-1.215608)"
  ],
  "wall_s_total": 7.504415663075633,
  "wall_s_per_eq": [
    7.504415663075633
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*0.2339504 + y)*(-1.215608)",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.169120640547295e-16,
      "pred_coeffs": {
        "y": -1.4999999778431998
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.504415663075633,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=5.799424329301232e-16 cons=0.0 wall_s=7.589 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.799424329301232e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(y - 0.15629598*(y - 1*(-1.5783158e-8)))*(-1.7778747)"
  ],
  "wall_s_total": 7.589377039927058,
  "wall_s_per_eq": [
    7.589377039927058
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y - 0.15629598*(y - 1*(-1.5783158e-8)))*(-1.7778747)",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 5.799424329301232e-16,
      "pred_coeffs": {
        "1": 4.385739797980773e-09,
        "y": -1.500000031446294
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.589377039927058,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=2.3406680236685243e-19 cons=0.0 wall_s=7.848 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.3406680236685243e-19,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.75547105) + (y - 0.05434814)*(-0.74452895) - 0.040463764"
  ],
  "wall_s_total": 7.848383323987946,
  "wall_s_per_eq": [
    7.848383323987946
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.75547105) + (y - 0.05434814)*(-0.74452895) - 0.040463764",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.3406680236685243e-19,
      "pred_coeffs": {
        "1": -3.9134699647558335e-10,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.848383323987946,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=7.689 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 7.689126270008273,
  "wall_s_per_eq": [
    7.689126270008273
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.689126270008273,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=7.198 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 7.198011475964449,
  "wall_s_per_eq": [
    7.198011475964449
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.198011475964449,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=9.785459180797605e-18 cons=0.0 wall_s=7.373 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 9.785459180797605e-18,
  "conservation_residual": 0.0,
  "equations": [
    "-y + y*(-0.4938881) - 0.006111896*y"
  ],
  "wall_s_total": 7.373241012915969,
  "wall_s_per_eq": [
    7.373241012915969
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-y + y*(-0.4938881) - 0.006111896*y",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 9.785459180797605e-18,
      "pred_coeffs": {
        "y": -1.499999996
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.373241012915969,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=2.991529203030397e-15 cons=0.0 wall_s=7.714 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.991529203030397e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-y + y*(-0.5207677) + y*0.020767665 + (-y - y)*1.4669193e-8"
  ],
  "wall_s_total": 7.714038953999989,
  "wall_s_per_eq": [
    7.714038953999989
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-y + y*(-0.5207677) + y*0.020767665 + (-y - y)*1.4669193e-8",
      "r2_train": 0.9999999999999972,
      "reward": null,
      "residual_heldout": 2.991529203030397e-15,
      "pred_coeffs": {
        "y": -1.500000064338386
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.714038953999989,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=3.831543473358756e-17 cons=0.0 wall_s=7.575 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.831543473358756e-17,
  "conservation_residual": 0.0,
  "equations": [
    "-y + y*(-0.40576893) - (y*0.09423107 - 1*(-4.660363e-9))"
  ],
  "wall_s_total": 7.575478080078028,
  "wall_s_per_eq": [
    7.575478080078028
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-y + y*(-0.40576893) - (y*0.09423107 - 1*(-4.660363e-9))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.831543473358756e-17,
      "pred_coeffs": {
        "1": -4.660363e-09,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.575478080078028,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=9.401968878922036e-16 cons=0.0 wall_s=8.639 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 9.401968878922036e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.2446667) - (y*(0.25533336 + y*(-1.3605912e-8)) - 1*7.589355e-9)"
  ],
  "wall_s_total": 8.63935048901476,
  "wall_s_per_eq": [
    8.63935048901476
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.2446667) - (y*(0.25533336 + y*(-1.3605912e-8)) - 1*7.589355e-9)",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 9.401968878922036e-16,
      "pred_coeffs": {
        "y^2": 1.3605912e-08,
        "1": 7.589355e-09,
        "y": -1.50000006
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.63935048901476,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=2.2840897302338696e-16 cons=0.0 wall_s=7.411 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.2840897302338696e-16,
  "conservation_residual": 0.0,
  "equations": [
    "-y + y*(-0.3102798) + (y + y)*(-0.17701846) + (y + y)*0.08215835"
  ],
  "wall_s_total": 7.411100849043578,
  "wall_s_per_eq": [
    7.411100849043578
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-y + y*(-0.3102798) + (y + y)*(-0.17701846) + (y + y)*0.08215835",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 2.2840897302338696e-16,
      "pred_coeffs": {
        "y": -1.5000000199999999
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.411100849043578,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=7.828736640540823e-15 cons=0.0 wall_s=7.901 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.828736640540823e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-5*k*y"
  ],
  "wall_s_total": 7.900910662021488,
  "wall_s_per_eq": [
    7.900910662021488
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-5*k*y",
      "r2_train": 0.9999999999999973,
      "reward": null,
      "residual_heldout": 7.828736640540823e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.900910662021488,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.900910662021488,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=3.899866063027462e-15 cons=0.0 wall_s=8.071 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.899866063027462e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.070968925021589,
  "wall_s_per_eq": [
    8.070968925021589
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.999999999999998,
      "reward": null,
      "residual_heldout": 3.899866063027462e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.070968925021589,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.070968925021589,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=2.697145826743344e-15 cons=0.0 wall_s=6.983 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.697145826743344e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.983138298033737,
  "wall_s_per_eq": [
    6.983138298033737
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999976,
      "reward": null,
      "residual_heldout": 2.697145826743344e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.983138298033737,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.983138298033737,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=2.0903828490402286e-15 cons=0.0 wall_s=7.683 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.0903828490402286e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.682935427990742,
  "wall_s_per_eq": [
    7.682935427990742
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999964,
      "reward": null,
      "residual_heldout": 2.0903828490402286e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.682935427990742,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.682935427990742,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=2.921490270793219e-15 cons=0.0 wall_s=7.522 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.921490270793219e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.521788890007883,
  "wall_s_per_eq": [
    7.521788890007883
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999957,
      "reward": null,
      "residual_heldout": 2.921490270793219e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.521788890007883,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.521788890007883,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=2.90436584390246e-15 cons=0.0 wall_s=6.692 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.90436584390246e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-3*k*y"
  ],
  "wall_s_total": 6.69157013297081,
  "wall_s_per_eq": [
    6.69157013297081
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-3*k*y",
      "r2_train": 0.9999999999999961,
      "reward": null,
      "residual_heldout": 2.90436584390246e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.69157013297081,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.69157013297081,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=2.3616506200641383e-15 cons=0.0 wall_s=7.937 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.3616506200641383e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.937369691906497,
  "wall_s_per_eq": [
    7.937369691906497
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999972,
      "reward": null,
      "residual_heldout": 2.3616506200641383e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.937369691906497,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.937369691906497,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=3.313794271248956e-15 cons=0.0 wall_s=7.576 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.313794271248956e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.57586351595819,
  "wall_s_per_eq": [
    7.57586351595819
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999983,
      "reward": null,
      "residual_heldout": 3.313794271248956e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.57586351595819,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.57586351595819,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=1.8410931877085574e-15 cons=0.0 wall_s=6.643 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.8410931877085574e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.64320344699081,
  "wall_s_per_eq": [
    6.64320344699081
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999978,
      "reward": null,
      "residual_heldout": 1.8410931877085574e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.64320344699081,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.64320344699081,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=1.709516036885106e-15 cons=0.0 wall_s=7.828 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.709516036885106e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.828336560050957,
  "wall_s_per_eq": [
    7.828336560050957
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999981,
      "reward": null,
      "residual_heldout": 1.709516036885106e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.828336560050957,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.828336560050957,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=8.998147960071747e-16 cons=0.0 wall_s=6.803 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 8.998147960071747e-16,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.802713779034093,
  "wall_s_per_eq": [
    6.802713779034093
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999977,
      "reward": null,
      "residual_heldout": 8.998147960071747e-16,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.802713779034093,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.802713779034093,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=2.378514569671989e-15 cons=0.0 wall_s=7.915 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.378514569671989e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-3*k*y"
  ],
  "wall_s_total": 7.914583674981259,
  "wall_s_per_eq": [
    7.914583674981259
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-3*k*y",
      "r2_train": 0.9999999999999981,
      "reward": null,
      "residual_heldout": 2.378514569671989e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.914583674981259,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.914583674981259,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=2.6860124345651523e-15 cons=0.0 wall_s=7.720 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.6860124345651523e-15,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.7195329800015315,
  "wall_s_per_eq": [
    7.7195329800015315
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999968,
      "reward": null,
      "residual_heldout": 2.6860124345651523e-15,
      "pred_coeffs": {
        "y": -1.4999999999999993
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.7195329800015315,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.7195329800015315,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4999999999999993
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=2.43351854662317e-15 cons=0.0 wall_s=6.869 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.43351854662317e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 6.868660212960094,
  "wall_s_per_eq": [
    6.868660212960094
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.9999999999999969,
      "reward": null,
      "residual_heldout": 2.43351854662317e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.868660212960094,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.868660212960094,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.75
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=3.043602079457752e-15 cons=0.0 wall_s=8.049 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.043602079457752e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.049328185035847,
  "wall_s_per_eq": [
    8.049328185035847
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999977,
      "reward": null,
      "residual_heldout": 3.043602079457752e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.049328185035847,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.049328185035847,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=4.660647261657426e-15 cons=0.0 wall_s=6.952 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.660647261657426e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.952372647006996,
  "wall_s_per_eq": [
    6.952372647006996
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999964,
      "reward": null,
      "residual_heldout": 4.660647261657426e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.952372647006996,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.952372647006996,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=4.999628204139586e-15 cons=0.0 wall_s=8.463 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.999628204139586e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-3*k*y"
  ],
  "wall_s_total": 8.463173852069303,
  "wall_s_per_eq": [
    8.463173852069303
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-3*k*y",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 4.999628204139586e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.463173852069303,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.463173852069303,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=1.630906716848759e-15 cons=0.0 wall_s=6.762 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.630906716848759e-15,
  "conservation_residual": 0.0,
  "equations": [
    "4*k*y"
  ],
  "wall_s_total": 6.761696900008246,
  "wall_s_per_eq": [
    6.761696900008246
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "4*k*y",
      "r2_train": 0.9999999999999962,
      "reward": null,
      "residual_heldout": 1.630906716848759e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.761696900008246,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.761696900008246,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.375
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=3.0432197273119413e-15 cons=0.0 wall_s=8.623 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.0432197273119413e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.622601978015155,
  "wall_s_per_eq": [
    8.622601978015155
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999973,
      "reward": null,
      "residual_heldout": 3.0432197273119413e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.622601978015155,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.622601978015155,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=2.2324580783383725e-15 cons=0.0 wall_s=6.937 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.2324580783383725e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.937370399944484,
  "wall_s_per_eq": [
    6.937370399944484
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999978,
      "reward": null,
      "residual_heldout": 2.2324580783383725e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.937370399944484,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.937370399944484,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=8.250 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 8.249922720948234,
  "wall_s_per_eq": [
    8.249922720948234
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.249922720948234,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=5.198953194183285e-16 cons=0.0 wall_s=8.545 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.198953194183285e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(-y + y*(-0.008435311))*1.4874529"
  ],
  "wall_s_total": 8.544538338086568,
  "wall_s_per_eq": [
    8.544538338086568
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-y + y*(-0.008435311))*1.4874529",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 5.198953194183285e-16,
      "pred_coeffs": {
        "y": -1.500000027809352
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.544538338086568,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=5.997059365258314e-16 cons=0.0 wall_s=8.644 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.997059365258314e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.3694534) + y*(-0.13054657)"
  ],
  "wall_s_total": 8.643924797070213,
  "wall_s_per_eq": [
    8.643924797070213
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.3694534) + y*(-0.13054657)",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 5.997059365258314e-16,
      "pred_coeffs": {
        "y": -1.49999997
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.643924797070213,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=8.820 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "-1*y*1.5"
  ],
  "wall_s_total": 8.819555548019707,
  "wall_s_per_eq": [
    8.819555548019707
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-1*y*1.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.819555548019707,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=8.226 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 8.22571385896299,
  "wall_s_per_eq": [
    8.22571385896299
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.22571385896299,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=8.277 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 8.277233466971666,
  "wall_s_per_eq": [
    8.277233466971666
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.277233466971666,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=3.22349457987475e-17 cons=0.0 wall_s=8.301 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.22349457987475e-17,
  "conservation_residual": 0.0,
  "equations": [
    "(y*(y + 1.4274431)*9.548887e-9 + y*(-0.022754533) + y)*(-1.5349265)"
  ],
  "wall_s_total": 8.301425948971882,
  "wall_s_per_eq": [
    8.301425948971882
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*(y + 1.4274431)*9.548887e-9 + y*(-0.022754533) + y)*(-1.5349265)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.22349457987475e-17,
      "pred_coeffs": {
        "y^2": -1.46568397018055e-08,
        "y": -1.4999999852249803
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.301425948971882,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=8.811 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 8.811286009964533,
  "wall_s_per_eq": [
    8.811286009964533
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.811286009964533,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=4.216740222436864e-16 cons=0.0 wall_s=7.925 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.216740222436864e-16,
  "conservation_residual": 0.0,
  "equations": [
    "-1.470032*y + y*(-0.029968025)"
  ],
  "wall_s_total": 7.925491968984716,
  "wall_s_per_eq": [
    7.925491968984716
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-1.470032*y + y*(-0.029968025)",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.216740222436864e-16,
      "pred_coeffs": {
        "y": -1.500000025
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.925491968984716,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=2.3537742751359794e-17 cons=0.0 wall_s=8.612 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.3537742751359794e-17,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.499102) + y*(-0.00089800585)"
  ],
  "wall_s_total": 8.61165578092914,
  "wall_s_per_eq": [
    8.61165578092914
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.499102) + y*(-0.00089800585)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.3537742751359794e-17,
      "pred_coeffs": {
        "y": -1.50000000585
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.61165578092914,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=8.441 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 8.441259653074667,
  "wall_s_per_eq": [
    8.441259653074667
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.441259653074667,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=7.142252801608317e-16 cons=0.0 wall_s=8.665 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.142252801608317e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4986297) + y*(-0.001370332)"
  ],
  "wall_s_total": 8.664948521996848,
  "wall_s_per_eq": [
    8.664948521996848
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4986297) + y*(-0.001370332)",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 7.142252801608317e-16,
      "pred_coeffs": {
        "y": -1.500000032
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.664948521996848,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=1.2594749948065107e-17 cons=0.0 wall_s=7.800 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.2594749948065107e-17,
  "conservation_residual": 0.0,
  "equations": [
    "(y*0.2448981 + y)*(-1.2049179)"
  ],
  "wall_s_total": 7.799670403008349,
  "wall_s_per_eq": [
    7.799670403008349
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*0.2448981 + y)*(-1.2049179)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.2594749948065107e-17,
      "pred_coeffs": {
        "y": -1.50000000436599
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.799670403008349,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=9.789504498702913e-16 cons=0.0 wall_s=8.174 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 9.789504498702913e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.3534114) + y*(-0.14658856)"
  ],
  "wall_s_total": 8.173509014071897,
  "wall_s_per_eq": [
    8.173509014071897
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.3534114) + y*(-0.14658856)",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 9.789504498702913e-16,
      "pred_coeffs": {
        "y": -1.49999996
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.173509014071897,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=9.4329954479461e-16 cons=0.0 wall_s=8.150 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 9.4329954479461e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*0.146451 - 1.646451*(-(-1)*9.537153e-9*y*y*y + y)"
  ],
  "wall_s_total": 8.150163248064928,
  "wall_s_per_eq": [
    8.150163248064928
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*0.146451 - 1.646451*(-(-1)*9.537153e-9*y*y*y + y)",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 9.4329954479461e-16,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.150163248064928,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=1.227247348208919e-15 cons=0.0 wall_s=7.945 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.227247348208919e-15,
  "conservation_residual": 0.0,
  "equations": [
    "(y*0.2621406 + y)*(-1.1884571)"
  ],
  "wall_s_total": 7.9447321279440075,
  "wall_s_per_eq": [
    7.9447321279440075
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*0.2621406 + y)*(-1.1884571)",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 1.227247348208919e-15,
      "pred_coeffs": {
        "y": -1.4999999572682599
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.9447321279440075,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=4.3815002586178106e-16 cons=0.0 wall_s=8.183 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.3815002586178106e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4754219) + y*(-0.024578126)"
  ],
  "wall_s_total": 8.183202848071232,
  "wall_s_per_eq": [
    8.183202848071232
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4754219) + y*(-0.024578126)",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.3815002586178106e-16,
      "pred_coeffs": {
        "y": -1.500000026
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.183202848071232,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=8.259 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5)"
  ],
  "wall_s_total": 8.258616850012913,
  "wall_s_per_eq": [
    8.258616850012913
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.258616850012913,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=6.924072098472684e-17 cons=0.0 wall_s=8.166 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.924072098472684e-17,
  "conservation_residual": 0.0,
  "equations": [
    "-1.2591504*y + y*(-0.24084961)"
  ],
  "wall_s_total": 8.166329425992444,
  "wall_s_per_eq": [
    8.166329425992444
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-1.2591504*y + y*(-0.24084961)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 6.924072098472684e-17,
      "pred_coeffs": {
        "y": -1.50000001
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.166329425992444,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=6.567411101265826e-17 cons=0.0 wall_s=7.994 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.567411101265826e-17,
  "conservation_residual": 0.0,
  "equations": [
    "-y + y*(-0.26102862) - 0.23897137*y"
  ],
  "wall_s_total": 7.9938222910277545,
  "wall_s_per_eq": [
    7.9938222910277545
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-y + y*(-0.26102862) - 0.23897137*y",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 6.567411101265826e-17,
      "pred_coeffs": {
        "y": -1.49999999
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.9938222910277545,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=1.535742933266101e-15 cons=0.0 wall_s=8.277 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.535742933266101e-15,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 8.276947545004077,
  "wall_s_per_eq": [
    8.276947545004077
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999971,
      "reward": null,
      "residual_heldout": 1.535742933266101e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.276947545004077,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.276947545004077,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=3.009607545924919e-15 cons=0.0 wall_s=7.490 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.009607545924919e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.4901702150236815,
  "wall_s_per_eq": [
    7.4901702150236815
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999977,
      "reward": null,
      "residual_heldout": 3.009607545924919e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.4901702150236815,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.4901702150236815,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=2.6815527148882258e-15 cons=0.0 wall_s=8.187 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.6815527148882258e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.187415067921393,
  "wall_s_per_eq": [
    8.187415067921393
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999974,
      "reward": null,
      "residual_heldout": 2.6815527148882258e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.187415067921393,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.187415067921393,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=3.1197720688070023e-15 cons=0.0 wall_s=6.922 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.1197720688070023e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.922033299924806,
  "wall_s_per_eq": [
    6.922033299924806
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999977,
      "reward": null,
      "residual_heldout": 3.1197720688070023e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.922033299924806,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.922033299924806,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=3.087106297217029e-15 cons=0.0 wall_s=8.368 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.087106297217029e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.36776822397951,
  "wall_s_per_eq": [
    8.36776822397951
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999977,
      "reward": null,
      "residual_heldout": 3.087106297217029e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.36776822397951,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.36776822397951,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=2.352123260078131e-15 cons=0.0 wall_s=6.965 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.352123260078131e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.964966680039652,
  "wall_s_per_eq": [
    6.964966680039652
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999973,
      "reward": null,
      "residual_heldout": 2.352123260078131e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.964966680039652,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.964966680039652,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=1.510900720910819e-15 cons=0.0 wall_s=6.742 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.510900720910819e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.741923986002803,
  "wall_s_per_eq": [
    6.741923986002803
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999971,
      "reward": null,
      "residual_heldout": 1.510900720910819e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.741923986002803,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.741923986002803,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=2.963414077423016e-15 cons=0.0 wall_s=8.531 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.963414077423016e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.531174339936115,
  "wall_s_per_eq": [
    8.531174339936115
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999976,
      "reward": null,
      "residual_heldout": 2.963414077423016e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.531174339936115,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.531174339936115,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=1.906064754169035e-15 cons=0.0 wall_s=6.536 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.906064754169035e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.535901056951843,
  "wall_s_per_eq": [
    6.535901056951843
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999971,
      "reward": null,
      "residual_heldout": 1.906064754169035e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.535901056951843,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.535901056951843,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=2.3762310012184566e-15 cons=0.0 wall_s=8.723 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.3762310012184566e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.722978087025695,
  "wall_s_per_eq": [
    8.722978087025695
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999973,
      "reward": null,
      "residual_heldout": 2.3762310012184566e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.722978087025695,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.722978087025695,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=2.0480370589565273e-15 cons=0.0 wall_s=6.951 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.0480370589565273e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.951175848953426,
  "wall_s_per_eq": [
    6.951175848953426
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999972,
      "reward": null,
      "residual_heldout": 2.0480370589565273e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.951175848953426,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.951175848953426,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=3.2266358366467356e-15 cons=0.0 wall_s=8.564 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.2266358366467356e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-3*k*y"
  ],
  "wall_s_total": 8.564375032903627,
  "wall_s_per_eq": [
    8.564375032903627
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-3*k*y",
      "r2_train": 0.9999999999999978,
      "reward": null,
      "residual_heldout": 3.2266358366467356e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.564375032903627,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.564375032903627,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=3.166566066078465e-15 cons=0.0 wall_s=6.774 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.166566066078465e-15,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.773535285028629,
  "wall_s_per_eq": [
    6.773535285028629
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999977,
      "reward": null,
      "residual_heldout": 3.166566066078465e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.773535285028629,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.773535285028629,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=1.4052435119422344e-15 cons=0.0 wall_s=6.818 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.4052435119422344e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.81813674303703,
  "wall_s_per_eq": [
    6.81813674303703
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.999999999999997,
      "reward": null,
      "residual_heldout": 1.4052435119422344e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.81813674303703,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.81813674303703,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=3.4103408216726123e-15 cons=0.0 wall_s=8.659 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.4103408216726123e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.659378936048597,
  "wall_s_per_eq": [
    8.659378936048597
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999978,
      "reward": null,
      "residual_heldout": 3.4103408216726123e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.659378936048597,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.659378936048597,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=2.805055906060807e-15 cons=0.0 wall_s=7.065 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.805055906060807e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.0651513210032135,
  "wall_s_per_eq": [
    7.0651513210032135
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999976,
      "reward": null,
      "residual_heldout": 2.805055906060807e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.0651513210032135,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.0651513210032135,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=3.0800128361390315e-15 cons=0.0 wall_s=7.256 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.0800128361390315e-15,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.255664216005243,
  "wall_s_per_eq": [
    7.255664216005243
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9999999999999977,
      "reward": null,
      "residual_heldout": 3.0800128361390315e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.255664216005243,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.255664216005243,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=2.7739881290805884e-15 cons=0.0 wall_s=8.990 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.7739881290805884e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.989664096967317,
  "wall_s_per_eq": [
    8.989664096967317
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999976,
      "reward": null,
      "residual_heldout": 2.7739881290805884e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.989664096967317,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.989664096967317,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=3.0450350724108536e-15 cons=0.0 wall_s=7.188 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.0450350724108536e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.188362476066686,
  "wall_s_per_eq": [
    7.188362476066686
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999977,
      "reward": null,
      "residual_heldout": 3.0450350724108536e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.188362476066686,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.188362476066686,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=2.65441742499155e-15 cons=0.0 wall_s=8.861 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.65441742499155e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.861258919001557,
  "wall_s_per_eq": [
    8.861258919001557
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9999999999999974,
      "reward": null,
      "residual_heldout": 2.65441742499155e-15,
      "pred_coeffs": {
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.861258919001557,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.861258919001557,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.006967425198895488 cons=0.0 wall_s=7.877 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006967425198895488,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5146722)"
  ],
  "wall_s_total": 7.877121580066159,
  "wall_s_per_eq": [
    7.877121580066159
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5146722)",
      "r2_train": 0.9948529422188512,
      "reward": null,
      "residual_heldout": 0.006967425198895488,
      "pred_coeffs": {
        "y": -1.5146722
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.877121580066159,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.01910875610190978 cons=0.0 wall_s=7.748 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01910875610190978,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.503507)"
  ],
  "wall_s_total": 7.748289703973569,
  "wall_s_per_eq": [
    7.748289703973569
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.503507)",
      "r2_train": 0.9975858474013406,
      "reward": null,
      "residual_heldout": 0.01910875610190978,
      "pred_coeffs": {
        "y": -1.503507
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.748289703973569,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0025193471505726146 cons=0.0 wall_s=7.921 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0025193471505726146,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5033771)"
  ],
  "wall_s_total": 7.921266085002571,
  "wall_s_per_eq": [
    7.921266085002571
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5033771)",
      "r2_train": 0.9958336750227295,
      "reward": null,
      "residual_heldout": 0.0025193471505726146,
      "pred_coeffs": {
        "y": -1.5033771
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.921266085002571,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.002366156171610759 cons=0.0 wall_s=7.742 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.002366156171610759,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4971718)"
  ],
  "wall_s_total": 7.742145751020871,
  "wall_s_per_eq": [
    7.742145751020871
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4971718)",
      "r2_train": 0.995926586717162,
      "reward": null,
      "residual_heldout": 0.002366156171610759,
      "pred_coeffs": {
        "y": -1.4971718
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.742145751020871,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.003825953010759903 cons=0.0 wall_s=8.022 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003825953010759903,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5009359)"
  ],
  "wall_s_total": 8.0215209859889,
  "wall_s_per_eq": [
    8.0215209859889
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5009359)",
      "r2_train": 0.99311922092991,
      "reward": null,
      "residual_heldout": 0.003825953010759903,
      "pred_coeffs": {
        "y": -1.5009359
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.0215209859889,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0031161256360054367 cons=0.0 wall_s=7.826 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0031161256360054367,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4889591)"
  ],
  "wall_s_total": 7.825887425919063,
  "wall_s_per_eq": [
    7.825887425919063
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4889591)",
      "r2_train": 0.9949392588860908,
      "reward": null,
      "residual_heldout": 0.0031161256360054367,
      "pred_coeffs": {
        "y": -1.4889591
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.825887425919063,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005123638505690752 cons=0.0 wall_s=7.956 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005123638505690752,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.48376)"
  ],
  "wall_s_total": 7.955651993048377,
  "wall_s_per_eq": [
    7.955651993048377
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.48376)",
      "r2_train": 0.9964289796387851,
      "reward": null,
      "residual_heldout": 0.005123638505690752,
      "pred_coeffs": {
        "y": -1.48376
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.955651993048377,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.006092122779606195 cons=0.0 wall_s=7.929 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006092122779606195,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5141355)"
  ],
  "wall_s_total": 7.92859407607466,
  "wall_s_per_eq": [
    7.92859407607466
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5141355)",
      "r2_train": 0.9950829599277013,
      "reward": null,
      "residual_heldout": 0.006092122779606195,
      "pred_coeffs": {
        "y": -1.5141355
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.92859407607466,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0061021539614793865 cons=0.0 wall_s=7.862 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0061021539614793865,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4933896)"
  ],
  "wall_s_total": 7.862393492017873,
  "wall_s_per_eq": [
    7.862393492017873
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4933896)",
      "r2_train": 0.9965261471988763,
      "reward": null,
      "residual_heldout": 0.0061021539614793865,
      "pred_coeffs": {
        "y": -1.4933896
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.862393492017873,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0052380721773174505 cons=0.0 wall_s=7.750 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0052380721773174505,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4868935)"
  ],
  "wall_s_total": 7.7497129699913785,
  "wall_s_per_eq": [
    7.7497129699913785
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4868935)",
      "r2_train": 0.9928791869691698,
      "reward": null,
      "residual_heldout": 0.0052380721773174505,
      "pred_coeffs": {
        "y": -1.4868935
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.7497129699913785,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.002272474804930927 cons=0.0 wall_s=7.699 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.002272474804930927,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4929453)"
  ],
  "wall_s_total": 7.698578232084401,
  "wall_s_per_eq": [
    7.698578232084401
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4929453)",
      "r2_train": 0.9925611929943164,
      "reward": null,
      "residual_heldout": 0.002272474804930927,
      "pred_coeffs": {
        "y": -1.4929453
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.698578232084401,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.01840947182191435 cons=0.0 wall_s=7.502 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01840947182191435,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4856136)"
  ],
  "wall_s_total": 7.501603793934919,
  "wall_s_per_eq": [
    7.501603793934919
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4856136)",
      "r2_train": 0.9933448317666561,
      "reward": null,
      "residual_heldout": 0.01840947182191435,
      "pred_coeffs": {
        "y": -1.4856136
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.501603793934919,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.01681457997371855 cons=0.0 wall_s=8.118 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01681457997371855,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4763714)"
  ],
  "wall_s_total": 8.118285601958632,
  "wall_s_per_eq": [
    8.118285601958632
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4763714)",
      "r2_train": 0.997416662495587,
      "reward": null,
      "residual_heldout": 0.01681457997371855,
      "pred_coeffs": {
        "y": -1.4763714
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.118285601958632,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0065746245000306725 cons=0.0 wall_s=7.670 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0065746245000306725,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4669738)"
  ],
  "wall_s_total": 7.670058612013236,
  "wall_s_per_eq": [
    7.670058612013236
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4669738)",
      "r2_train": 0.9938702177987115,
      "reward": null,
      "residual_heldout": 0.0065746245000306725,
      "pred_coeffs": {
        "y": -1.4669738
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.670058612013236,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.006999236465186366 cons=0.0 wall_s=7.932 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006999236465186366,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5006899)"
  ],
  "wall_s_total": 7.93170201999601,
  "wall_s_per_eq": [
    7.93170201999601
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5006899)",
      "r2_train": 0.9925365872066064,
      "reward": null,
      "residual_heldout": 0.006999236465186366,
      "pred_coeffs": {
        "y": -1.5006899
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.93170201999601,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.004864656978979799 cons=0.0 wall_s=7.718 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004864656978979799,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5147799)"
  ],
  "wall_s_total": 7.717883712030016,
  "wall_s_per_eq": [
    7.717883712030016
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5147799)",
      "r2_train": 0.9922436460642664,
      "reward": null,
      "residual_heldout": 0.004864656978979799,
      "pred_coeffs": {
        "y": -1.5147799
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.717883712030016,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.02683307018061243 cons=0.0 wall_s=7.806 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.02683307018061243,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4906397)"
  ],
  "wall_s_total": 7.805552200996317,
  "wall_s_per_eq": [
    7.805552200996317
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4906397)",
      "r2_train": 0.9947574776272081,
      "reward": null,
      "residual_heldout": 0.02683307018061243,
      "pred_coeffs": {
        "y": -1.4906397
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.805552200996317,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.009286338716663381 cons=0.0 wall_s=7.546 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.009286338716663381,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4930592)"
  ],
  "wall_s_total": 7.5458312219707295,
  "wall_s_per_eq": [
    7.5458312219707295
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4930592)",
      "r2_train": 0.9948238561489281,
      "reward": null,
      "residual_heldout": 0.009286338716663381,
      "pred_coeffs": {
        "y": -1.4930592
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.5458312219707295,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0016550630171954287 cons=0.0 wall_s=7.899 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0016550630171954287,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4924666)"
  ],
  "wall_s_total": 7.898629858973436,
  "wall_s_per_eq": [
    7.898629858973436
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4924666)",
      "r2_train": 0.9972918475423037,
      "reward": null,
      "residual_heldout": 0.0016550630171954287,
      "pred_coeffs": {
        "y": -1.4924666
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.898629858973436,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=50 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.004460900098313495 cons=0.0 wall_s=7.927 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004460900098313495,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5008821)"
  ],
  "wall_s_total": 7.926600749022327,
  "wall_s_per_eq": [
    7.926600749022327
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5008821)",
      "r2_train": 0.9936696859815587,
      "reward": null,
      "residual_heldout": 0.004460900098313495,
      "pred_coeffs": {
        "y": -1.5008821
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.926600749022327,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.006967472060817491 cons=0.0 wall_s=8.236 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006967472060817491,
  "conservation_residual": 0.0,
  "equations": [
    "3*k*y"
  ],
  "wall_s_total": 8.235549928969704,
  "wall_s_per_eq": [
    8.235549928969704
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "3*k*y",
      "r2_train": 0.9948529431498238,
      "reward": null,
      "residual_heldout": 0.006967472060817491,
      "pred_coeffs": {
        "y": -1.5146732080994763
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.235549928969704,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.235549928969704,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5048910693664921
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.019108757315618195 cons=0.0 wall_s=7.519 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.019108757315618195,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 7.5194722060114145,
  "wall_s_per_eq": [
    7.5194722060114145
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.9975858483859437,
      "reward": null,
      "residual_heldout": 0.019108757315618195,
      "pred_coeffs": {
        "y": -1.5035070000457322
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.5194722060114145,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.5194722060114145,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7517535000228661
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0025187845113809107 cons=0.0 wall_s=9.372 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0025187845113809107,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 9.37165162502788,
  "wall_s_per_eq": [
    9.37165162502788
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9958336745565521,
      "reward": null,
      "residual_heldout": 0.0025187845113809107,
      "pred_coeffs": {
        "y": -1.5033907745822535
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.37165162502788,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.37165162502788,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5033907745822535
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0023661309885150135 cons=0.0 wall_s=7.038 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0023661309885150135,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.0380169990239665,
  "wall_s_per_eq": [
    7.0380169990239665
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9959265866947901,
      "reward": null,
      "residual_heldout": 0.0023661309885150135,
      "pred_coeffs": {
        "y": -1.4971727522396123
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.0380169990239665,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.0380169990239665,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.4971727522396123
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.003825944894089871 cons=0.0 wall_s=7.144 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003825944894089871,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.144385473919101,
  "wall_s_per_eq": [
    7.144385473919101
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9931192199512497,
      "reward": null,
      "residual_heldout": 0.003825944894089871,
      "pred_coeffs": {
        "y": -1.500934847266252
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.144385473919101,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.144385473919101,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.500934847266252
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.003116590315777381 cons=0.0 wall_s=9.721 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003116590315777381,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 9.72081958304625,
  "wall_s_per_eq": [
    9.72081958304625
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.994939258777848,
      "reward": null,
      "residual_heldout": 0.003116590315777381,
      "pred_coeffs": {
        "y": -1.4889452095316922
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.72081958304625,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.72081958304625,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.4889452095316922
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005123639019779823 cons=0.0 wall_s=7.147 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005123639019779823,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.147409043973312,
  "wall_s_per_eq": [
    7.147409043973312
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9964289793018292,
      "reward": null,
      "residual_heldout": 0.005123639019779823,
      "pred_coeffs": {
        "y": -1.4837600144666456
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.147409043973312,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.147409043973312,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4837600144666456
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.006092259132833191 cons=0.0 wall_s=6.675 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006092259132833191,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.674577072961256,
  "wall_s_per_eq": [
    6.674577072961256
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9950829595352204,
      "reward": null,
      "residual_heldout": 0.006092259132833191,
      "pred_coeffs": {
        "y": -1.514138017586808
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.674577072961256,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.674577072961256,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.514138017586808
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0061021489316806996 cons=0.0 wall_s=9.300 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0061021489316806996,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 9.299792840960436,
  "wall_s_per_eq": [
    9.299792840960436
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9965261469873997,
      "reward": null,
      "residual_heldout": 0.0061021489316806996,
      "pred_coeffs": {
        "y": -1.4933895556222376
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.299792840960436,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.299792840960436,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4933895556222376
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0052381560337363435 cons=0.0 wall_s=7.473 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0052381560337363435,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.472651052987203,
  "wall_s_per_eq": [
    7.472651052987203
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9928791874483163,
      "reward": null,
      "residual_heldout": 0.0052381560337363435,
      "pred_coeffs": {
        "y": -1.4868987744164137
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.472651052987203,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.472651052987203,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4868987744164137
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0022727546509823896 cons=0.0 wall_s=7.061 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0022727546509823896,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 7.061026692041196,
  "wall_s_per_eq": [
    7.061026692041196
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9925611916820206,
      "reward": null,
      "residual_heldout": 0.0022727546509823896,
      "pred_coeffs": {
        "y": -1.4929313246226825
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.061026692041196,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.061026692041196,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.4929313246226825
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.01840957651958942 cons=0.0 wall_s=6.920 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01840957651958942,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.919663518900052,
  "wall_s_per_eq": [
    6.919663518900052
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9933448319519995,
      "reward": null,
      "residual_heldout": 0.01840957651958942,
      "pred_coeffs": {
        "y": -1.4856202116921875
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.919663518900052,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.919663518900052,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4856202116921875
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.016814575440283513 cons=0.0 wall_s=9.087 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.016814575440283513,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 9.086567719001323,
  "wall_s_per_eq": [
    9.086567719001323
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9974166624733822,
      "reward": null,
      "residual_heldout": 0.016814575440283513,
      "pred_coeffs": {
        "y": -1.4763715160780195
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.086567719001323,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.086567719001323,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4763715160780195
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.006574696470902333 cons=0.0 wall_s=6.964 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006574696470902333,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 6.964033799013123,
  "wall_s_per_eq": [
    6.964033799013123
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.9938702184948349,
      "reward": null,
      "residual_heldout": 0.006574696470902333,
      "pred_coeffs": {
        "y": -1.4669721462822207
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.964033799013123,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.964033799013123,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7334860731411104
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.006999235683141823 cons=0.0 wall_s=7.042 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006999235683141823,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.041580165037885,
  "wall_s_per_eq": [
    7.041580165037885
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.992536586571976,
      "reward": null,
      "residual_heldout": 0.006999235683141823,
      "pred_coeffs": {
        "y": -1.5006898857101914
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.041580165037885,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.041580165037885,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5006898857101914
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.004864695432776622 cons=0.0 wall_s=9.621 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004864695432776622,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 9.621375647024252,
  "wall_s_per_eq": [
    9.621375647024252
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9922436466727226,
      "reward": null,
      "residual_heldout": 0.004864695432776622,
      "pred_coeffs": {
        "y": -1.5147805246513222
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.621375647024252,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.621375647024252,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5147805246513222
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.02683270879975159 cons=0.0 wall_s=7.425 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.02683270879975159,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.424758256063797,
  "wall_s_per_eq": [
    7.424758256063797
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.994757478842873,
      "reward": null,
      "residual_heldout": 0.02683270879975159,
      "pred_coeffs": {
        "y": -1.49065180722892
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.424758256063797,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.424758256063797,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.49065180722892
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.00928634168127847 cons=0.0 wall_s=7.289 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00928634168127847,
  "conservation_residual": 0.0,
  "equations": [
    "2*k*y"
  ],
  "wall_s_total": 7.28872611396946,
  "wall_s_per_eq": [
    7.28872611396946
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*k*y",
      "r2_train": 0.994823858396267,
      "reward": null,
      "residual_heldout": 0.00928634168127847,
      "pred_coeffs": {
        "y": -1.493059217417993
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.28872611396946,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.28872611396946,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7465296087089965
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.001655428694684543 cons=0.0 wall_s=7.263 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.001655428694684543,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.263422460993752,
  "wall_s_per_eq": [
    7.263422460993752
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9972918480044064,
      "reward": null,
      "residual_heldout": 0.001655428694684543,
      "pred_coeffs": {
        "y": -1.4924545514883887
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.263422460993752,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.263422460993752,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4924545514883887
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=50 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.004460883124527616 cons=0.0 wall_s=9.810 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004460883124527616,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 9.81015025707893,
  "wall_s_per_eq": [
    9.81015025707893
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9936696857785702,
      "reward": null,
      "residual_heldout": 0.004460883124527616,
      "pred_coeffs": {
        "y": -1.5008832900060975
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.81015025707893,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.81015025707893,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5008832900060975
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.004806660125614221 cons=0.0 wall_s=8.176 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004806660125614221,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4875386)"
  ],
  "wall_s_total": 8.176404042053036,
  "wall_s_per_eq": [
    8.176404042053036
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4875386)",
      "r2_train": 0.9962507426755243,
      "reward": null,
      "residual_heldout": 0.004806660125614221,
      "pred_coeffs": {
        "y": -1.4875386
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.176404042053036,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0024758976175004352 cons=0.0 wall_s=7.948 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0024758976175004352,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4825978)"
  ],
  "wall_s_total": 7.948146666050889,
  "wall_s_per_eq": [
    7.948146666050889
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4825978)",
      "r2_train": 0.9926167584418882,
      "reward": null,
      "residual_heldout": 0.0024758976175004352,
      "pred_coeffs": {
        "y": -1.4825978
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.948146666050889,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.005801342576568146 cons=0.0 wall_s=8.010 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005801342576568146,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4935333)"
  ],
  "wall_s_total": 8.010249993996695,
  "wall_s_per_eq": [
    8.010249993996695
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4935333)",
      "r2_train": 0.9942443650442526,
      "reward": null,
      "residual_heldout": 0.005801342576568146,
      "pred_coeffs": {
        "y": -1.4935333
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.010249993996695,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0037992650066714564 cons=0.0 wall_s=8.080 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0037992650066714564,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4873593)"
  ],
  "wall_s_total": 8.079932765918784,
  "wall_s_per_eq": [
    8.079932765918784
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4873593)",
      "r2_train": 0.9910121622587384,
      "reward": null,
      "residual_heldout": 0.0037992650066714564,
      "pred_coeffs": {
        "y": -1.4873593
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.079932765918784,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.008392588727255927 cons=0.0 wall_s=8.139 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008392588727255927,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4972839)"
  ],
  "wall_s_total": 8.139083529007621,
  "wall_s_per_eq": [
    8.139083529007621
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4972839)",
      "r2_train": 0.9956609326515014,
      "reward": null,
      "residual_heldout": 0.008392588727255927,
      "pred_coeffs": {
        "y": -1.4972839
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.139083529007621,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0033633509099812537 cons=0.0 wall_s=7.951 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0033633509099812537,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5008984)"
  ],
  "wall_s_total": 7.950871848966926,
  "wall_s_per_eq": [
    7.950871848966926
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5008984)",
      "r2_train": 0.9958863766485131,
      "reward": null,
      "residual_heldout": 0.0033633509099812537,
      "pred_coeffs": {
        "y": -1.5008984
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.950871848966926,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005412305776729381 cons=0.0 wall_s=7.725 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005412305776729381,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5109127)"
  ],
  "wall_s_total": 7.724979048944078,
  "wall_s_per_eq": [
    7.724979048944078
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5109127)",
      "r2_train": 0.9941020246137815,
      "reward": null,
      "residual_heldout": 0.005412305776729381,
      "pred_coeffs": {
        "y": -1.5109127
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.724979048944078,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.007586737928163869 cons=0.0 wall_s=8.020 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007586737928163869,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4796809)"
  ],
  "wall_s_total": 8.020448499009944,
  "wall_s_per_eq": [
    8.020448499009944
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4796809)",
      "r2_train": 0.9938470705624017,
      "reward": null,
      "residual_heldout": 0.007586737928163869,
      "pred_coeffs": {
        "y": -1.4796809
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.020448499009944,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.003279415654904781 cons=0.0 wall_s=7.720 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003279415654904781,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4810392)"
  ],
  "wall_s_total": 7.719520212034695,
  "wall_s_per_eq": [
    7.719520212034695
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4810392)",
      "r2_train": 0.9944234005262576,
      "reward": null,
      "residual_heldout": 0.003279415654904781,
      "pred_coeffs": {
        "y": -1.4810392
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.719520212034695,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.006156025067378326 cons=0.0 wall_s=8.021 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006156025067378326,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4969875)"
  ],
  "wall_s_total": 8.02141554292757,
  "wall_s_per_eq": [
    8.02141554292757
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4969875)",
      "r2_train": 0.9953928710817996,
      "reward": null,
      "residual_heldout": 0.006156025067378326,
      "pred_coeffs": {
        "y": -1.4969875
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.02141554292757,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.016956332895680437 cons=0.0 wall_s=7.787 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.016956332895680437,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4970127)"
  ],
  "wall_s_total": 7.786642023012973,
  "wall_s_per_eq": [
    7.786642023012973
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4970127)",
      "r2_train": 0.9960763757422716,
      "reward": null,
      "residual_heldout": 0.016956332895680437,
      "pred_coeffs": {
        "y": -1.4970127
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.786642023012973,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0027439018572009708 cons=0.0 wall_s=7.695 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0027439018572009708,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4903314)"
  ],
  "wall_s_total": 7.694680875982158,
  "wall_s_per_eq": [
    7.694680875982158
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4903314)",
      "r2_train": 0.9933818843311265,
      "reward": null,
      "residual_heldout": 0.0027439018572009708,
      "pred_coeffs": {
        "y": -1.4903314
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.694680875982158,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.00507866668546778 cons=0.0 wall_s=8.010 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00507866668546778,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5052922)"
  ],
  "wall_s_total": 8.009808484930545,
  "wall_s_per_eq": [
    8.009808484930545
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5052922)",
      "r2_train": 0.995912877973044,
      "reward": null,
      "residual_heldout": 0.00507866668546778,
      "pred_coeffs": {
        "y": -1.5052922
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.009808484930545,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.00591870403250894 cons=0.0 wall_s=8.756 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00591870403250894,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4842806)"
  ],
  "wall_s_total": 8.755549735971726,
  "wall_s_per_eq": [
    8.755549735971726
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4842806)",
      "r2_train": 0.9949700219734071,
      "reward": null,
      "residual_heldout": 0.00591870403250894,
      "pred_coeffs": {
        "y": -1.4842806
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.755549735971726,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0033351527427831758 cons=0.0 wall_s=8.155 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0033351527427831758,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5036882)"
  ],
  "wall_s_total": 8.1554920070339,
  "wall_s_per_eq": [
    8.1554920070339
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5036882)",
      "r2_train": 0.9953309303350149,
      "reward": null,
      "residual_heldout": 0.0033351527427831758,
      "pred_coeffs": {
        "y": -1.5036882
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.1554920070339,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.003468767122422152 cons=0.0 wall_s=8.113 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003468767122422152,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4938209)"
  ],
  "wall_s_total": 8.112579287029803,
  "wall_s_per_eq": [
    8.112579287029803
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4938209)",
      "r2_train": 0.995972708466361,
      "reward": null,
      "residual_heldout": 0.003468767122422152,
      "pred_coeffs": {
        "y": -1.4938209
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.112579287029803,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.005899135987297595 cons=0.0 wall_s=8.058 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005899135987297595,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.498017)"
  ],
  "wall_s_total": 8.057839924935251,
  "wall_s_per_eq": [
    8.057839924935251
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.498017)",
      "r2_train": 0.9957272684787803,
      "reward": null,
      "residual_heldout": 0.005899135987297595,
      "pred_coeffs": {
        "y": -1.498017
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.057839924935251,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0026814716207541945 cons=0.0 wall_s=7.779 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0026814716207541945,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.484705)"
  ],
  "wall_s_total": 7.779328375007026,
  "wall_s_per_eq": [
    7.779328375007026
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.484705)",
      "r2_train": 0.9943510994025667,
      "reward": null,
      "residual_heldout": 0.0026814716207541945,
      "pred_coeffs": {
        "y": -1.484705
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.779328375007026,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0019891758102640383 cons=0.0 wall_s=7.935 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0019891758102640383,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4891361)"
  ],
  "wall_s_total": 7.934919237042777,
  "wall_s_per_eq": [
    7.934919237042777
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4891361)",
      "r2_train": 0.9951064660207015,
      "reward": null,
      "residual_heldout": 0.0019891758102640383,
      "pred_coeffs": {
        "y": -1.4891361
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.934919237042777,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=100 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.005072749766067867 cons=0.0 wall_s=7.539 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005072749766067867,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4837093)"
  ],
  "wall_s_total": 7.538528991979547,
  "wall_s_per_eq": [
    7.538528991979547
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4837093)",
      "r2_train": 0.9960711103144962,
      "reward": null,
      "residual_heldout": 0.005072749766067867,
      "pred_coeffs": {
        "y": -1.4837093
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.538528991979547,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0048066578484216175 cons=0.0 wall_s=7.034 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0048066578484216175,
  "conservation_residual": 0.0,
  "equations": [
    "3*k*y"
  ],
  "wall_s_total": 7.034456711029634,
  "wall_s_per_eq": [
    7.034456711029634
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "3*k*y",
      "r2_train": 0.9962507434139952,
      "reward": null,
      "residual_heldout": 0.0048066578484216175,
      "pred_coeffs": {
        "y": -1.4875385728045027
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.034456711029634,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.034456711029634,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49584619093483423
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0024754856406917418 cons=0.0 wall_s=7.695 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0024754856406917418,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.695490450016223,
  "wall_s_per_eq": [
    7.695490450016223
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9926167603778158,
      "reward": null,
      "residual_heldout": 0.0024754856406917418,
      "pred_coeffs": {
        "y": -1.482612237375615
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.695490450016223,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.695490450016223,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.482612237375615
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.005801499757230987 cons=0.0 wall_s=9.437 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005801499757230987,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 9.43654093996156,
  "wall_s_per_eq": [
    9.43654093996156
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9942443651747336,
      "reward": null,
      "residual_heldout": 0.005801499757230987,
      "pred_coeffs": {
        "y": -1.4935415771677532
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.43654093996156,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.43654093996156,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4935415771677532
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0037993922340340508 cons=0.0 wall_s=6.820 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0037993922340340508,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.820039566024207,
  "wall_s_per_eq": [
    6.820039566024207
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9910121623190209,
      "reward": null,
      "residual_heldout": 0.0037993922340340508,
      "pred_coeffs": {
        "y": -1.487355106051853
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.820039566024207,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.820039566024207,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.487355106051853
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.00839257585348776 cons=0.0 wall_s=6.419 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00839257585348776,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.418780609034002,
  "wall_s_per_eq": [
    6.418780609034002
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.995660932332076,
      "reward": null,
      "residual_heldout": 0.00839257585348776,
      "pred_coeffs": {
        "y": -1.4972863110538084
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.418780609034002,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.418780609034002,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.4972863110538084
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0033633503402519162 cons=0.0 wall_s=6.605 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0033633503402519162,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.604934483999386,
  "wall_s_per_eq": [
    6.604934483999386
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.995886376078736,
      "reward": null,
      "residual_heldout": 0.0033633503402519162,
      "pred_coeffs": {
        "y": -1.5008983742338524
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.604934483999386,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.604934483999386,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5008983742338524
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005411786892275902 cons=0.0 wall_s=10.129 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005411786892275902,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 10.12924572697375,
  "wall_s_per_eq": [
    10.12924572697375
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9941020251786826,
      "reward": null,
      "residual_heldout": 0.005411786892275902,
      "pred_coeffs": {
        "y": -1.5108992275437008
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 10.12924572697375,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.12924572697375,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5108992275437008
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.007586728663454113 cons=0.0 wall_s=6.529 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007586728663454113,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.529463757062331,
  "wall_s_per_eq": [
    6.529463757062331
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9938470705811424,
      "reward": null,
      "residual_heldout": 0.007586728663454113,
      "pred_coeffs": {
        "y": -1.4796810746591191
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.529463757062331,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.529463757062331,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4796810746591191
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.003279324925330038 cons=0.0 wall_s=6.427 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003279324925330038,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.4267641780897975,
  "wall_s_per_eq": [
    6.4267641780897975
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9944233997114227,
      "reward": null,
      "residual_heldout": 0.003279324925330038,
      "pred_coeffs": {
        "y": -1.4810411950300566
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.4267641780897975,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.4267641780897975,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4810411950300566
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.006155998789614532 cons=0.0 wall_s=7.040 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006155998789614532,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.04011522908695,
  "wall_s_per_eq": [
    7.04011522908695
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.995392870681403,
      "reward": null,
      "residual_heldout": 0.006155998789614532,
      "pred_coeffs": {
        "y": -1.4969852558258951
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.04011522908695,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.04011522908695,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4969852558258951
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.01695639621465747 cons=0.0 wall_s=9.810 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01695639621465747,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 9.81033041793853,
  "wall_s_per_eq": [
    9.81033041793853
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9960763742759711,
      "reward": null,
      "residual_heldout": 0.01695639621465747,
      "pred_coeffs": {
        "y": -1.497014124380157
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.81033041793853,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.81033041793853,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.497014124380157
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.002744052229965866 cons=0.0 wall_s=6.618 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.002744052229965866,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.618284660973586,
  "wall_s_per_eq": [
    6.618284660973586
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9933818828051951,
      "reward": null,
      "residual_heldout": 0.002744052229965866,
      "pred_coeffs": {
        "y": -1.4903271993626663
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.618284660973586,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.618284660973586,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4903271993626663
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.005078667213227888 cons=0.0 wall_s=6.565 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005078667213227888,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.56461701693479,
  "wall_s_per_eq": [
    6.56461701693479
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9959128776900598,
      "reward": null,
      "residual_heldout": 0.005078667213227888,
      "pred_coeffs": {
        "y": -1.5052921706102758
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.56461701693479,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.56461701693479,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5052921706102758
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.005918655829112154 cons=0.0 wall_s=6.828 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005918655829112154,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 6.827830104040913,
  "wall_s_per_eq": [
    6.827830104040913
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.9949700210012304,
      "reward": null,
      "residual_heldout": 0.005918655829112154,
      "pred_coeffs": {
        "y": -1.4842709629324595
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.827830104040913,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.827830104040913,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7421354814662298
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.00333513799662311 cons=0.0 wall_s=9.954 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00333513799662311,
  "conservation_residual": 0.0,
  "equations": [
    "2*k*y"
  ],
  "wall_s_total": 9.954478180967271,
  "wall_s_per_eq": [
    9.954478180967271
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*k*y",
      "r2_train": 0.9953309301216976,
      "reward": null,
      "residual_heldout": 0.00333513799662311,
      "pred_coeffs": {
        "y": -1.5036957607097892
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.954478180967271,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.954478180967271,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7518478803548946
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0034687712816567277 cons=0.0 wall_s=6.731 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0034687712816567277,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.731365905026905,
  "wall_s_per_eq": [
    6.731365905026905
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9959727081312068,
      "reward": null,
      "residual_heldout": 0.0034687712816567277,
      "pred_coeffs": {
        "y": -1.4938207966800168
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.731365905026905,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.731365905026905,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.4938207966800168
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.005899134639115398 cons=0.0 wall_s=6.595 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005899134639115398,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.595182023011148,
  "wall_s_per_eq": [
    6.595182023011148
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9957272679409566,
      "reward": null,
      "residual_heldout": 0.005899134639115398,
      "pred_coeffs": {
        "y": -1.4980170150403613
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.595182023011148,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.595182023011148,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4980170150403613
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0026813754778043626 cons=0.0 wall_s=6.756 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0026813754778043626,
  "conservation_residual": 0.0,
  "equations": [
    "2*k*y"
  ],
  "wall_s_total": 6.756179629941471,
  "wall_s_per_eq": [
    6.756179629941471
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*k*y",
      "r2_train": 0.9943510989228911,
      "reward": null,
      "residual_heldout": 0.0026813754778043626,
      "pred_coeffs": {
        "y": -1.4847132813780217
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.756179629941471,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.756179629941471,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7423566406890109
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0019890947526804777 cons=0.0 wall_s=9.817 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0019890947526804777,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 9.81658892298583,
  "wall_s_per_eq": [
    9.81658892298583
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9951064657402235,
      "reward": null,
      "residual_heldout": 0.0019890947526804777,
      "pred_coeffs": {
        "y": -1.489145851349603
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.81658892298583,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.81658892298583,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.489145851349603
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=100 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.005072612341425699 cons=0.0 wall_s=6.818 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005072612341425699,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.818201374961063,
  "wall_s_per_eq": [
    6.818201374961063
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9960711100731455,
      "reward": null,
      "residual_heldout": 0.005072612341425699,
      "pred_coeffs": {
        "y": -1.4837152827475106
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.818201374961063,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.818201374961063,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.4837152827475106
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.005215247699070976 cons=0.0 wall_s=8.463 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005215247699070976,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4908396)"
  ],
  "wall_s_total": 8.462837030994706,
  "wall_s_per_eq": [
    8.462837030994706
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4908396)",
      "r2_train": 0.9963431054153358,
      "reward": null,
      "residual_heldout": 0.005215247699070976,
      "pred_coeffs": {
        "y": -1.4908396
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.462837030994706,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.006084126954977749 cons=0.0 wall_s=8.301 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006084126954977749,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5002123)"
  ],
  "wall_s_total": 8.300566021935083,
  "wall_s_per_eq": [
    8.300566021935083
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5002123)",
      "r2_train": 0.9958541691822934,
      "reward": null,
      "residual_heldout": 0.006084126954977749,
      "pred_coeffs": {
        "y": -1.5002123
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.300566021935083,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.005456370046546666 cons=0.0 wall_s=8.153 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005456370046546666,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4976177)"
  ],
  "wall_s_total": 8.153405739925802,
  "wall_s_per_eq": [
    8.153405739925802
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4976177)",
      "r2_train": 0.9950032758604199,
      "reward": null,
      "residual_heldout": 0.005456370046546666,
      "pred_coeffs": {
        "y": -1.4976177
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.153405739925802,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.004645491315568854 cons=0.0 wall_s=8.716 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004645491315568854,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.495847)"
  ],
  "wall_s_total": 8.716318393009715,
  "wall_s_per_eq": [
    8.716318393009715
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.495847)",
      "r2_train": 0.9945867492335723,
      "reward": null,
      "residual_heldout": 0.004645491315568854,
      "pred_coeffs": {
        "y": -1.495847
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.716318393009715,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.004798467696828938 cons=0.0 wall_s=8.338 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004798467696828938,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4965147)"
  ],
  "wall_s_total": 8.338157769991085,
  "wall_s_per_eq": [
    8.338157769991085
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4965147)",
      "r2_train": 0.9949596365254227,
      "reward": null,
      "residual_heldout": 0.004798467696828938,
      "pred_coeffs": {
        "y": -1.4965147
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.338157769991085,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.003534721826201473 cons=0.0 wall_s=8.533 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003534721826201473,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4961259)"
  ],
  "wall_s_total": 8.532860297011212,
  "wall_s_per_eq": [
    8.532860297011212
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4961259)",
      "r2_train": 0.9947420481575002,
      "reward": null,
      "residual_heldout": 0.003534721826201473,
      "pred_coeffs": {
        "y": -1.4961259
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.532860297011212,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005116245231682016 cons=0.0 wall_s=9.442 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005116245231682016,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5014648)"
  ],
  "wall_s_total": 9.442080753971823,
  "wall_s_per_eq": [
    9.442080753971823
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5014648)",
      "r2_train": 0.9950580343655195,
      "reward": null,
      "residual_heldout": 0.005116245231682016,
      "pred_coeffs": {
        "y": -1.5014648
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.442080753971823,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.004187114767771306 cons=0.0 wall_s=8.476 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004187114767771306,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4895595)"
  ],
  "wall_s_total": 8.475968256010674,
  "wall_s_per_eq": [
    8.475968256010674
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4895595)",
      "r2_train": 0.994579848599276,
      "reward": null,
      "residual_heldout": 0.004187114767771306,
      "pred_coeffs": {
        "y": -1.4895595
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.475968256010674,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.005073263406585004 cons=0.0 wall_s=8.753 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005073263406585004,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4872793)"
  ],
  "wall_s_total": 8.753371123922989,
  "wall_s_per_eq": [
    8.753371123922989
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4872793)",
      "r2_train": 0.994840876425804,
      "reward": null,
      "residual_heldout": 0.005073263406585004,
      "pred_coeffs": {
        "y": -1.4872793
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.753371123922989,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004849403732545869 cons=0.0 wall_s=8.599 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004849403732545869,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4980797)"
  ],
  "wall_s_total": 8.598620112985373,
  "wall_s_per_eq": [
    8.598620112985373
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4980797)",
      "r2_train": 0.9945657772502773,
      "reward": null,
      "residual_heldout": 0.004849403732545869,
      "pred_coeffs": {
        "y": -1.4980797
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.598620112985373,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.004532314395773188 cons=0.0 wall_s=8.916 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004532314395773188,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5014184)"
  ],
  "wall_s_total": 8.915638908045366,
  "wall_s_per_eq": [
    8.915638908045366
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5014184)",
      "r2_train": 0.9940812714253295,
      "reward": null,
      "residual_heldout": 0.004532314395773188,
      "pred_coeffs": {
        "y": -1.5014184
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.915638908045366,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.004441701958224668 cons=0.0 wall_s=8.341 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004441701958224668,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5004277)"
  ],
  "wall_s_total": 8.341321734944358,
  "wall_s_per_eq": [
    8.341321734944358
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5004277)",
      "r2_train": 0.9952029842507061,
      "reward": null,
      "residual_heldout": 0.004441701958224668,
      "pred_coeffs": {
        "y": -1.5004277
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.341321734944358,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0039647900238774314 cons=0.0 wall_s=8.485 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0039647900238774314,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4983628)"
  ],
  "wall_s_total": 8.48455279902555,
  "wall_s_per_eq": [
    8.48455279902555
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4983628)",
      "r2_train": 0.9949309144978937,
      "reward": null,
      "residual_heldout": 0.0039647900238774314,
      "pred_coeffs": {
        "y": -1.4983628
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.48455279902555,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.004795410253198578 cons=0.0 wall_s=8.633 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004795410253198578,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4878051)"
  ],
  "wall_s_total": 8.632957236026414,
  "wall_s_per_eq": [
    8.632957236026414
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4878051)",
      "r2_train": 0.9942971903358977,
      "reward": null,
      "residual_heldout": 0.004795410253198578,
      "pred_coeffs": {
        "y": -1.4878051
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.632957236026414,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.006734551697696746 cons=0.0 wall_s=8.416 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006734551697696746,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4935759)"
  ],
  "wall_s_total": 8.415636815014295,
  "wall_s_per_eq": [
    8.415636815014295
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4935759)",
      "r2_train": 0.9948647096270635,
      "reward": null,
      "residual_heldout": 0.006734551697696746,
      "pred_coeffs": {
        "y": -1.4935759
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.415636815014295,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.00434265538284585 cons=0.0 wall_s=8.445 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00434265538284585,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5004615)"
  ],
  "wall_s_total": 8.445391718996689,
  "wall_s_per_eq": [
    8.445391718996689
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5004615)",
      "r2_train": 0.9949055696512469,
      "reward": null,
      "residual_heldout": 0.00434265538284585,
      "pred_coeffs": {
        "y": -1.5004615
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.445391718996689,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.005643029432576739 cons=0.0 wall_s=8.514 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005643029432576739,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4914687)"
  ],
  "wall_s_total": 8.513698393944651,
  "wall_s_per_eq": [
    8.513698393944651
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4914687)",
      "r2_train": 0.9958500169836235,
      "reward": null,
      "residual_heldout": 0.005643029432576739,
      "pred_coeffs": {
        "y": -1.4914687
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.513698393944651,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.005746370450600957 cons=0.0 wall_s=8.110 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005746370450600957,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5037394)"
  ],
  "wall_s_total": 8.110343760927208,
  "wall_s_per_eq": [
    8.110343760927208
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5037394)",
      "r2_train": 0.9945140525945593,
      "reward": null,
      "residual_heldout": 0.005746370450600957,
      "pred_coeffs": {
        "y": -1.5037394
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.110343760927208,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.003816611330170777 cons=0.0 wall_s=8.324 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003816611330170777,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.4999514)"
  ],
  "wall_s_total": 8.324485389050096,
  "wall_s_per_eq": [
    8.324485389050096
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.4999514)",
      "r2_train": 0.9950368809549078,
      "reward": null,
      "residual_heldout": 0.003816611330170777,
      "pred_coeffs": {
        "y": -1.4999514
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.324485389050096,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `linear_decay` / N=400 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.006021047838264006 cons=0.0 wall_s=8.498 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006021047838264006,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.500493)"
  ],
  "wall_s_total": 8.497819183045067,
  "wall_s_per_eq": [
    8.497819183045067
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.500493)",
      "r2_train": 0.9951587106140247,
      "reward": null,
      "residual_heldout": 0.006021047838264006,
      "pred_coeffs": {
        "y": -1.500493
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.497819183045067,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.005215196587294647 cons=0.0 wall_s=6.694 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005215196587294647,
  "conservation_residual": 0.0,
  "equations": [
    "3*k*y"
  ],
  "wall_s_total": 6.693871324998327,
  "wall_s_per_eq": [
    6.693871324998327
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "3*k*y",
      "r2_train": 0.9963431051593542,
      "reward": null,
      "residual_heldout": 0.005215196587294647,
      "pred_coeffs": {
        "y": -1.4908437532239518
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.693871324998327,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.693871324998327,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49694791774131725
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0060838442497920435 cons=0.0 wall_s=6.734 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0060838442497920435,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.734393027960323,
  "wall_s_per_eq": [
    6.734393027960323
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9958541698488063,
      "reward": null,
      "residual_heldout": 0.0060838442497920435,
      "pred_coeffs": {
        "y": -1.5002303773228625
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.734393027960323,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.734393027960323,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5002303773228625
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.005456556623376238 cons=0.0 wall_s=6.583 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005456556623376238,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.5828189719468355,
  "wall_s_per_eq": [
    6.5828189719468355
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9950032756707767,
      "reward": null,
      "residual_heldout": 0.005456556623376238,
      "pred_coeffs": {
        "y": -1.4976266892465657
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.5828189719468355,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.5828189719468355,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4976266892465657
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.00464546543407111 cons=0.0 wall_s=9.734 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00464546543407111,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 9.733990259002894,
  "wall_s_per_eq": [
    9.733990259002894
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9945867491002367,
      "reward": null,
      "residual_heldout": 0.00464546543407111,
      "pred_coeffs": {
        "y": -1.4958549267085013
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.733990259002894,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.733990259002894,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.4958549267085013
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.00479860664031086 cons=0.0 wall_s=6.912 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00479860664031086,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.912245125044137,
  "wall_s_per_eq": [
    6.912245125044137
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9949596368259636,
      "reward": null,
      "residual_heldout": 0.00479860664031086,
      "pred_coeffs": {
        "y": -1.496520071773411
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.912245125044137,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.912245125044137,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.496520071773411
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.003534721743421176 cons=0.0 wall_s=6.498 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003534721743421176,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.49789904395584,
  "wall_s_per_eq": [
    6.49789904395584
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9947420486560342,
      "reward": null,
      "residual_heldout": 0.003534721743421176,
      "pred_coeffs": {
        "y": -1.4961259065649843
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.49789904395584,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.49789904395584,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.4961259065649843
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005116454240119418 cons=0.0 wall_s=6.440 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005116454240119418,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.439822635031305,
  "wall_s_per_eq": [
    6.439822635031305
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9950580345446788,
      "reward": null,
      "residual_heldout": 0.005116454240119418,
      "pred_coeffs": {
        "y": -1.5014484163545405
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.439822635031305,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.439822635031305,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5014484163545405
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.00418707157361445 cons=0.0 wall_s=9.774 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00418707157361445,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 9.773592280922458,
  "wall_s_per_eq": [
    9.773592280922458
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9945798487370532,
      "reward": null,
      "residual_heldout": 0.00418707157361445,
      "pred_coeffs": {
        "y": -1.489564843280546
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.773592280922458,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.773592280922458,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.489564843280546
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0050732485681123 cons=0.0 wall_s=6.514 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0050732485681123,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.5143011920154095,
  "wall_s_per_eq": [
    6.5143011920154095
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9948408764224184,
      "reward": null,
      "residual_heldout": 0.0050732485681123,
      "pred_coeffs": {
        "y": -1.4872807729085968
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.5143011920154095,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.5143011920154095,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4872807729085968
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004848742581713925 cons=0.0 wall_s=6.455 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004848742581713925,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.4548310689860955,
  "wall_s_per_eq": [
    6.4548310689860955
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9945657779420232,
      "reward": null,
      "residual_heldout": 0.004848742581713925,
      "pred_coeffs": {
        "y": -1.4980537704293428
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.4548310689860955,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.4548310689860955,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4980537704293428
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.004532281519034824 cons=0.0 wall_s=6.531 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004532281519034824,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.530817387974821,
  "wall_s_per_eq": [
    6.530817387974821
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9940812707299641,
      "reward": null,
      "residual_heldout": 0.004532281519034824,
      "pred_coeffs": {
        "y": -1.5014115743754657
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.530817387974821,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.530817387974821,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5014115743754657
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.004441715582807797 cons=0.0 wall_s=6.760 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004441715582807797,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.760085951071233,
  "wall_s_per_eq": [
    6.760085951071233
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9952029842118352,
      "reward": null,
      "residual_heldout": 0.004441715582807797,
      "pred_coeffs": {
        "y": -1.5004305248899927
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.760085951071233,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.760085951071233,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.5004305248899927
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0039647904459360304 cons=0.0 wall_s=9.966 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0039647904459360304,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 9.966325487010181,
  "wall_s_per_eq": [
    9.966325487010181
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9949309148565818,
      "reward": null,
      "residual_heldout": 0.0039647904459360304,
      "pred_coeffs": {
        "y": -1.4983628269382299
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 9.966325487010181,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.966325487010181,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4983628269382299
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.004795389967314777 cons=0.0 wall_s=6.648 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004795389967314777,
  "conservation_residual": 0.0,
  "equations": [
    "-2*k*y"
  ],
  "wall_s_total": 6.648471805965528,
  "wall_s_per_eq": [
    6.648471805965528
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-2*k*y",
      "r2_train": 0.9942971907346292,
      "reward": null,
      "residual_heldout": 0.004795389967314777,
      "pred_coeffs": {
        "y": -1.4878073252081407
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.648471805965528,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.648471805965528,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7439036626040704
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.006734564020946884 cons=0.0 wall_s=6.694 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006734564020946884,
  "conservation_residual": 0.0,
  "equations": [
    "3*k*y"
  ],
  "wall_s_total": 6.693710957071744,
  "wall_s_per_eq": [
    6.693710957071744
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "3*k*y",
      "r2_train": 0.9948647095327996,
      "reward": null,
      "residual_heldout": 0.006734564020946884,
      "pred_coeffs": {
        "y": -1.4935700808507173
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.693710957071744,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.693710957071744,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49785669361690577
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.004342625259679151 cons=0.0 wall_s=6.715 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004342625259679151,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 6.714991985936649,
  "wall_s_per_eq": [
    6.714991985936649
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9949055695263596,
      "reward": null,
      "residual_heldout": 0.004342625259679151,
      "pred_coeffs": {
        "y": -1.5004514771250317
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.714991985936649,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.714991985936649,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5004514771250317
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.005643139882998588 cons=0.0 wall_s=6.668 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005643139882998588,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 6.668058363953605,
  "wall_s_per_eq": [
    6.668058363953605
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9958500177213402,
      "reward": null,
      "residual_heldout": 0.005643139882998588,
      "pred_coeffs": {
        "y": -1.4914598174362896
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 6.668058363953605,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.668058363953605,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4914598174362896
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.005747143313888414 cons=0.0 wall_s=10.556 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005747143313888414,
  "conservation_residual": 0.0,
  "equations": [
    "2*k*y"
  ],
  "wall_s_total": 10.556011958047748,
  "wall_s_per_eq": [
    10.556011958047748
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*k*y",
      "r2_train": 0.9945140532781818,
      "reward": null,
      "residual_heldout": 0.005747143313888414,
      "pred_coeffs": {
        "y": -1.5037582437324044
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 10.556011958047748,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.556011958047748,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7518791218662022
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.003816594265981562 cons=0.0 wall_s=7.956 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003816594265981562,
  "conservation_residual": 0.0,
  "equations": [
    "k*y"
  ],
  "wall_s_total": 7.956309920991771,
  "wall_s_per_eq": [
    7.956309920991771
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y",
      "r2_train": 0.9950368805891433,
      "reward": null,
      "residual_heldout": 0.003816594265981562,
      "pred_coeffs": {
        "y": -1.4999498146055765
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 7.956309920991771,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.956309920991771,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.4999498146055765
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `linear_decay` / N=400 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.006021200790136635 cons=0.0 wall_s=8.473 ok=True

```json
{
  "law": "linear_decay",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006021200790136635,
  "conservation_residual": 0.0,
  "equations": [
    "-k*y"
  ],
  "wall_s_total": 8.472569968085736,
  "wall_s_per_eq": [
    8.472569968085736
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-k*y",
      "r2_train": 0.9951587111407961,
      "reward": null,
      "residual_heldout": 0.006021200790136635,
      "pred_coeffs": {
        "y": -1.5004997852957422
      },
      "true_coeffs": {
        "y": -1.5
      },
      "structure_ok": true,
      "wall_s": 8.472569968085736,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.472569968085736,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.5004997852957422
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.523 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.523420812096447,
  "wall_s_per_eq": [
    8.581383979064412,
    8.942036833032034
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.581383979064412,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.942036833032034,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.396 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.39619187801145,
  "wall_s_per_eq": [
    8.188216342939995,
    8.207975535071455
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.188216342939995,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.207975535071455,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.104 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.104346251115203,
  "wall_s_per_eq": [
    8.108701341086999,
    7.995644910028204
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.108701341086999,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.995644910028204,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.254 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.253927907091565,
  "wall_s_per_eq": [
    8.358437120099552,
    7.8954907869920135
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.358437120099552,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.8954907869920135,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.004 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.004338592174463,
  "wall_s_per_eq": [
    8.007806176086888,
    8.996532416087575
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.007806176086888,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.996532416087575,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.485 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.484542857157066,
  "wall_s_per_eq": [
    8.384468030068092,
    8.100074827088974
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.384468030068092,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.100074827088974,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.997 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.996576929930598,
  "wall_s_per_eq": [
    8.641133461962454,
    8.355443467968144
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.641133461962454,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.355443467968144,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.931 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.930993880028836,
  "wall_s_per_eq": [
    8.31347860605456,
    8.617515273974277
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.31347860605456,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.617515273974277,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.548 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.547682495904155,
  "wall_s_per_eq": [
    8.10081332793925,
    8.446869167964906
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.10081332793925,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.446869167964906,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.493 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.492711914004758,
  "wall_s_per_eq": [
    7.926628974964842,
    8.566082939039916
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.926628974964842,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.566082939039916,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.896 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.89646947197616,
  "wall_s_per_eq": [
    8.582524162018672,
    8.31394530995749
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.582524162018672,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.31394530995749,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.151 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.15140770911239,
  "wall_s_per_eq": [
    8.203210488078184,
    7.9481972210342064
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.203210488078184,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.9481972210342064,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.335 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.3353108210722,
  "wall_s_per_eq": [
    8.109062111005187,
    9.226248710067011
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.109062111005187,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.226248710067011,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.318 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.3182680940954,
  "wall_s_per_eq": [
    8.330458455020562,
    7.98780963907484
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.330458455020562,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.98780963907484,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.451 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.450641229981557,
  "wall_s_per_eq": [
    8.110311560914852,
    8.340329669066705
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.110311560914852,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.340329669066705,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.240 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.239720321027562,
  "wall_s_per_eq": [
    8.567370116012171,
    8.672350205015391
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.567370116012171,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.672350205015391,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.332 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.332385690999217,
  "wall_s_per_eq": [
    8.004449977073818,
    8.327935713925399
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.004449977073818,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.327935713925399,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.943 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.942813800065778,
  "wall_s_per_eq": [
    8.350003069033846,
    8.592810731031932
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.350003069033846,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.592810731031932,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.307 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.306974456994794,
  "wall_s_per_eq": [
    7.9935777930077165,
    8.313396663987078
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.9935777930077165,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.313396663987078,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.431 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.43125181796495,
  "wall_s_per_eq": [
    8.95414665993303,
    8.477105158031918
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.95414665993303,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.477105158031918,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=5.643615552475121e-16 cons=6.748621999774394e-32 wall_s=20.530 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.643615552475121e-16,
  "conservation_residual": 6.748621999774394e-32,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 20.52996302698739,
  "wall_s_per_eq": [
    9.736112548038363,
    10.793850478949025
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 7.391549471157913e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.736112548038363,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.736112548038363,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.895681633792329e-16,
      "pred_coeffs": {
        "x": -3.999999999999999
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 10.793850478949025,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.793850478949025,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.999999999999999
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=5.030979245727107e-16 cons=0.0 wall_s=23.937 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.030979245727107e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 23.936749808955938,
  "wall_s_per_eq": [
    13.664917232003063,
    10.271832576952875
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.031241959930418e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 13.664917232003063,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.664917232003063,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.030716531523796e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 10.271832576952875,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.271832576952875,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=7.975939028196522e-15 cons=0.0 wall_s=17.896 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.975939028196522e-15,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 17.89623807813041,
  "wall_s_per_eq": [
    8.92047417210415,
    8.975763906026259
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999862,
      "reward": null,
      "residual_heldout": 1.5461394029103148e-14,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.92047417210415,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.92047417210415,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.90484027289896e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.975763906026259,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.975763906026259,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5688754193807638 cons=1.0077511114416062 wall_s=20.734 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5688754193807638,
  "conservation_residual": 1.0077511114416062,
  "equations": [
    "2*v",
    "-w2*x"
  ],
  "wall_s_total": 20.73388736601919,
  "wall_s_per_eq": [
    8.638946418999694,
    12.094940947019495
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.001670375088272058,
      "reward": null,
      "residual_heldout": 1.137750838761527,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.638946418999694,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.638946418999694,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 6.054290654539346e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 12.094940947019495,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.094940947019495,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=4.779760440013398e-16 cons=0.0 wall_s=17.142 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.779760440013398e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-4*w2*x"
  ],
  "wall_s_total": 17.141929561970755,
  "wall_s_per_eq": [
    7.934997349977493,
    9.206932211993262
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.658557667551278e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.934997349977493,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.934997349977493,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-4*w2*x",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.900963212475519e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.206932211993262,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.206932211993262,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=6.881611038050035e-16 cons=0.0 wall_s=20.714 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.881611038050035e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 20.713528648018837,
  "wall_s_per_eq": [
    9.281034910003655,
    11.432493738015182
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 6.767845376076718e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.281034910003655,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.281034910003655,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 6.995376700023353e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 11.432493738015182,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.432493738015182,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=3.6320374912769554e-16 cons=0.0 wall_s=27.278 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.6320374912769554e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 27.278319303994067,
  "wall_s_per_eq": [
    10.523069181013852,
    16.755250122980215
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.4882278771644135e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.523069181013852,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.523069181013852,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.7758471053894973e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 16.755250122980215,
      "wall_pad_s": 0.0,
      "wall_raw_s": 16.755250122980215,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=5.081229177518814e-16 cons=0.0 wall_s=20.258 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.081229177518814e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 20.257686027907766,
  "wall_s_per_eq": [
    9.387493594898842,
    10.870192433008924
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 7.130044752511257e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.387493594898842,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.387493594898842,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 3.0324136025263707e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 10.870192433008924,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.870192433008924,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=4.710571964982391e-16 cons=0.0 wall_s=20.793 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.710571964982391e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 20.79320501710754,
  "wall_s_per_eq": [
    9.499361620051786,
    11.293843397055753
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "reward": null,
      "residual_heldout": 3.855642159154824e-16,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.499361620051786,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.499361620051786,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.565501770809958e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 11.293843397055753,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.293843397055753,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=4.185046039316352e-16 cons=0.0 wall_s=21.161 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.185046039316352e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 21.160500024911016,
  "wall_s_per_eq": [
    13.29752765991725,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v",
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 13.29752765991725,
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      "wall_raw_s": 13.29752765991725,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.021220421844296e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.862972364993766,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.862972364993766,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=5.154297349196044e-16 cons=0.0 wall_s=15.825 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.154297349196044e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.825406680931337,
  "wall_s_per_eq": [
    7.851161022903398,
    7.9742456580279395
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 4.6960891267834385e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.851161022903398,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.851161022903398,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.612505571608651e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.9742456580279395,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.9742456580279395,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=4.522706864493704e-16 cons=0.0 wall_s=14.205 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.522706864493704e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-4*w2*x"
  ],
  "wall_s_total": 14.205364936031401,
  "wall_s_per_eq": [
    7.072604230022989,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.712460525959955e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.072604230022989,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.072604230022989,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-4*w2*x",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.3329532030274535e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.132760706008412,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.132760706008412,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=5.165886330677808e-16 cons=0.0 wall_s=20.153 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.165886330677808e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 20.153262406005524,
  "wall_s_per_eq": [
    12.488946655998006,
    7.664315750007518
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.920055073561919e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 12.488946655998006,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.488946655998006,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 5.411717587793696e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.664315750007518,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.664315750007518,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=4.827784909087003e-16 cons=0.0 wall_s=14.102 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.827784909087003e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 14.102094006026164,
  "wall_s_per_eq": [
    7.296324169030413,
    6.805769836995751
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.626105087829336e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.296324169030413,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.296324169030413,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 6.029464730344671e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.805769836995751,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.805769836995751,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=3.6428667441688374e-16 cons=0.0 wall_s=14.269 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.6428667441688374e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 14.269219106063247,
  "wall_s_per_eq": [
    7.345617788028903,
    6.923601318034343
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.0233811153215493e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.345617788028903,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.345617788028903,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.2623523730161255e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.923601318034343,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.923601318034343,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=5.952665205458363e-16 cons=0.0 wall_s=19.811 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.952665205458363e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 19.811373905977234,
  "wall_s_per_eq": [
    12.645354176987894,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
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      "reward": null,
      "residual_heldout": 4.727310908733285e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 12.645354176987894,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.645354176987894,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 7.178019502183441e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.16601972898934,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.16601972898934,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=3.394871521558815e-16 cons=0.0 wall_s=14.791 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.394871521558815e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-4*w2*x"
  ],
  "wall_s_total": 14.790882510016672,
  "wall_s_per_eq": [
    7.208092323038727,
    7.582790186977945
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.051222778713525e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.208092323038727,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.208092323038727,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-4*w2*x",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 2.738520264404105e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.582790186977945,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.582790186977945,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=5.668028284538196e-16 cons=0.0 wall_s=14.007 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.668028284538196e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-3*w2*x"
  ],
  "wall_s_total": 14.00725102913566,
  "wall_s_per_eq": [
    7.152073379023932,
    6.855177650111727
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.82478453058475e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.152073379023932,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.152073379023932,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-3*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.511272038491642e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.855177650111727,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.855177650111727,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.3333333333333333
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=4.45322861385179e-16 cons=0.0 wall_s=21.245 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.45322861385179e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "3*w2*x"
  ],
  "wall_s_total": 21.245453387964517,
  "wall_s_per_eq": [
    8.451627583010122,
    12.793825804954395
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.72992879869927e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.451627583010122,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.451627583010122,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "3*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.1765284290043095e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 12.793825804954395,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.793825804954395,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.3333333333333335
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=3.7243712929284854e-16 cons=0.0 wall_s=16.527 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.7243712929284854e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 16.52664369298145,
  "wall_s_per_eq": [
    8.461819516960531,
    8.06482417602092
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 2.8979948220347147e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.461819516960531,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.461819516960531,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 4.550747763822257e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.06482417602092,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.06482417602092,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.646 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.646164907957427,
  "wall_s_per_eq": [
    9.107791116926819,
    9.538373791030608
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.107791116926819,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.538373791030608,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.932 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 19.931800734018907,
  "wall_s_per_eq": [
    10.499013577005826,
    9.432787157013081
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.499013577005826,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.432787157013081,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.585 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.584517920040525,
  "wall_s_per_eq": [
    9.615789799951017,
    8.968728120089509
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.615789799951017,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.968728120089509,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.477 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.477341957972385,
  "wall_s_per_eq": [
    9.52970816695597,
    8.947633791016415
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.52970816695597,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.947633791016415,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=23.801 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 23.80079916806426,
  "wall_s_per_eq": [
    9.337246499024332,
    14.463552669039927
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.337246499024332,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 14.463552669039927,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.979 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.97937680198811,
  "wall_s_per_eq": [
    8.60625443898607,
    8.37312236300204
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.60625443898607,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.37312236300204,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.289 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.288505568169057,
  "wall_s_per_eq": [
    8.603783386060968,
    7.684722182108089
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.603783386060968,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.684722182108089,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.664 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.66415572911501,
  "wall_s_per_eq": [
    8.591039102058858,
    9.073116627056152
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.591039102058858,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.073116627056152,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.271 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.271193949040025,
  "wall_s_per_eq": [
    8.054962211055681,
    8.216231737984344
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.054962211055681,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.216231737984344,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.422 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.42213687801268,
  "wall_s_per_eq": [
    9.415983072016388,
    9.006153805996291
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.415983072016388,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.006153805996291,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.641 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.640859610051848,
  "wall_s_per_eq": [
    9.384539443999529,
    8.256320166052319
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.384539443999529,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.256320166052319,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.200 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 19.200050164130516,
  "wall_s_per_eq": [
    9.89914747804869,
    9.300902686081827
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.89914747804869,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.300902686081827,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.371 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.37061102106236,
  "wall_s_per_eq": [
    9.377061940031126,
    8.993549081031233
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.377061940031126,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.993549081031233,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.573 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 16.57265178312082,
  "wall_s_per_eq": [
    8.765407977043651,
    7.807243806077167
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.765407977043651,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.807243806077167,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.101 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.100515133002773,
  "wall_s_per_eq": [
    9.035885735996999,
    9.064629397005774
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.035885735996999,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.064629397005774,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.325 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.32524789706804,
  "wall_s_per_eq": [
    8.932734276051633,
    9.392513621016406
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.932734276051633,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.392513621016406,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.982 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.981683352030814,
  "wall_s_per_eq": [
    9.106720390031114,
    8.8749629619997
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.106720390031114,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.8749629619997,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.900 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.899735409999266,
  "wall_s_per_eq": [
    9.153621418983676,
    9.74611399101559
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.153621418983676,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.74611399101559,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.710 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.709786228951998,
  "wall_s_per_eq": [
    8.587463321979158,
    9.12232290697284
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.587463321979158,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.12232290697284,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.942 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.941902836901136,
  "wall_s_per_eq": [
    8.47805981291458,
    9.463843023986556
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.47805981291458,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.463843023986556,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=4.0708880607261047e-16 cons=0.0 wall_s=14.896 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.0708880607261047e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 14.895594551926479,
  "wall_s_per_eq": [
    7.588067214936018,
    7.307527336990461
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 3.622036293406937e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.588067214936018,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.588067214936018,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 4.519739828045272e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.307527336990461,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.307527336990461,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=4.519701477691267e-16 cons=0.0 wall_s=20.672 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.519701477691267e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 20.67238874605391,
  "wall_s_per_eq": [
    7.766451359959319,
    12.905937386094593
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.0450172250932e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.766451359959319,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.766451359959319,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.994385730289335e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 12.905937386094593,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.905937386094593,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=7.409737555639346e-15 cons=0.0 wall_s=14.892 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.409737555639346e-15,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 14.891660558991134,
  "wall_s_per_eq": [
    7.31716893997509,
    7.574491619016044
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999865,
      "reward": null,
      "residual_heldout": 1.4363349727490065e-14,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.31716893997509,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.31716893997509,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.561253837886262e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.574491619016044,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.574491619016044,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5091890328339368 cons=1.007016057861822 wall_s=15.741 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5091890328339368,
  "conservation_residual": 1.007016057861822,
  "equations": [
    "2*v",
    "-w2*x"
  ],
  "wall_s_total": 15.741050511947833,
  "wall_s_per_eq": [
    8.110637378995307,
    7.630413132952526
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.07674713387010423,
      "reward": null,
      "residual_heldout": 1.0183780656678731,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.110637378995307,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.110637378995307,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.887749656888597e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.630413132952526,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.630413132952526,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=3.8905399420855947e-16 cons=0.0 wall_s=21.719 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.8905399420855947e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-4*w2*x"
  ],
  "wall_s_total": 21.71872109710239,
  "wall_s_per_eq": [
    14.846162495086901,
    6.872558602015488
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.2634581379752417e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 14.846162495086901,
      "wall_pad_s": 0.0,
      "wall_raw_s": 14.846162495086901,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-4*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.5176217461959473e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.872558602015488,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.872558602015488,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=4.368657781487814e-16 cons=0.0 wall_s=19.371 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.368657781487814e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 19.370878665940836,
  "wall_s_per_eq": [
    12.139061487978324,
    7.231817177962512
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.344869690375718e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 12.139061487978324,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.139061487978324,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.3924458725999097e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.231817177962512,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.231817177962512,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=4.485771132844037e-16 cons=0.0 wall_s=15.637 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.485771132844037e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.636835701880045,
  "wall_s_per_eq": [
    7.644488482968882,
    7.9923472189111635
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.847380714145257e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.644488482968882,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.644488482968882,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.124161551542816e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.9923472189111635,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.9923472189111635,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=4.352342278569722e-16 cons=0.0 wall_s=13.406 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.352342278569722e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 13.406187026994303,
  "wall_s_per_eq": [
    6.567875740001909,
    6.838311286992393
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.091443775617765e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.567875740001909,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.567875740001909,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.6132407815216785e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.838311286992393,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.838311286992393,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=4.753519939084354e-16 cons=0.0 wall_s=20.016 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.753519939084354e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 20.015990050975233,
  "wall_s_per_eq": [
    7.075895464979112,
    12.940094585996121
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.0324798617567743e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.075895464979112,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.075895464979112,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.474560016411934e-16,
      "pred_coeffs": {
        "x": -4.0
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 12.940094585996121,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.940094585996121,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=4.174864863848443e-16 cons=0.0 wall_s=13.660 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.174864863848443e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-3*w2*x"
  ],
  "wall_s_total": 13.659886668086983,
  "wall_s_per_eq": [
    6.7914953080471605,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.5304383040036e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.7914953080471605,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.7914953080471605,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-3*w2*x",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 4.819291423693286e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.868391360039823,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.868391360039823,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.3333333333333335
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=3.8588233621832294e-16 cons=0.0 wall_s=13.841 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.8588233621832294e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 13.840898381080478,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.8169666751352283e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.857862947974354,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.857862947974354,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.90068004923123e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.983035433106124,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.983035433106124,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=3.48917324138057e-16 cons=0.0 wall_s=13.243 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.48917324138057e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 13.243364390917122,
  "wall_s_per_eq": [
    6.808441406930797,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "reward": null,
      "residual_heldout": 2.804839113981477e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.808441406930797,
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      "wall_raw_s": 6.808441406930797,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
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      "reward": null,
      "residual_heldout": 4.173507368779663e-16,
      "pred_coeffs": {
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 6.434922983986326,
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      "wall_raw_s": 6.434922983986326,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=3.947752001023714e-16 cons=0.0 wall_s=29.752 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.947752001023714e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 29.751937827910297,
  "wall_s_per_eq": [
    13.843189804931171,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 13.843189804931171,
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      "wall_raw_s": 13.843189804931171,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.758585481165372e-16,
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        "x": -4.0
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 15.908748022979125,
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      "wall_raw_s": 15.908748022979125,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=4.413225099451932e-16 cons=0.0 wall_s=13.482 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.413225099451932e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 13.48239508701954,
  "wall_s_per_eq": [
    6.849985065986402,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 5.285188332917944e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.849985065986402,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.849985065986402,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.5412618659859196e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.632410021033138,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.632410021033138,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=4.0014219164252913e-16 cons=0.0 wall_s=14.661 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.0014219164252913e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 14.66088824113831,
  "wall_s_per_eq": [
    7.648511104052886,
    7.012377137085423
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.9175384677150905e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.648511104052886,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.648511104052886,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.0853053651354917e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.012377137085423,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.012377137085423,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=4.395082948566494e-16 cons=0.0 wall_s=13.307 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.395082948566494e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 13.306807262822986,
  "wall_s_per_eq": [
    6.723870478919707,
    6.582936783903278
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.981436079043559e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.723870478919707,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.723870478919707,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.808729818089429e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.582936783903278,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.582936783903278,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=3.8604425191085805e-16 cons=0.0 wall_s=20.866 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.8604425191085805e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-4*w2*x"
  ],
  "wall_s_total": 20.86554857902229,
  "wall_s_per_eq": [
    13.61093248706311,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.343174434582809e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 13.61093248706311,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.61093248706311,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-4*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.3777106036343524e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.2546160919591784,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.2546160919591784,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=4.12913695262583e-16 cons=0.0 wall_s=14.238 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.12913695262583e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-3*w2*x"
  ],
  "wall_s_total": 14.238481343956664,
  "wall_s_per_eq": [
    7.092014887952246,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.8619313042851634e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.092014887952246,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.092014887952246,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-3*w2*x",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 4.396342600966497e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.146466456004418,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.146466456004418,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.3333333333333335
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=3.440540673612405e-16 cons=0.0 wall_s=16.740 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.440540673612405e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 16.73950721696019,
  "wall_s_per_eq": [
    6.962605420034379,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.6289699589773533e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.962605420034379,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.962605420034379,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.2521113882474566e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.776901796925813,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.776901796925813,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=3.592831503560105e-16 cons=0.0 wall_s=16.638 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.592831503560105e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 16.638000897946768,
  "wall_s_per_eq": [
    6.751294596935622,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "reward": null,
      "residual_heldout": 3.187521347247668e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.751294596935622,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.751294596935622,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.9981416598725417e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.886706301011145,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.886706301011145,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.749 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.749297050060704,
  "wall_s_per_eq": [
    9.8046897680033,
    7.9446072820574045
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.8046897680033,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.9446072820574045,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.887 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.886762981070206,
  "wall_s_per_eq": [
    8.682007822091691,
    9.204755158978514
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.682007822091691,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.204755158978514,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.780 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.780248448019847,
  "wall_s_per_eq": [
    8.63250462396536,
    9.147743824054487
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.63250462396536,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.147743824054487,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.852 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.852113853907213,
  "wall_s_per_eq": [
    8.99051845294889,
    8.861595400958322
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.99051845294889,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.861595400958322,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.712 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.712185906013474,
  "wall_s_per_eq": [
    9.26450854097493,
    9.447677365038544
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.26450854097493,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.447677365038544,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.459 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.45857234997675,
  "wall_s_per_eq": [
    8.697161710937507,
    8.76141063903924
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.697161710937507,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.76141063903924,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.242 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.242486040922813,
  "wall_s_per_eq": [
    9.100902587990277,
    9.141583452932537
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.100902587990277,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.141583452932537,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.176 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.176270384108648,
  "wall_s_per_eq": [
    9.119504419039004,
    9.056765965069644
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.119504419039004,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.056765965069644,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.125 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.12540949997492,
  "wall_s_per_eq": [
    9.160654174047522,
    8.964755325927399
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.160654174047522,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.964755325927399,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.765 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.76513741305098,
  "wall_s_per_eq": [
    9.546048747026362,
    9.219088666024618
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.546048747026362,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.219088666024618,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.760 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 19.7595312850317,
  "wall_s_per_eq": [
    9.568686692044139,
    10.19084459298756
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.568686692044139,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 10.19084459298756,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.662 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.662202771985903,
  "wall_s_per_eq": [
    9.41687268903479,
    9.245330082951114
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.41687268903479,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.245330082951114,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.774 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.77385665103793,
  "wall_s_per_eq": [
    9.255276183015667,
    9.518580468022265
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.255276183015667,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.518580468022265,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.104 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.103908736957237,
  "wall_s_per_eq": [
    8.800784035935067,
    9.30312470102217
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.800784035935067,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.30312470102217,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.763 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.762558364891447,
  "wall_s_per_eq": [
    9.407821993925609,
    8.354736370965838
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.407821993925609,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.354736370965838,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.771 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.770659819128923,
  "wall_s_per_eq": [
    9.084545378107578,
    8.686114441021346
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.084545378107578,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.686114441021346,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.127 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.127366041997448,
  "wall_s_per_eq": [
    9.211466416949406,
    8.915899625048041
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.211466416949406,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.915899625048041,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.814 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.813676921883598,
  "wall_s_per_eq": [
    9.325786805944517,
    9.48789011593908
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.325786805944517,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.48789011593908,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.283 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 18.283163181040436,
  "wall_s_per_eq": [
    9.366121739032678,
    8.917041442007758
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.366121739032678,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.917041442007758,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.470 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0)"
  ],
  "wall_s_total": 17.469921180978417,
  "wall_s_per_eq": [
    8.937569269910455,
    8.532351911067963
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.937569269910455,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.532351911067963,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=4.573341497854676e-16 cons=0.0 wall_s=20.601 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.573341497854676e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 20.601483710110188,
  "wall_s_per_eq": [
    13.76480139407795,
    6.836682316032238
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.334353341562084e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 13.76480139407795,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.76480139407795,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.8123296541472675e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.836682316032238,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.836682316032238,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=3.761959470818724e-16 cons=0.0 wall_s=13.752 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.761959470818724e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 13.751777276978828,
  "wall_s_per_eq": [
    6.986313530942425,
    6.765463746036403
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.1670910572992593e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.986313530942425,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.986313530942425,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.356827884338189e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.765463746036403,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.765463746036403,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=7.495657968003281e-15 cons=0.0 wall_s=13.167 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.495657968003281e-15,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 13.167288732016459,
  "wall_s_per_eq": [
    6.700535665033385,
    6.466753066983074
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999853,
      "reward": null,
      "residual_heldout": 1.45365046310889e-14,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.700535665033385,
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      "wall_raw_s": 6.700535665033385,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.548113049176617e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.466753066983074,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.466753066983074,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5038685170094251 cons=1.003090742945693 wall_s=13.554 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5038685170094251,
  "conservation_residual": 1.003090742945693,
  "equations": [
    "2*v",
    "-w2*x"
  ],
  "wall_s_total": 13.553780724992976,
  "wall_s_per_eq": [
    6.576428447966464,
    6.977352277026512
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.000677449723523349,
      "reward": null,
      "residual_heldout": 1.0077370340188498,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 6.576428447966464,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.576428447966464,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.4705969403312954e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.977352277026512,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.977352277026512,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=4.415855320539848e-16 cons=0.0 wall_s=21.176 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.415855320539848e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-4*w2*x"
  ],
  "wall_s_total": 21.176321643055417,
  "wall_s_per_eq": [
    14.442857476999052,
    6.733464166056365
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.603794068539509e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 14.442857476999052,
      "wall_pad_s": 0.0,
      "wall_raw_s": 14.442857476999052,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-4*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.2279165725401873e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.733464166056365,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.733464166056365,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=4.2972706235709683e-16 cons=0.0 wall_s=13.651 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.2972706235709683e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 13.651106991921552,
  "wall_s_per_eq": [
    6.778134271968156,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.412738080208166e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.778134271968156,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.778134271968156,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.1818031669337707e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.872972719953395,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.872972719953395,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=4.745073558059973e-16 cons=0.0 wall_s=12.977 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.745073558059973e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 12.97689315106254,
  "wall_s_per_eq": [
    6.58594353008084,
    6.390949620981701
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.557583682579931e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.58594353008084,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.58594353008084,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.932563433540016e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.390949620981701,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.390949620981701,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=3.836213364647911e-16 cons=0.0 wall_s=13.506 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.836213364647911e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 13.506416475982405,
  "wall_s_per_eq": [
    6.678743300959468,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.827382182306965e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.678743300959468,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.678743300959468,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 3.8450445469888565e-16,
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        "x": -4.0
      },
      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 6.827673175022937,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.827673175022937,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=4.65407269578944e-16 cons=0.0 wall_s=32.960 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.65407269578944e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 32.96030616306234,
  "wall_s_per_eq": [
    23.483059047022834,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 23.483059047022834,
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      "wall_raw_s": 23.483059047022834,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.316171220298445e-16,
      "pred_coeffs": {
        "x": -4.0
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 9.477247116039507,
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      "wall_raw_s": 9.477247116039507,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=4.566463965942341e-16 cons=0.0 wall_s=27.920 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.566463965942341e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 27.920242481981404,
  "wall_s_per_eq": [
    20.444217376061715,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 20.444217376061715,
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      "wall_raw_s": 20.444217376061715,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.404651868162168e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.476025105919689,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.476025105919689,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=4.64986958734978e-16 cons=0.0 wall_s=18.160 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.64986958734978e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 18.159653090056963,
  "wall_s_per_eq": [
    10.293005755986087,
    7.866647334070876
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.301416294684058e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.293005755986087,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.293005755986087,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.998322880015501e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.866647334070876,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.866647334070876,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=4.989560620513271e-16 cons=0.0 wall_s=13.529 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.989560620513271e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 13.528853007941507,
  "wall_s_per_eq": [
    7.005398363922723,
    6.523454644018784
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.957521266160333e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.005398363922723,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.005398363922723,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.02159997486621e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.523454644018784,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.523454644018784,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=4.486117179384248e-16 cons=0.0 wall_s=22.067 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.486117179384248e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 22.066825182992034,
  "wall_s_per_eq": [
    6.964524167007767,
    15.102301015984267
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.549509540808496e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.964524167007767,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.964524167007767,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.42272481796e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 15.102301015984267,
      "wall_pad_s": 0.0,
      "wall_raw_s": 15.102301015984267,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=4.469837008417859e-16 cons=0.0 wall_s=25.807 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.469837008417859e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 25.80676517309621,
  "wall_s_per_eq": [
    9.556211517076008,
    16.2505536560202
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.719476376997965e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.556211517076008,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.556211517076008,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.220197639837753e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 16.2505536560202,
      "wall_pad_s": 0.0,
      "wall_raw_s": 16.2505536560202,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=4.4337088119637973e-16 cons=0.0 wall_s=13.350 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.4337088119637973e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 13.349516176967882,
  "wall_s_per_eq": [
    6.894285521004349,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.1870742602606277e-16,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.894285521004349,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.894285521004349,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.680343363666966e-16,
      "pred_coeffs": {
        "x": -4.0
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 6.455230655963533,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.455230655963533,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=4.820983878476952e-16 cons=0.0 wall_s=23.817 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.820983878476952e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 23.816677046008408,
  "wall_s_per_eq": [
    10.345308433985338,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 10.345308433985338,
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      "wall_raw_s": 10.345308433985338,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.962462749692497e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 13.47136861202307,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.47136861202307,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=3.9904657805340453e-16 cons=0.0 wall_s=32.193 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.9904657805340453e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 32.19314417405985,
  "wall_s_per_eq": [
    25.006190686021,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
      "residual_heldout": 3.7668966784690116e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 25.006190686021,
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      "wall_raw_s": 25.006190686021,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.214034882599079e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.186953488038853,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.186953488038853,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=4.1840789969079947e-16 cons=0.0 wall_s=21.458 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.1840789969079947e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 21.45829576300457,
  "wall_s_per_eq": [
    14.417558390996419,
    7.040737372008152
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.048412164169377e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 14.417558390996419,
      "wall_pad_s": 0.0,
      "wall_raw_s": 14.417558390996419,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.3197458296466127e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.040737372008152,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.040737372008152,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=4.245210822621686e-16 cons=0.0 wall_s=13.934 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.245210822621686e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 13.933980704052374,
  "wall_s_per_eq": [
    6.852166312979534,
    7.0818143910728395
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.436907759825663e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.852166312979534,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.852166312979534,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.0535138854177086e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.0818143910728395,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.0818143910728395,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=4.581485137400789e-16 cons=0.0 wall_s=36.112 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.581485137400789e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 36.11197303200606,
  "wall_s_per_eq": [
    12.495176144060679,
    23.616796887945384
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 4.0685847893910376e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 12.495176144060679,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.495176144060679,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 5.09438548541054e-16,
      "pred_coeffs": {
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 23.616796887945384,
      "wall_pad_s": 0.0,
      "wall_raw_s": 23.616796887945384,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.007372433304222186 cons=1.9071006276927983e-05 wall_s=40.624 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007372433304222186,
  "conservation_residual": 1.9071006276927983e-05,
  "equations": [
    "(v - 1*1.3104124)*v*0.03130101*v*x + v",
    "x*(-3.9840803)"
  ],
  "wall_s_total": 40.6237715909956,
  "wall_s_per_eq": [
    26.880429387907498,
    13.743342203088105
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(v - 1*1.3104124)*v*0.03130101*v*x + v",
      "r2_train": 0.9938510730573316,
      "reward": null,
      "residual_heldout": 0.01103549996496208,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 26.880429387907498,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9840803)",
      "r2_train": 0.9966771645426927,
      "reward": null,
      "residual_heldout": 0.0037093666434822917,
      "pred_coeffs": {
        "x": -3.9840803
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 13.743342203088105,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.008055987092929894 cons=231.45016721876988 wall_s=23.269 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008055987092929894,
  "conservation_residual": 231.45016721876988,
  "equations": [
    "v + x*0.038918246",
    "x*(-3.8490858) - (-0.18453084)*((x - 0.3481148)*(-v*x*(-v + x) + x) - 0.777319)"
  ],
  "wall_s_total": 23.26946723088622,
  "wall_s_per_eq": [
    8.03185102995485,
    15.23761620093137
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + x*0.038918246",
      "r2_train": 0.9968809925668201,
      "reward": null,
      "residual_heldout": 0.009725195450714683,
      "pred_coeffs": {
        "v": 1.0,
        "x": 0.038918246
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.03185102995485,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.8490858) - (-0.18453084)*((x - 0.3481148)*(-v*x*(-v + x) + x) - 0.777319)",
      "r2_train": 0.9955479602175111,
      "reward": null,
      "residual_heldout": 0.0063867787351451055,
      "pred_coeffs": {
        "1": -0.14343932801796
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": false,
      "wall_s": 15.23761620093137,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.004908041773936035 cons=0.005059777848012814 wall_s=19.292 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004908041773936035,
  "conservation_residual": 0.005059777848012814,
  "equations": [
    "v*(0.069728084 - 0.04117409*v*v*(x*x - 1*(-0.39014474))) + v",
    "x*(-4.017359)"
  ],
  "wall_s_total": 19.292440093006007,
  "wall_s_per_eq": [
    7.986172572011128,
    11.30626752099488
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(0.069728084 - 0.04117409*v*v*(x*x - 1*(-0.39014474))) + v",
      "r2_train": 0.996601537306891,
      "reward": null,
      "residual_heldout": 0.004692520316392343,
      "pred_coeffs": {
        "v": 1.069728084
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.986172572011128,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.017359)",
      "r2_train": 0.995086116982182,
      "reward": null,
      "residual_heldout": 0.005123563231479728,
      "pred_coeffs": {
        "x": -4.017359
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 11.30626752099488,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.0053505088130108664 cons=1.2743389569703236 wall_s=16.377 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0053505088130108664,
  "conservation_residual": 1.2743389569703236,
  "equations": [
    "(1.1180475 - 0.027887335*(v + 0.9373306)*(v + x*x*(v - x)))*(v - 1*(-0.061570566))",
    "x*(-3.8793225)"
  ],
  "wall_s_total": 16.377113860100508,
  "wall_s_per_eq": [
    7.939109216094948,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(1.1180475 - 0.027887335*(v + 0.9373306)*(v + x*x*(v - x)))*(v - 1*(-0.061570566))",
      "r2_train": 0.9954825683751698,
      "reward": null,
      "residual_heldout": 0.005627646763286237,
      "pred_coeffs": {
        "1": 0.06883881738988501
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 7.939109216094948,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.8793225)",
      "r2_train": 0.991574744960154,
      "reward": null,
      "residual_heldout": 0.005073370862735496,
      "pred_coeffs": {
        "x": -3.8793225
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.43800464400556,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.005544726779507727 cons=0.0008181826874492298 wall_s=17.191 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005544726779507727,
  "conservation_residual": 0.0008181826874492298,
  "equations": [
    "v*(x*v*v*x*0.04644893 - 0.027053732) + v - 0.021962106",
    "x*(-3.9548337)"
  ],
  "wall_s_total": 17.190948489937,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(x*v*v*x*0.04644893 - 0.027053732) + v - 0.021962106",
      "r2_train": 0.9960519936580965,
      "reward": null,
      "residual_heldout": 0.005877267371094432,
      "pred_coeffs": {
        "1": -0.021962106,
        "v": 0.972946268
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 9.410683928988874,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9548337)",
      "r2_train": 0.9962887531951097,
      "reward": null,
      "residual_heldout": 0.005212186187921022,
      "pred_coeffs": {
        "x": -3.9548337
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        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.780264560948126,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.005901625331609872 cons=0.0002331353198112771 wall_s=15.907 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005901625331609872,
  "conservation_residual": 0.0002331353198112771,
  "equations": [
    "v*v*(0.2664471 - x*(x - 1*(-0.37125847)))*0.07521793 + v",
    "x*(-3.9400134)"
  ],
  "wall_s_total": 15.906669834046625,
  "wall_s_per_eq": [
    7.634933170047589,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*v*(0.2664471 - x*(x - 1*(-0.37125847)))*0.07521793 + v",
      "r2_train": 0.9955922492840247,
      "reward": null,
      "residual_heldout": 0.008488038745540145,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.634933170047589,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9400134)",
      "r2_train": 0.9952564564275677,
      "reward": null,
      "residual_heldout": 0.0033152119176795987,
      "pred_coeffs": {
        "x": -3.9400134
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.271736663999036,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.004300043940385983 cons=0.6060755086730608 wall_s=15.188 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004300043940385983,
  "conservation_residual": 0.6060755086730608,
  "equations": [
    "-0.055223677*v*x + v",
    "(x - 0.033146646)*(v*x*v*(-0.1886316) - 3.9763381)"
  ],
  "wall_s_total": 15.187619409989566,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-0.055223677*v*x + v",
      "r2_train": 0.9964912493260355,
      "reward": null,
      "residual_heldout": 0.004730318168035414,
      "pred_coeffs": {
        "x*v": -0.055223677
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 7.542257223976776,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(x - 0.033146646)*(v*x*v*(-0.1886316) - 3.9763381)",
      "r2_train": 0.9956212273915086,
      "reward": null,
      "residual_heldout": 0.003869769712736552,
      "pred_coeffs": {
        "1": 0.13180227137701261
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        "x": -4.0
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      "structure_ok": false,
      "wall_s": 7.64536218601279,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.00409147587889091 cons=0.004250186787029262 wall_s=15.528 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00409147587889091,
  "conservation_residual": 0.004250186787029262,
  "equations": [
    "v*x*v*0.09058264*x + v - 0.06575127",
    "x*(-3.9269319)"
  ],
  "wall_s_total": 15.528425263008103,
  "wall_s_per_eq": [
    7.722270964994095,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*x*v*0.09058264*x + v - 0.06575127",
      "r2_train": 0.996162331869464,
      "reward": null,
      "residual_heldout": 0.003055367075443325,
      "pred_coeffs": {
        "1": -0.06575127,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.722270964994095,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9269319)",
      "r2_train": 0.9950334089281114,
      "reward": null,
      "residual_heldout": 0.005127584682338495,
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        "x": -3.9269319
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.8061542980140075,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0036570403217752534 cons=0.009956909517534938 wall_s=15.451 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0036570403217752534,
  "conservation_residual": 0.009956909517534938,
  "equations": [
    "v - ((-v*v*x + 0.4962054)*0.14155902*(x + 0.35245848) + 0.06569597)",
    "x*(-3.9741664)"
  ],
  "wall_s_total": 15.451192620908841,
  "wall_s_per_eq": [
    7.465864826925099,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - ((-v*v*x + 0.4962054)*0.14155902*(x + 0.35245848) + 0.06569597)",
      "r2_train": 0.9943430789187022,
      "reward": null,
      "residual_heldout": 0.004574825404602096,
      "pred_coeffs": {
        "1": -0.09045348196292666,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.465864826925099,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9741664)",
      "r2_train": 0.9922121805396138,
      "reward": null,
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        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.985327793983743,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.005840553058928188 cons=0.02280551057128152 wall_s=15.640 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005840553058928188,
  "conservation_residual": 0.02280551057128152,
  "equations": [
    "v - (-0.025777513)*(2.7858088 - (v*v - 0.81468266))*(v*v - 0.5890365)",
    "x*(-3.9242275)"
  ],
  "wall_s_total": 15.64018521097023,
  "wall_s_per_eq": [
    7.362088241032325,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - (-0.025777513)*(2.7858088 - (v*v - 0.81468266))*(v*v - 0.5890365)",
      "r2_train": 0.9964540549546076,
      "reward": null,
      "residual_heldout": 0.0047014492487121706,
      "pred_coeffs": {
        "v^2": 0.10799561145276347,
        "1": -0.05466948800795415,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.362088241032325,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9242275)",
      "r2_train": 0.9950923119666744,
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        "x": -4.0
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      "structure_ok": true,
      "wall_s": 8.278096969937906,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.006273464809374475 cons=0.0007499652212258959 wall_s=15.977 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006273464809374475,
  "conservation_residual": 0.0007499652212258959,
  "equations": [
    "v*1.0170703",
    "x*(-3.9637957)"
  ],
  "wall_s_total": 15.976718139019795,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*1.0170703",
      "r2_train": 0.9964736617187635,
      "reward": null,
      "residual_heldout": 0.003358912134372287,
      "pred_coeffs": {
        "v": 1.0170703
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.545683517004363,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9637957)",
      "r2_train": 0.9941534141630105,
      "reward": null,
      "residual_heldout": 0.009188017484376663,
      "pred_coeffs": {
        "x": -3.9637957
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.431034622015432,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.006786935812331953 cons=0.15568089116724634 wall_s=15.793 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006786935812331953,
  "conservation_residual": 0.15568089116724634,
  "equations": [
    "v - (-x)*x*x*(x*x - 1.3764372) + x*0.4358168",
    "x*(-3.9346704)"
  ],
  "wall_s_total": 15.792667728033848,
  "wall_s_per_eq": [
    7.84440402709879,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - (-x)*x*x*(x*x - 1.3764372) + x*0.4358168",
      "r2_train": 0.9959595298988477,
      "reward": null,
      "residual_heldout": 0.008319647123754301,
      "pred_coeffs": {
        "v": 1.0,
        "x": 0.4358168
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 7.84440402709879,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9346704)",
      "r2_train": 0.995946665662514,
      "reward": null,
      "residual_heldout": 0.005254224500909604,
      "pred_coeffs": {
        "x": -3.9346704
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.948263700935058,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.006340138279842746 cons=174.0995153209219 wall_s=16.027 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006340138279842746,
  "conservation_residual": 174.0995153209219,
  "equations": [
    "v*0.9721855",
    "-1*v*(-0.045712546) + x*(v*(v*(v*0.0860945 + 0.069198854) - 0.24188901) - 4.0286884)"
  ],
  "wall_s_total": 16.026918256888166,
  "wall_s_per_eq": [
    8.457709989976138,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*0.9721855",
      "r2_train": 0.9917214026216528,
      "reward": null,
      "residual_heldout": 0.0048189002614477654,
      "pred_coeffs": {
        "v": 0.9721855
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.457709989976138,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-1*v*(-0.045712546) + x*(v*(v*(v*0.0860945 + 0.069198854) - 0.24188901) - 4.0286884)",
      "r2_train": 0.9978855774452415,
      "reward": null,
      "residual_heldout": 0.007861376298237726,
      "pred_coeffs": {
        "x*v": -0.24188901
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": false,
      "wall_s": 7.569208266912028,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.009272175995973367 cons=0.0021467841031920193 wall_s=16.319 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.009272175995973367,
  "conservation_residual": 0.0021467841031920193,
  "equations": [
    "v*(1.0609932 - 0.16614404*x*x)",
    "x*(-3.9397013)"
  ],
  "wall_s_total": 16.3188524490688,
  "wall_s_per_eq": [
    7.522051114006899,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v*(1.0609932 - 0.16614404*x*x)",
      "r2_train": 0.9938608576706768,
      "reward": null,
      "residual_heldout": 0.0064711200093881364,
      "pred_coeffs": {
        "v": 1.0609932,
        "x^2*v": -0.16614404000000021
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.522051114006899,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9397013)",
      "r2_train": 0.997277728316785,
      "reward": null,
      "residual_heldout": 0.012073231982558595,
      "pred_coeffs": {
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.7968013350619,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.00548456164350776 cons=1.043957630636624 wall_s=15.538 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00548456164350776,
  "conservation_residual": 1.043957630636624,
  "equations": [
    "v*x*(v - 1*(-0.8198899))*(x*(v*(-0.072230026) - 1*(-0.13780898)) - 1*(-0.024196198)) + v - 1*0.05862473",
    "x*(-4.016038)"
  ],
  "wall_s_total": 15.538485975936055,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*x*(v - 1*(-0.8198899))*(x*(v*(-0.072230026) - 1*(-0.13780898)) - 1*(-0.024196198)) + v - 1*0.05862473",
      "r2_train": 0.9970433438715933,
      "reward": null,
      "residual_heldout": 0.007911202397538465,
      "pred_coeffs": {
        "x*v": 0.0198382183586002,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 7.8921687179245055,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
      "eq_i": 1,
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      "equation": "x*(-4.016038)",
      "r2_train": 0.9962666048127798,
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      "structure_ok": true,
      "wall_s": 7.64631725801155,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0057313170928052215 cons=0.021214976910085958 wall_s=16.455 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0057313170928052215,
  "conservation_residual": 0.021214976910085958,
  "equations": [
    "v + x*(0.17400233 - 0.21640459*x*x)",
    "x*(-3.9620936)"
  ],
  "wall_s_total": 16.454971107072197,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9961076240572959,
      "reward": null,
      "residual_heldout": 0.009021029307378345,
      "pred_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.501440100022592,
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      "wall_raw_s": null,
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      "free_const_values": null,
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    {
      "eq_i": 1,
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      "equation": "x*(-3.9620936)",
      "r2_train": 0.9949045912789076,
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      "structure_ok": true,
      "wall_s": 8.953531007049605,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.00475971723382816 cons=0.0002780702158267582 wall_s=15.083 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00475971723382816,
  "conservation_residual": 0.0002780702158267582,
  "equations": [
    "v - x*(v*v*0.04636264 - 1*0.058246687)",
    "x*(-3.9344106)"
  ],
  "wall_s_total": 15.082747956970707,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v - x*(v*v*0.04636264 - 1*0.058246687)",
      "r2_train": 0.9979527003367504,
      "reward": null,
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      },
      "structure_ok": true,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9344106)",
      "r2_train": 0.9972038068665328,
      "reward": null,
      "residual_heldout": 0.0035669481026925254,
      "pred_coeffs": {
        "x": -3.9344106
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.481734797009267,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.007576337161765007 cons=0.00893674214669856 wall_s=17.901 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007576337161765007,
  "conservation_residual": 0.00893674214669856,
  "equations": [
    "v + (-v*v*v*(x*x + 0.13397433) + v)*0.087355845",
    "x*(-3.9766102)"
  ],
  "wall_s_total": 17.901453470927663,
  "wall_s_per_eq": [
    7.981432465952821,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + (-v*v*v*(x*x + 0.13397433) + v)*0.087355845",
      "r2_train": 0.994676403258533,
      "reward": null,
      "residual_heldout": 0.005697217685239877,
      "pred_coeffs": {
        "v": 1.087355845
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.981432465952821,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9766102)",
      "r2_train": 0.9961456102674102,
      "reward": null,
      "residual_heldout": 0.009455456638290135,
      "pred_coeffs": {
        "x": -3.9766102
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.920021004974842,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.006749911322400373 cons=0.008260828579403898 wall_s=16.175 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006749911322400373,
  "conservation_residual": 0.008260828579403898,
  "equations": [
    "(1.0778784 - 0.025111826*v*v)*(v + 0.047510684)",
    "x*(-4.0233884)"
  ],
  "wall_s_total": 16.175354907056317,
  "wall_s_per_eq": [
    7.968867059098557,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(1.0778784 - 0.025111826*v*v)*(v + 0.047510684)",
      "r2_train": 0.9953185330841822,
      "reward": null,
      "residual_heldout": 0.006927685178542289,
      "pred_coeffs": {
        "v^2": -0.0011930800297489839,
        "1": 0.051210740052825596,
        "v": 1.0778784
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.968867059098557,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0233884)",
      "r2_train": 0.9962141366324468,
      "reward": null,
      "residual_heldout": 0.006572137466258457,
      "pred_coeffs": {
        "x": -4.0233884
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.20648784795776,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0065197193200677555 cons=0.0003941512726326671 wall_s=16.869 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0065197193200677555,
  "conservation_residual": 0.0003941512726326671,
  "equations": [
    "-v*v*(v*0.012499312 + 0.02277866)*(v*x + 0.35523444) + v",
    "x*(-3.9280224)"
  ],
  "wall_s_total": 16.86932560009882,
  "wall_s_per_eq": [
    7.9534533160040155,
    8.915872284094803
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-v*v*(v*0.012499312 + 0.02277866)*(v*x + 0.35523444) + v",
      "r2_train": 0.996724134965338,
      "reward": null,
      "residual_heldout": 0.00892819391549353,
      "pred_coeffs": {
        "v^2": -0.008091764529050399,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.9534533160040155,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9280224)",
      "r2_train": 0.996124999307835,
      "reward": null,
      "residual_heldout": 0.004111244724641981,
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        "x": -3.9280224
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.915872284094803,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.00560836760243719 cons=2.6661302306222008e-05 wall_s=15.708 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00560836760243719,
  "conservation_residual": 2.6661302306222008e-05,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.707838719000392,
  "wall_s_per_eq": [
    8.566216990000157,
    7.141621729000235
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9931689491328461,
      "reward": null,
      "residual_heldout": 0.006014793944500842,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.566216990000157,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.566216990000157,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9961443391957968,
      "reward": null,
      "residual_heldout": 0.005201941260373537,
      "pred_coeffs": {
        "x": -4.019493565486891
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.141621729000235,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.141621729000235,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.019493565486891
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.005268999571161694 cons=0.0003663407027286206 wall_s=18.954 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005268999571161694,
  "conservation_residual": 0.0003663407027286206,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 18.954387236000457,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9930794312453961,
      "reward": null,
      "residual_heldout": 0.0035498339836828527,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.71387704100016,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.71387704100016,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9946656243883236,
      "reward": null,
      "residual_heldout": 0.006988165158640535,
      "pred_coeffs": {
        "x": -3.9267137189779664
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 10.240510195000297,
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      "wall_raw_s": 10.240510195000297,
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      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.9267137189779664
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.005016054582022453 cons=1.7604544874195333e-05 wall_s=15.617 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005016054582022453,
  "conservation_residual": 1.7604544874195333e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 15.617181845999767,
  "wall_s_per_eq": [
    7.817171834999954,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.99791700290074,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.817171834999954,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.817171834999954,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9918941010168851,
      "reward": null,
      "residual_heldout": 0.0065820776252630345,
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        "x": -3.9833625465636486
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.800010010999813,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.800010010999813,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.9833625465636486
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.605055420326739 cons=1.0219627539981175 wall_s=15.162 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.605055420326739,
  "conservation_residual": 1.0219627539981175,
  "equations": [
    "2*v",
    "-w2*x"
  ],
  "wall_s_total": 15.162383880999641,
  "wall_s_per_eq": [
    8.017639291999785,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.10145515409258343,
      "reward": null,
      "residual_heldout": 1.2063288256395037,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.017639291999785,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.017639291999785,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9960071394595568,
      "reward": null,
      "residual_heldout": 0.003782015013974322,
      "pred_coeffs": {
        "x": -3.9868396886898365
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.144744588999856,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.144744588999856,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.9868396886898365
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.00914840390719178 cons=0.00024716906974715726 wall_s=16.413 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00914840390719178,
  "conservation_residual": 0.00024716906974715726,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 16.41334822800036,
  "wall_s_per_eq": [
    7.444040686000335,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9959514205023413,
      "reward": null,
      "residual_heldout": 0.011274809280954336,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.444040686000335,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.444040686000335,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9963796107427882,
      "reward": null,
      "residual_heldout": 0.007021998533429224,
      "pred_coeffs": {
        "x": -4.061592198633844
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.969307542000024,
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      "wall_raw_s": 8.969307542000024,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.061592198633844
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.003627307920706611 cons=2.816732126265884e-05 wall_s=14.773 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003627307920706611,
  "conservation_residual": 2.816732126265884e-05,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 14.772715290999713,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v",
      "r2_train": 0.9941838191830719,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.566530925999814,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.566530925999814,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9929336504802264,
      "reward": null,
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      "pred_coeffs": {
        "x": -3.980370371058639
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.206184364999899,
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      "wall_raw_s": 7.206184364999899,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.980370371058639
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.008588241968547194 cons=0.0001557975442701643 wall_s=15.786 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008588241968547194,
  "conservation_residual": 0.0001557975442701643,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.786097936999795,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9941500434963256,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.575256486999933,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.575256486999933,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9951156329608756,
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      "pred_coeffs": {
        "x": -3.9522117297359185
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      "structure_ok": true,
      "wall_s": 8.210841449999862,
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      "wall_raw_s": 8.210841449999862,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.9522117297359185
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.006268702903195995 cons=1.722503562205926e-05 wall_s=16.527 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006268702903195995,
  "conservation_residual": 1.722503562205926e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 16.52724990300021,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.278718217999995,
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      "wall_raw_s": 8.278718217999995,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9949667499473871,
      "reward": null,
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      "pred_coeffs": {
        "x": -4.01656331623099
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 8.248531685000216,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.248531685000216,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.01656331623099
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.004145653610700022 cons=0.0003133738205684463 wall_s=15.746 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004145653610700022,
  "conservation_residual": 0.0003133738205684463,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 15.745878021999488,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "reward": null,
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.96246631799977,
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      "wall_raw_s": 7.96246631799977,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9970911639401545,
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        "x": -3.930427900507346
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      "structure_ok": true,
      "wall_s": 7.783411703999718,
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      "wall_raw_s": 7.783411703999718,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.965213950253673
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004558752084969742 cons=8.054817873579757e-05 wall_s=15.830 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004558752084969742,
  "conservation_residual": 8.054817873579757e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 15.83000124399996,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.629352878000191,
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      "wall_raw_s": 7.629352878000191,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9947130771543385,
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        "x": -3.969406299136126
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 8.200648365999768,
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      "wall_raw_s": 8.200648365999768,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -3.969406299136126
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.007314577851631671 cons=3.368614847076791e-05 wall_s=15.753 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007314577851631671,
  "conservation_residual": 3.368614847076791e-05,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.752668793999874,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v",
      "r2_train": 0.9943772446583156,
      "reward": null,
      "residual_heldout": 0.00661608411579006,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.529911224999978,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.529911224999978,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9934696641097555,
      "reward": null,
      "residual_heldout": 0.00801307158747328,
      "pred_coeffs": {
        "x": -3.977504535278557
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.222757568999896,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.222757568999896,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.977504535278557
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.005792245879100193 cons=0.0007409906757930521 wall_s=15.622 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005792245879100193,
  "conservation_residual": 0.0007409906757930521,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.622210406999784,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9919650166145774,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.854982393999762,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.854982393999762,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9953492554811568,
      "reward": null,
      "residual_heldout": 0.005924183078368949,
      "pred_coeffs": {
        "x": -3.895899512818409
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.767228013000022,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.767228013000022,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.895899512818409
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.005624472113998786 cons=1.7378383013174757e-05 wall_s=14.845 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005624472113998786,
  "conservation_residual": 1.7378383013174757e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 14.844942846999857,
  "wall_s_per_eq": [
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    6.93117868399986
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9951513654004391,
      "reward": null,
      "residual_heldout": 0.0064928313301116,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.913764162999996,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.913764162999996,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9965360745953843,
      "reward": null,
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      "pred_coeffs": {
        "x": -3.98368289747256
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 6.93117868399986,
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      "wall_raw_s": 6.93117868399986,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.98368289747256
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.006796719072105536 cons=1.0832119791020892e-05 wall_s=16.190 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006796719072105536,
  "conservation_residual": 1.0832119791020892e-05,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 16.19048462100045,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9965111014755108,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.149584529000094,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.149584529000094,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9946163261320096,
      "reward": null,
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        "x": -4.013055013086283
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 8.040900092000356,
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      "wall_raw_s": 8.040900092000356,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0065275065431414
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.004946238363726627 cons=0.00015581869881607866 wall_s=14.965 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004946238363726627,
  "conservation_residual": 0.00015581869881607866,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 14.965300163999927,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.8857704649999505,
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      "wall_raw_s": 6.8857704649999505,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9953611327360145,
      "reward": null,
      "residual_heldout": 0.0029823328998520348,
      "pred_coeffs": {
        "x": -3.954280578058775
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 8.079529698999977,
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      "wall_raw_s": 8.079529698999977,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.954280578058775
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.006057570282207165 cons=0.00010096402315333188 wall_s=15.343 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006057570282207165,
  "conservation_residual": 0.00010096402315333188,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.34291195500009,
  "wall_s_per_eq": [
    8.292147949000082,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.292147949000082,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.292147949000082,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.992783028494134,
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        "x": -3.9625052580544633
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.0507640060000085,
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      "wall_raw_s": 7.0507640060000085,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.9625052580544633
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.006459370754617016 cons=2.1268439459971998e-06 wall_s=15.617 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006459370754617016,
  "conservation_residual": 2.1268439459971998e-06,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.617221540000173,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9937017439191415,
      "reward": null,
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.537853937999898,
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      "wall_raw_s": 8.537853937999898,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.996057337835036,
      "reward": null,
      "residual_heldout": 0.005460371030894638,
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        "x": -3.9947132067795685
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.079367602000275,
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      "wall_raw_s": 7.079367602000275,
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      "timed_out": false,
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      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.9947132067795685
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.006195730528800912 cons=0.0010587217800206257 wall_s=15.048 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006195730528800912,
  "conservation_residual": 0.0010587217800206257,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.047952298999917,
  "wall_s_per_eq": [
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    6.781621084000108
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9939869908675181,
      "reward": null,
      "residual_heldout": 0.004138694658855828,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.26633121499981,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.26633121499981,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9969976752340782,
      "reward": null,
      "residual_heldout": 0.008252766398745996,
      "pred_coeffs": {
        "x": -3.8866062211257093
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.781621084000108,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.781621084000108,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.8866062211257093
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.004251569283608388 cons=5.298990169650523e-05 wall_s=14.732 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004251569283608388,
  "conservation_residual": 5.298990169650523e-05,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 14.731868353000209,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9948538158219037,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.070119901999988,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.070119901999988,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9932760048487879,
      "reward": null,
      "residual_heldout": 0.005402474183822201,
      "pred_coeffs": {
        "x": -3.972018474910306
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.661748451000221,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.661748451000221,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.972018474910306
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=50 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0076139004298193 cons=1.3712642769871043e-07 wall_s=16.391 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0076139004298193,
  "conservation_residual": 1.3712642769871043e-07,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 16.390745670000342,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "reward": null,
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.70076136500029,
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      "wall_raw_s": 8.70076136500029,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9952261038352387,
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        "x": -3.9985193268328505
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.689984305000053,
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      "wall_raw_s": 7.689984305000053,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.9985193268328505
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.005514736243824271 cons=0.00038758223526400205 wall_s=39.202 ok=True

```json
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005514736243824271,
  "conservation_residual": 0.00038758223526400205,
  "equations": [
    "v*v*(0.037362587 - 0.010637863*v*(v + x))*(v + x + x) + v",
    "x*(-4.0801587)"
  ],
  "wall_s_total": 39.20179197300013,
  "wall_s_per_eq": [
    31.284860277000007,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*v*(0.037362587 - 0.010637863*v*(v + x))*(v + x + x) + v",
      "r2_train": 0.9942028612051477,
      "reward": null,
      "residual_heldout": 0.005503520097623286,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 31.284860277000007,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0801587)",
      "r2_train": 0.9958966919035137,
      "reward": null,
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.91693169600012,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0062203105693084985 cons=0.0007494627225705175 wall_s=15.256 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0062203105693084985,
  "conservation_residual": 0.0007494627225705175,
  "equations": [
    "x*(-0.04486276)*v*x*(v + 1.1720046) + v",
    "x*(-3.9357967)"
  ],
  "wall_s_total": 15.256145927000034,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-0.04486276)*v*x*(v + 1.1720046) + v",
      "r2_train": 0.9955226742999951,
      "reward": null,
      "residual_heldout": 0.0033494643360293757,
      "pred_coeffs": {
        "1": 0.027403326647303383,
        "v": 1.0120921950670663,
        "x": 0.025031267807700236,
        "v^2": -0.01074162966820225,
        "x*v": 0.009251029547492406,
        "x^2": -0.050765180525490936,
        "v^3": -0.00345381669964844,
        "x*v^2": -0.0020905284457720568,
        "x^2*v": -0.052698310261457285,
        "x^3": -0.024188326557295643
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.441206548000082,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9357967)",
      "r2_train": 0.9954537489328418,
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        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.814939378999952,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.004141977694566184 cons=0.000317697329556622 wall_s=15.845 ok=True

```json
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
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  "residual": 0.004141977694566184,
  "conservation_residual": 0.000317697329556622,
  "equations": [
    "v*(v*v*(-0.011172093) + 1.0222552)",
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  ],
  "wall_s_total": 15.844767188999867,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(v*v*(-0.011172093) + 1.0222552)",
      "r2_train": 0.9956177383824046,
      "reward": null,
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        "v": 1.0222552
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      "structure_ok": true,
      "wall_s": 7.787566782999875,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.017537)",
      "r2_train": 0.993782772024651,
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      "structure_ok": true,
      "wall_s": 8.057200405999993,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.003677609435363791 cons=0.0005286826737389242 wall_s=16.701 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
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  "residual": 0.003677609435363791,
  "conservation_residual": 0.0005286826737389242,
  "equations": [
    "v + x*x*0.07458601 - 0.03620106",
    "x*(-3.944694)"
  ],
  "wall_s_total": 16.70102324299978,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v + x*x*0.07458601 - 0.03620106",
      "r2_train": 0.9958010928837899,
      "reward": null,
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        "x^2": 0.07458601,
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      "structure_ok": true,
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
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      "equation": "x*(-3.944694)",
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      "structure_ok": true,
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        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.004630546335701861 cons=1.0139381880763267 wall_s=16.313 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004630546335701861,
  "conservation_residual": 1.0139381880763267,
  "equations": [
    "v - (-0.19642085*v*x*(-1.4003094*x*x*x + x) - 0.0105708605)",
    "x*(-4.0243855)"
  ],
  "wall_s_total": 16.313162203000047,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - (-0.19642085*v*x*(-1.4003094*x*x*x + x) - 0.0105708605)",
      "r2_train": 0.9953347304509812,
      "reward": null,
      "residual_heldout": 0.004491250283680725,
      "pred_coeffs": {
        "1": 0.0105708605
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.158473978000075,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0243855)",
      "r2_train": 0.9948502415213051,
      "reward": null,
      "residual_heldout": 0.004769842387722997,
      "pred_coeffs": {
        "x": -4.0243855
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 8.154688224999973,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.004647949904257786 cons=0.0006177862633278136 wall_s=15.656 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004647949904257786,
  "conservation_residual": 0.0006177862633278136,
  "equations": [
    "v - 1*0.022903316",
    "x*(-3.9591727)"
  ],
  "wall_s_total": 15.656363643999612,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 1*0.022903316",
      "r2_train": 0.995727061837676,
      "reward": null,
      "residual_heldout": 0.0033269633793366828,
      "pred_coeffs": {
        "1": -0.022903316,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.6774930329997915,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9591727)",
      "r2_train": 0.9964223772201469,
      "reward": null,
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      "pred_coeffs": {
        "x": -3.9591727
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.97887061099982,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.006198586528033153 cons=4.8460537174176865e-05 wall_s=15.540 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006198586528033153,
  "conservation_residual": 4.8460537174176865e-05,
  "equations": [
    "v*(x*v*(-0.032268953) + 0.9928608)",
    "x*(-3.9984412)"
  ],
  "wall_s_total": 15.540144333000171,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(x*v*(-0.032268953) + 0.9928608)",
      "r2_train": 0.9953077684772431,
      "reward": null,
      "residual_heldout": 0.00575167988362878,
      "pred_coeffs": {
        "v": 0.9928608
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.663102883000192,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9984412)",
      "r2_train": 0.9935651491346852,
      "reward": null,
      "residual_heldout": 0.006645493172437525,
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      },
      "structure_ok": true,
      "wall_s": 7.877041449999979,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.006412123716569086 cons=0.0008324616380397607 wall_s=15.998 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006412123716569086,
  "conservation_residual": 0.0008324616380397607,
  "equations": [
    "v - (x*v*v*v*v*x*(-0.031918842) - 1*(-0.029356334))",
    "x*(-4.003933)"
  ],
  "wall_s_total": 15.998256873000173,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - (x*v*v*v*v*x*(-0.031918842) - 1*(-0.029356334))",
      "r2_train": 0.9952493784281409,
      "reward": null,
      "residual_heldout": 0.0039793269073952215,
      "pred_coeffs": {
        "1": -0.029356334,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.394590669000081,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.003933)",
      "r2_train": 0.9969174032305966,
      "reward": null,
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      "pred_coeffs": {
        "x": -4.003933
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.603666204000092,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.0037877801429091872 cons=0.0009343276798967566 wall_s=15.947 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0037877801429091872,
  "conservation_residual": 0.0009343276798967566,
  "equations": [
    "(v + x)*x*x*v*0.03366702 + v",
    "x*(-(-0.292621)*v*v + x*x - 5.0507183)"
  ],
  "wall_s_total": 15.947085585999957,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "(v + x)*x*x*v*0.03366702 + v",
      "r2_train": 0.9952523195523985,
      "reward": null,
      "residual_heldout": 0.004030105837011869,
      "pred_coeffs": {
        "1": -0.041695064541731525,
        "v": 1.0233225143309939,
        "x": 0.0887261144408323,
        "v^2": 0.014969628218580356,
        "x*v": 0.01220931137116014,
        "x^2": 0.05820886304802689,
        "v^3": -0.005525782004774772,
        "x*v^2": -0.021154467626964532,
        "x^2*v": -0.024502523232038713,
        "x^3": -0.0920260681291559
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.691464895000081,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-(-0.292621)*v*v + x*x - 5.0507183)",
      "r2_train": 0.9960822321998266,
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        "x": -5.050718299999998,
        "x*v^2": 0.29262100000000024,
        "x^3": 0.9999999999999989
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        "x": -4.0
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      "structure_ok": false,
      "wall_s": 8.255620690999876,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004129854719113956 cons=0.0036176451751347774 wall_s=16.035 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004129854719113956,
  "conservation_residual": 0.0036176451751347774,
  "equations": [
    "v*(v*(v*(-0.016549194) - 0.009385335) - 1*(-1.053))",
    "x*(-3.99903)"
  ],
  "wall_s_total": 16.034747050000078,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "v*(v*(v*(-0.016549194) - 0.009385335) - 1*(-1.053))",
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      "structure_ok": true,
      "wall_s": 8.154304094000054,
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.99903)",
      "r2_train": 0.9942677880528656,
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      "wall_s": 7.880442956000024,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0056760951495226355 cons=0.0004632906618378617 wall_s=15.286 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0056760951495226355,
  "conservation_residual": 0.0004632906618378617,
  "equations": [
    "v*1.0223786",
    "x*(-4.0042834)"
  ],
  "wall_s_total": 15.286355126000217,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v*1.0223786",
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        "v": 1.0223786
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 7.513478132999808,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0042834)",
      "r2_train": 0.9948371024432215,
      "reward": null,
      "residual_heldout": 0.003242477214704238,
      "pred_coeffs": {
        "x": -4.0042834
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.772876993000409,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.00594422837731054 cons=0.961878889743284 wall_s=16.110 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00594422837731054,
  "conservation_residual": 0.961878889743284,
  "equations": [
    "v*x*(v*v*(-0.047367677) + 0.09959365) + v",
    "x*(-3.9926221)"
  ],
  "wall_s_total": 16.110212389000026,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*x*(v*v*(-0.047367677) + 0.09959365) + v",
      "r2_train": 0.9944860738022332,
      "reward": null,
      "residual_heldout": 0.005783932493168455,
      "pred_coeffs": {
        "x*v": 0.09959365
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.351286078000157,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9926221)",
      "r2_train": 0.995264989600072,
      "reward": null,
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      "structure_ok": true,
      "wall_s": 7.758926310999868,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.006542909882042699 cons=0.0002320471982955004 wall_s=16.054 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006542909882042699,
  "conservation_residual": 0.0002320471982955004,
  "equations": [
    "v - x*(v*0.030310437*v - 1*0.046111774)",
    "x*(-4.0611796)"
  ],
  "wall_s_total": 16.053589919000387,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - x*(v*0.030310437*v - 1*0.046111774)",
      "r2_train": 0.9961491032844996,
      "reward": null,
      "residual_heldout": 0.004913945676063478,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.759730294000292,
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      "wall_raw_s": null,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0611796)",
      "r2_train": 0.9965969339364592,
      "reward": null,
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        "x": -4.0611796
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 8.293859625000096,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.005015321088281968 cons=0.0005958651749841549 wall_s=16.356 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005015321088281968,
  "conservation_residual": 0.0005958651749841549,
  "equations": [
    "v*(-v*v*(v*v*0.0143031515 - 0.058055498) + 0.9663122)",
    "x*(-3.9616144)"
  ],
  "wall_s_total": 16.355812070999946,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(-v*v*(v*v*0.0143031515 - 0.058055498) + 0.9663122)",
      "r2_train": 0.996941523906837,
      "reward": null,
      "residual_heldout": 0.004992086026371417,
      "pred_coeffs": {
        "v": 0.9663122
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.063668237999991,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9616144)",
      "r2_train": 0.9958968070134843,
      "reward": null,
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      "structure_ok": true,
      "wall_s": 8.292143832999955,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.004678542300354271 cons=0.0004856049951151656 wall_s=16.592 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004678542300354271,
  "conservation_residual": 0.0004856049951151656,
  "equations": [
    "v*((-(-v)*v + x)*x*x*v*v*(-0.022248384) + 1.0165175)",
    "x*(-3.9854884)"
  ],
  "wall_s_total": 16.591618580999693,
  "wall_s_per_eq": [
    7.6605451469999934,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*((-(-v)*v + x)*x*x*v*v*(-0.022248384) + 1.0165175)",
      "r2_train": 0.9954354191529892,
      "reward": null,
      "residual_heldout": 0.0047949494408251565,
      "pred_coeffs": {
        "v": 1.0165175
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.6605451469999934,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9854884)",
      "r2_train": 0.9963573416815034,
      "reward": null,
      "residual_heldout": 0.004562135159883385,
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        "x": -3.9854884
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 8.9310734339997,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.004353960202848919 cons=0.0016204253385362008 wall_s=17.864 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004353960202848919,
  "conservation_residual": 0.0016204253385362008,
  "equations": [
    "v*(-1*(0.28823858 - v*x)*v*(0.07972526 - x)*0.04434694 + 1.0166142)",
    "x*(v*0.5536773*v + x*2.3581138*x - 6.3450603)"
  ],
  "wall_s_total": 17.864143586999944,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(-1*(0.28823858 - v*x)*v*(0.07972526 - x)*0.04434694 + 1.0166142)",
      "r2_train": 0.9946132513251834,
      "reward": null,
      "residual_heldout": 0.005355189735723635,
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        "v": 1.0166142
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 9.478314342999965,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(v*0.5536773*v + x*2.3581138*x - 6.3450603)",
      "r2_train": 0.996688233886136,
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        "x": -6.3450602999999965,
        "x*v^2": 0.5536773000000008,
        "x^3": 2.3581138000000004
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": false,
      "wall_s": 8.385829243999979,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.004535663360398657 cons=0.001198679319594885 wall_s=16.231 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004535663360398657,
  "conservation_residual": 0.001198679319594885,
  "equations": [
    "v - 0.02187246",
    "x*(-3.911712)"
  ],
  "wall_s_total": 16.23086028700027,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v - 0.02187246",
      "r2_train": 0.9955283763201778,
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        "1": -0.02187246,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.222627104999901,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
      "zero_eq": false,
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    {
      "eq_i": 1,
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      "equation": "x*(-3.911712)",
      "r2_train": 0.9953033853956033,
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      "structure_ok": true,
      "wall_s": 8.008233182000367,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.005905549793257602 cons=0.00028532216066291425 wall_s=15.774 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005905549793257602,
  "conservation_residual": 0.00028532216066291425,
  "equations": [
    "v*v*(v*x*x*(-0.032161027) - 1*(-0.011409431)) + v",
    "x*(-3.9760036)"
  ],
  "wall_s_total": 15.773702211999534,
  "wall_s_per_eq": [
    7.434787870999571,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*v*(v*x*x*(-0.032161027) - 1*(-0.011409431)) + v",
      "r2_train": 0.9942810727086475,
      "reward": null,
      "residual_heldout": 0.0046054363983599415,
      "pred_coeffs": {
        "v^2": 0.011409431,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.434787870999571,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9760036)",
      "r2_train": 0.9956180869443244,
      "reward": null,
      "residual_heldout": 0.007205663188155263,
      "pred_coeffs": {
        "x": -3.9760036
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.338914340999963,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.007539449528735627 cons=1.0301594520644597 wall_s=15.709 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007539449528735627,
  "conservation_residual": 1.0301594520644597,
  "equations": [
    "v + (v*x - 0.68081105)*x*(v*v*x + v)*0.108705 - 0.04019582",
    "x*(-4.0424614)"
  ],
  "wall_s_total": 15.708620248999978,
  "wall_s_per_eq": [
    7.596074889999727,
    8.11254535900025
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + (v*x - 0.68081105)*x*(v*v*x + v)*0.108705 - 0.04019582",
      "r2_train": 0.9957030726655841,
      "reward": null,
      "residual_heldout": 0.009832299427714191,
      "pred_coeffs": {
        "x*v": -0.07400756519025,
        "1": -0.04019582
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 7.596074889999727,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0424614)",
      "r2_train": 0.9943829362226112,
      "reward": null,
      "residual_heldout": 0.005246599629757061,
      "pred_coeffs": {
        "x": -4.0424614
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.11254535900025,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.005903572476073255 cons=0.021736056495864933 wall_s=15.721 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005903572476073255,
  "conservation_residual": 0.021736056495864933,
  "equations": [
    "(0.09828462*v*v*v*(-x*x - 0.24092785) + v)*1.1422272",
    "x*(-3.9947195)"
  ],
  "wall_s_total": 15.720874935999746,
  "wall_s_per_eq": [
    7.466324658999838,
    8.254550276999908
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(0.09828462*v*v*v*(-x*x - 0.24092785) + v)*1.1422272",
      "r2_train": 0.9965924793024707,
      "reward": null,
      "residual_heldout": 0.005900044605049034,
      "pred_coeffs": {
        "v": 1.1422272
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.466324658999838,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9947195)",
      "r2_train": 0.9953642660574513,
      "reward": null,
      "residual_heldout": 0.005907100347097475,
      "pred_coeffs": {
        "x": -3.9947195
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.254550276999908,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.004984165599594762 cons=0.00038810186520647603 wall_s=15.775 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004984165599594762,
  "conservation_residual": 0.00038810186520647603,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.775463606999892,
  "wall_s_per_eq": [
    8.901607658000103,
    6.87385594899979
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9934128472276975,
      "reward": null,
      "residual_heldout": 0.004441768406928337,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.901607658000103,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.901607658000103,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9958966923588957,
      "reward": null,
      "residual_heldout": 0.005526562792261188,
      "pred_coeffs": {
        "x": -4.080213493416453
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.87385594899979,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.87385594899979,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.080213493416453
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.006032119251216731 cons=0.0002792683254935353 wall_s=15.425 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006032119251216731,
  "conservation_residual": 0.0002792683254935353,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 15.424931648999518,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9948305410023698,
      "reward": null,
      "residual_heldout": 0.0029723240275178428,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.558760515999893,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.558760515999893,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9954537484780895,
      "reward": null,
      "residual_heldout": 0.00909191447491562,
      "pred_coeffs": {
        "x": -3.935760789377079
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.866171132999625,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.866171132999625,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.935760789377079
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.004100261042970392 cons=1.911278904976277e-05 wall_s=16.373 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004100261042970392,
  "conservation_residual": 1.911278904976277e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 16.37329424599966,
  "wall_s_per_eq": [
    8.915165746999719,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9952933116160573,
      "reward": null,
      "residual_heldout": 0.005352564170966352,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.915165746999719,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.915165746999719,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9937827728929051,
      "reward": null,
      "residual_heldout": 0.002847957914974433,
      "pred_coeffs": {
        "x": -4.017533252086895
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.45812849899994,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.45812849899994,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.017533252086895
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5341044257380678 cons=1.0975330736375815 wall_s=15.629 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5341044257380678,
  "conservation_residual": 1.0975330736375815,
  "equations": [
    "2*v",
    "-w2*x"
  ],
  "wall_s_total": 15.628778241999953,
  "wall_s_per_eq": [
    8.696871783999995,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": 0.017181246807622452,
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      "residual_heldout": 1.064329085792015,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.696871783999995,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.696871783999995,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.996251731175021,
      "reward": null,
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      "pred_coeffs": {
        "x": -3.944660700249682
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.931906457999958,
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      "wall_raw_s": 6.931906457999958,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.944660700249682
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.003998893191387618 cons=3.7410814040909214e-05 wall_s=16.820 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003998893191387618,
  "conservation_residual": 3.7410814040909214e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 16.8202354619998,
  "wall_s_per_eq": [
    8.001676160999978,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9947048094270013,
      "reward": null,
      "residual_heldout": 0.0032279428359372375,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.001676160999978,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.001676160999978,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9948502413418346,
      "reward": null,
      "residual_heldout": 0.0047698435468379995,
      "pred_coeffs": {
        "x": -4.02438544948621
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.818559300999823,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.818559300999823,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.02438544948621
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.004269357452108571 cons=0.00010669885120564201 wall_s=15.736 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004269357452108571,
  "conservation_residual": 0.00010669885120564201,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 15.736313922000136,
  "wall_s_per_eq": [
    7.108855624000171,
    8.627458297999965
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9954549810294742,
      "reward": null,
      "residual_heldout": 0.0025698399963719858,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.108855624000171,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.108855624000171,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9964223775455668,
      "reward": null,
      "residual_heldout": 0.005968874907845157,
      "pred_coeffs": {
        "x": -3.959186631552351
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.627458297999965,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.627458297999965,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.959186631552351
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.006002670407054662 cons=1.5728798576020857e-07 wall_s=13.970 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006002670407054662,
  "conservation_residual": 1.5728798576020857e-07,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 13.96965760699959,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.99473234977255,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.172896412999762,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.172896412999762,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9935651490458567,
      "reward": null,
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      "pred_coeffs": {
        "x": -3.998461889617558
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 6.796761193999828,
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      "wall_raw_s": 6.796761193999828,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.998461889617558
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.006613646463587797 cons=9.858533599262065e-07 wall_s=15.919 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006613646463587797,
  "conservation_residual": 9.858533599262065e-07,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 15.919482045000223,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.965474117000213,
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      "wall_raw_s": 8.965474117000213,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9969174034257599,
      "reward": null,
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        "x": -4.003974540731143
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 6.95400792800001,
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      "wall_raw_s": 6.95400792800001,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.003974540731143
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.00411954868549933 cons=8.484759030456344e-06 wall_s=16.140 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00411954868549933,
  "conservation_residual": 8.484759030456344e-06,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 16.139870983000492,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.913446790000307,
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      "wall_raw_s": 6.913446790000307,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9948596419151604,
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        "x": -3.9883838694210683
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        "x": -4.0
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      "structure_ok": true,
      "wall_s": 9.226424193000184,
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      "wall_raw_s": 9.226424193000184,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.9941919347105341
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004309560782128152 cons=6.085419636950712e-08 wall_s=16.342 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004309560782128152,
  "conservation_residual": 6.085419636950712e-08,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 16.342319238000073,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.040447626000059,
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      "wall_raw_s": 7.040447626000059,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
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    {
      "eq_i": 1,
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      "equation": "w2*x",
      "r2_train": 0.9942677887199027,
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        "x": -3.9990369387529783
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      "structure_ok": true,
      "wall_s": 9.301871612000014,
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      "wall_raw_s": 9.301871612000014,
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      "timed_out": false,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.9990369387529783
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.005203934313179061 cons=1.1658453635197075e-06 wall_s=16.204 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005203934313179061,
  "conservation_residual": 1.1658453635197075e-06,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 16.2040520810001,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 6.942296567000085,
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      "wall_raw_s": 6.942296567000085,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      "free_const_values": [],
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    {
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      "structure_ok": true,
      "wall_s": 9.261755514000015,
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      "budget": {
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        "max_n_evaluations": 2500,
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      },
      "free_const_values": [
        4.004275534671217
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.004971396420178327 cons=3.4125715221411055e-06 wall_s=16.315 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004971396420178327,
  "conservation_residual": 3.4125715221411055e-06,
  "equations": [
    "v",
    "5*w2*x"
  ],
  "wall_s_total": 16.314977396999893,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9939206304467506,
      "reward": null,
      "residual_heldout": 0.0038382653272351335,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.529964176000249,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.529964176000249,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "5*w2*x",
      "r2_train": 0.9952649893187832,
      "reward": null,
      "residual_heldout": 0.00610452751312152,
      "pred_coeffs": {
        "x": -3.992624932813928
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.7850132209996445,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.7850132209996445,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7985249865627856
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.006570337493928612 cons=0.0002320479456754195 wall_s=17.052 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006570337493928612,
  "conservation_residual": 0.0002320479456754195,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 17.052283604000422,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v",
      "r2_train": 0.9958942141220611,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.967046235999987,
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      "wall_raw_s": 6.967046235999987,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9965969338008865,
      "reward": null,
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      "pred_coeffs": {
        "x": -4.061179700030767
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 10.085237368000435,
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      "wall_raw_s": 10.085237368000435,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.061179700030767
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.004661944254078161 cons=9.450961904234691e-05 wall_s=14.090 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004661944254078161,
  "conservation_residual": 9.450961904234691e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 14.090472415000022,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9962967121177295,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.181423564999932,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.181423564999932,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9958968069341473,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 6.90904885000009,
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      "wall_raw_s": 6.90904885000009,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.9616216036441156
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.004040499469041401 cons=1.5703593735949046e-05 wall_s=16.785 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004040499469041401,
  "conservation_residual": 1.5703593735949046e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 16.78471720699963,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 9.622729010999592,
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      "wall_raw_s": 9.622729010999592,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9963573410736586,
      "reward": null,
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      "pred_coeffs": {
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.161988196000038,
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      "wall_raw_s": 7.161988196000038,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.98550907554974
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0049763396761144385 cons=1.1186532269946394e-06 wall_s=13.574 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0049763396761144385,
  "conservation_residual": 1.1186532269946394e-06,
  "equations": [
    "v",
    "-w2*x"
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  "wall_s_total": 13.57357358499985,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.860987081000076,
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      "wall_raw_s": 6.860987081000076,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9947203355612312,
      "reward": null,
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        "x": -4.004191650848086
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 6.712586503999773,
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      "wall_raw_s": 6.712586503999773,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.004191650848086
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.004347574276258166 cons=0.0005352522408887128 wall_s=17.422 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004347574276258166,
  "conservation_residual": 0.0005352522408887128,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 17.421842108999954,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 9.675388870000006,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
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    {
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      "target": "dv/dt",
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      "r2_train": 0.9953033857003543,
      "reward": null,
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      "structure_ok": true,
      "wall_s": 7.746453238999948,
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      "wall_raw_s": 7.746453238999948,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.911711845784994
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.005449259224056752 cons=3.657920560556642e-05 wall_s=18.057 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005449259224056752,
  "conservation_residual": 3.657920560556642e-05,
  "equations": [
    "v",
    "3*w2*x"
  ],
  "wall_s_total": 18.057491508999647,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 6.971141761999661,
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      "wall_raw_s": 6.971141761999661,
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        "max_n_evaluations": 2500,
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    {
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      "r2_train": 0.9956180869963975,
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      "structure_ok": true,
      "wall_s": 11.086349746999986,
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      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.3253306367132727
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.006558995398367747 cons=0.00011880792760986642 wall_s=14.879 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006558995398367747,
  "conservation_residual": 0.00011880792760986642,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 14.879210068999782,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9950677643031014,
      "reward": null,
      "residual_heldout": 0.007872018700910173,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.459267762999843,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.459267762999843,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9943829359292549,
      "reward": null,
      "residual_heldout": 0.005245972095825321,
      "pred_coeffs": {
        "x": -4.042426335425448
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.419942305999939,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.419942305999939,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.042426335425448
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=100 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.005409875422283489 cons=1.82366907893582e-06 wall_s=17.114 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005409875422283489,
  "conservation_residual": 1.82366907893582e-06,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 17.113930267999876,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
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      "reward": null,
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 10.20242407700016,
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      "wall_raw_s": 10.20242407700016,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9953642672461924,
      "reward": null,
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        "x": -3.9947405537123295
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.911506190999717,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.911506190999717,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.9947405537123295
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.004597973102219988 cons=0.00023466558363541176 wall_s=18.871 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004597973102219988,
  "conservation_residual": 0.00023466558363541176,
  "equations": [
    "v*(1.0159632 - 0.03133729*v*x*x*(v - 0.52287257))",
    "x*(-4.002539)"
  ],
  "wall_s_total": 18.87117963799983,
  "wall_s_per_eq": [
    9.31727123599967,
    9.553908402000161
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(1.0159632 - 0.03133729*v*x*x*(v - 0.52287257))",
      "r2_train": 0.9956241385708492,
      "reward": null,
      "residual_heldout": 0.005143468893515007,
      "pred_coeffs": {
        "v": 1.0159632
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 9.31727123599967,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.002539)",
      "r2_train": 0.9946417296878687,
      "reward": null,
      "residual_heldout": 0.0040524773109249694,
      "pred_coeffs": {
        "x": -4.002539
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.553908402000161,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0047292235886556115 cons=9.002150100188052e-05 wall_s=18.256 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0047292235886556115,
  "conservation_residual": 9.002150100188052e-05,
  "equations": [
    "-0.18970573*v*x*x*(v*v*x*x - 0.7215203) + v",
    "x*(-3.96735)"
  ],
  "wall_s_total": 18.256218596000053,
  "wall_s_per_eq": [
    8.845605219999925,
    9.410613376000128
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-0.18970573*v*x*x*(v*v*x*x - 0.7215203) + v",
      "r2_train": 0.9953484074954747,
      "reward": null,
      "residual_heldout": 0.004874239307962723,
      "pred_coeffs": {
        "1": -0.0007641544444784793,
        "v": 1.0762041010895949,
        "x": -0.07051193722430446,
        "v^2": 2.8724044338928516e-05,
        "x*v": -0.004105823367491004,
        "x^2": -0.0026930739360943893,
        "v^3": -0.018384376886954386,
        "x*v^2": 0.020443428618159017,
        "x^2*v": -0.09639234409454396,
        "x^3": 0.06192402567125233
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.845605219999925,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
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      "r2_train": 0.9947050029137937,
      "reward": null,
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        "x": -3.96735
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 9.410613376000128,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.003600986972877156 cons=0.0012928819229971209 wall_s=16.782 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003600986972877156,
  "conservation_residual": 0.0012928819229971209,
  "equations": [
    "v*(1.5180637 - (v*v*0.1309565 - (-0.51049674)*x*x))",
    "x*(-4.0077257)"
  ],
  "wall_s_total": 16.781807818999823,
  "wall_s_per_eq": [
    8.249090980999881,
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(1.5180637 - (v*v*0.1309565 - (-0.51049674)*x*x))",
      "r2_train": 0.9960368933269583,
      "reward": null,
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        "v": 1.5180636999999986,
        "v^3": -0.13095650000000011,
        "x^2*v": -0.5104967399999989
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.249090980999881,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0077257)",
      "r2_train": 0.9944972942864762,
      "reward": null,
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.532716837999942,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.005207709730083946 cons=1.0741678498068852 wall_s=17.008 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005207709730083946,
  "conservation_residual": 1.0741678498068852,
  "equations": [
    "(v - 1*(-0.030751048))*(x*x*(-0.04831483)*v + 1.0036049)",
    "x*(-3.9890215)"
  ],
  "wall_s_total": 17.008139092999954,
  "wall_s_per_eq": [
    8.508744240999931,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "(v - 1*(-0.030751048))*(x*x*(-0.04831483)*v + 1.0036049)",
      "r2_train": 0.9953063298194518,
      "reward": null,
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        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.508744240999931,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9890215)",
      "r2_train": 0.9949734721371646,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.499394852000023,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "populations": 15,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.005454164192284409 cons=0.007995577055081684 wall_s=17.469 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005454164192284409,
  "conservation_residual": 0.007995577055081684,
  "equations": [
    "v*(v*(-v - x*x*(v + v))*0.023465889 - 1*(-1.0891529))",
    "x*(-4.000984)"
  ],
  "wall_s_total": 17.469338557000356,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(v*(-v - x*x*(v + v))*0.023465889 - 1*(-1.0891529))",
      "r2_train": 0.9960480224819593,
      "reward": null,
      "residual_heldout": 0.0052014681657294535,
      "pred_coeffs": {
        "v": 1.0891529
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.181244597000386,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.000984)",
      "r2_train": 0.995485795456142,
      "reward": null,
      "residual_heldout": 0.005706860218839364,
      "pred_coeffs": {
        "x": -4.000984
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.28809395999997,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0046783825143739835 cons=0.00017403735165908503 wall_s=17.093 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0046783825143739835,
  "conservation_residual": 0.00017403735165908503,
  "equations": [
    "v - 0.009445136",
    "x*(-3.9622555)"
  ],
  "wall_s_total": 17.093178986999646,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "v - 0.009445136",
      "r2_train": 0.9955571158841382,
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        "1": -0.009445136,
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.56823855499988,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
      "zero_eq": false,
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    {
      "eq_i": 1,
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      "equation": "x*(-3.9622555)",
      "r2_train": 0.9950418145131319,
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      "structure_ok": true,
      "wall_s": 8.524940431999767,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005273884646629789 cons=1.891009820353924e-05 wall_s=16.810 ok=True

```json
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  "n_samples": 400,
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  "recovered": true,
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  "accepted": true,
  "residual": 0.005273884646629789,
  "conservation_residual": 1.891009820353924e-05,
  "equations": [
    "v*v*v*(v*v*v*v*(-0.00096931023) + 0.01351975) + v",
    "x*(-3.9827034)"
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  "wall_s_total": 16.810194354000032,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v*v*v*(v*v*v*v*(-0.00096931023) + 0.01351975) + v",
      "r2_train": 0.9955070878496811,
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      "free_const_values": null,
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    {
      "eq_i": 1,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.004581141455970633 cons=9.437000246548564e-05 wall_s=16.746 ok=True

```json
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  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004581141455970633,
  "conservation_residual": 9.437000246548564e-05,
  "equations": [
    "v - 0.009630132",
    "x*(-3.9950929)"
  ],
  "wall_s_total": 16.74608607500022,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": true,
      "wall_s": 8.087860548000208,
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      "wall_raw_s": null,
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      "free_const_values": null,
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    {
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      "wall_s": 8.658225527000013,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.005656758193501529 cons=0.00016661192063669648 wall_s=17.275 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005656758193501529,
  "conservation_residual": 0.00016661192063669648,
  "equations": [
    "v + x*x*(v - 0.7437285)*(v*v*(-0.03431831) + 0.041661207)",
    "x*(-3.986487)"
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  "wall_s_total": 17.27490708300047,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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        "x^2*v": -0.037070200586956946,
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      "structure_ok": true,
      "wall_s": 8.36662931400042,
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      "wall_raw_s": null,
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      "free_const_values": null,
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    {
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      "wall_s": 8.908277769000051,
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      "budget": {
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004770003023350875 cons=7.653307238466137e-05 wall_s=17.035 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004770003023350875,
  "conservation_residual": 7.653307238466137e-05,
  "equations": [
    "(v*x - 1*(-0.78494006))*v*(x*(-v + x) - 1*(-0.4787019))*0.039212998 + v",
    "x*(-3.993591)"
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  "wall_s_total": 17.035048496999934,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "r2_train": 0.9952758001736665,
      "reward": null,
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      "structure_ok": true,
      "wall_s": 8.534439718000158,
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      "wall_raw_s": null,
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      "free_const_values": null,
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    {
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      "wall_s": 8.500608778999776,
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      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.00486526849155249 cons=0.0016581459007394238 wall_s=17.473 ok=True

```json
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  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00486526849155249,
  "conservation_residual": 0.0016581459007394238,
  "equations": [
    "v*v*(-0.13935915)*v + v + (v*x*x - v)*(-0.5725508)",
    "x*(-3.974026)"
  ],
  "wall_s_total": 17.472648087999914,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
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      "structure_ok": false,
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        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0051112097888475014 cons=0.0008742013716508525 wall_s=18.590 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0051112097888475014,
  "conservation_residual": 0.0008742013716508525,
  "equations": [
    "v - (-v + x*x*(v - 0.33970773))*(v*v*(-0.027373174) + 0.09094691)",
    "x*(-3.9779434)"
  ],
  "wall_s_total": 18.590187105999576,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - (-v + x*x*(v - 0.33970773))*(v*v*(-0.027373174) + 0.09094691)",
      "r2_train": 0.9950439794560203,
      "reward": null,
      "residual_heldout": 0.006172599959456287,
      "pred_coeffs": {
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        "v": 1.084018699913824,
        "x": -0.02003903833027745,
        "v^2": 0.0005750001187586554,
        "x*v": -0.00044317201556442044,
        "x^2": 0.03405548800537741,
        "v^3": -0.024115112541701286,
        "x*v^2": 0.004888527590574245,
        "x^2*v": -0.04610691150009905,
        "x^3": 0.021745497897590074
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.994377617999817,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9779434)",
      "r2_train": 0.9953471833208344,
      "reward": null,
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.595809487999759,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.004183294829886901 cons=0.0003733302700173548 wall_s=17.295 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004183294829886901,
  "conservation_residual": 0.0003733302700173548,
  "equations": [
    "-x + (v + x)*(v*0.019442337*(v*(-0.45295474) - x) - 1*(-1.0241799))",
    "x*(-3.9897697)"
  ],
  "wall_s_total": 17.29535449099967,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-x + (v + x)*(v*0.019442337*(v*(-0.45295474) - x) - 1*(-1.0241799))",
      "r2_train": 0.9950133328905821,
      "reward": null,
      "residual_heldout": 0.0035131618081512624,
      "pred_coeffs": {
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        "x*v^2": -0.028248835700827545,
        "x^2*v": -0.019442337000000205
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.657008347999636,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9897697)",
      "r2_train": 0.9956154863417531,
      "reward": null,
      "residual_heldout": 0.00485342785162254,
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.638346143000035,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.004994980373334556 cons=4.553728317494025e-05 wall_s=16.996 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004994980373334556,
  "conservation_residual": 4.553728317494025e-05,
  "equations": [
    "-(-0.0065481993)*v*v*v*((-v)*v + 3.4428537) + v",
    "x*(-3.9732864)"
  ],
  "wall_s_total": 16.99602157299978,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-(-0.0065481993)*v*v*v*((-v)*v + 3.4428537) + v",
      "r2_train": 0.995667149799292,
      "reward": null,
      "residual_heldout": 0.005249991683987784,
      "pred_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.390408789000048,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9732864)",
      "r2_train": 0.9950189991156072,
      "reward": null,
      "residual_heldout": 0.004739969062681329,
      "pred_coeffs": {
        "x": -3.9732864
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.605612783999732,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.004662924901068772 cons=0.0002470909497074052 wall_s=16.635 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004662924901068772,
  "conservation_residual": 0.0002470909497074052,
  "equations": [
    "v + x*(-0.019999042)",
    "x*(-4.0150623)"
  ],
  "wall_s_total": 16.63493031200005,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v + x*(-0.019999042)",
      "r2_train": 0.9957155648849987,
      "reward": null,
      "residual_heldout": 0.004362104040641298,
      "pred_coeffs": {
        "v": 1.0,
        "x": -0.019999042
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.986900289999994,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0150623)",
      "r2_train": 0.9952047494151102,
      "reward": null,
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 8.648030022000057,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.004152380839329294 cons=5.013105051740035e-06 wall_s=17.457 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004152380839329294,
  "conservation_residual": 5.013105051740035e-06,
  "equations": [
    "v*(x + 0.33372515)*v*(-0.017455034)*v*x + v",
    "x*(-3.9912426)"
  ],
  "wall_s_total": 17.457160382999973,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(x + 0.33372515)*v*(-0.017455034)*v*x + v",
      "r2_train": 0.9949344604240283,
      "reward": null,
      "residual_heldout": 0.0044524363473125135,
      "pred_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.210337288999654,
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      "wall_raw_s": null,
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      "free_const_values": null,
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    {
      "eq_i": 1,
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      "equation": "x*(-3.9912426)",
      "r2_train": 0.9952288500211167,
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      "structure_ok": true,
      "wall_s": 9.24682309400032,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.0038864629997500885 cons=0.0011971268302190345 wall_s=17.986 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0038864629997500885,
  "conservation_residual": 0.0011971268302190345,
  "equations": [
    "v*(-0.13111658*v*v - 0.51949173*x*x + 1.5252284)",
    "x*(-3.9799304)"
  ],
  "wall_s_total": 17.986004107999634,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "v*(-0.13111658*v*v - 0.51949173*x*x + 1.5252284)",
      "r2_train": 0.9965040072096714,
      "reward": null,
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      "pred_coeffs": {
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        "v^3": -0.13111657999999976,
        "x^2*v": -0.5194917299999996
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.917944176999754,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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    {
      "eq_i": 1,
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      "r2_train": 0.9949962760321082,
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      "structure_ok": true,
      "wall_s": 9.06805993099988,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.004917091772315143 cons=1.015993785922067 wall_s=17.969 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004917091772315143,
  "conservation_residual": 1.015993785922067,
  "equations": [
    "v + (-v - 0.6852397)*((v*v - x)*0.014631357 - 1*0.041293304)",
    "x*(-3.9967577)"
  ],
  "wall_s_total": 17.968915029000073,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
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  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v + (-v - 0.6852397)*((v*v - x)*0.014631357 - 1*0.041293304)",
      "r2_train": 0.9951890038052505,
      "reward": null,
      "residual_heldout": 0.004428705039415523,
      "pred_coeffs": {
        "v^2": -0.0100259866812729,
        "x*v": 0.014631357,
        "1": 0.028295811244968803
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.701744841999698,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9967577)",
      "r2_train": 0.9937626931023145,
      "reward": null,
      "residual_heldout": 0.005405478505214764,
      "pred_coeffs": {
        "x": -3.9967577
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.267170187000374,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.003962735819376737 cons=0.001994448465365273 wall_s=17.485 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003962735819376737,
  "conservation_residual": 0.001994448465365273,
  "equations": [
    "v*(v*v*(-0.14533928) + x*x*(-0.5768108) - 1*(-1.5827423))",
    "x*(-3.9640095)"
  ],
  "wall_s_total": 17.484893785000168,
  "wall_s_per_eq": [
    8.841900080999949,
    8.642993704000219
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(v*v*(-0.14533928) + x*x*(-0.5768108) - 1*(-1.5827423))",
      "r2_train": 0.9968692567385564,
      "reward": null,
      "residual_heldout": 0.003482019415493956,
      "pred_coeffs": {
        "v": 1.5827423000000012,
        "v^3": -0.14533928000000007,
        "x^2*v": -0.5768108000000018
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.841900080999949,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.9640095)",
      "r2_train": 0.9941114839826322,
      "reward": null,
      "residual_heldout": 0.004443452223259518,
      "pred_coeffs": {
        "x": -3.9640095
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.642993704000219,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.004455255663532274 cons=0.009412990136024897 wall_s=17.776 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004455255663532274,
  "conservation_residual": 0.009412990136024897,
  "equations": [
    "v*(1.0907819 - v*v*(x*x*0.06296417 - 1*(-0.019001413)))",
    "x*(-3.977787)"
  ],
  "wall_s_total": 17.775529484000344,
  "wall_s_per_eq": [
    8.30751379000003,
    9.468015694000314
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(1.0907819 - v*v*(x*x*0.06296417 - 1*(-0.019001413)))",
      "r2_train": 0.9956104469585224,
      "reward": null,
      "residual_heldout": 0.004341049865207558,
      "pred_coeffs": {
        "v": 1.0907819
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.30751379000003,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-3.977787)",
      "r2_train": 0.9939550446880243,
      "reward": null,
      "residual_heldout": 0.00456946146185699,
      "pred_coeffs": {
        "x": -3.977787
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 9.468015694000314,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.004565137223562782 cons=4.0252582932102e-07 wall_s=14.023 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004565137223562782,
  "conservation_residual": 4.0252582932102e-07,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 14.023413069000526,
  "wall_s_per_eq": [
    7.295320287000322,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9954314814059297,
      "reward": null,
      "residual_heldout": 0.005077797895112349,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.295320287000322,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.295320287000322,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9946417295247976,
      "reward": null,
      "residual_heldout": 0.004052476552013216,
      "pred_coeffs": {
        "x": -4.002539396125252
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.728092782000203,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.728092782000203,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        4.002539396125252
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0045785123684424466 cons=6.822000870919101e-05 wall_s=17.286 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0045785123684424466,
  "conservation_residual": 6.822000870919101e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 17.28579872299997,
  "wall_s_per_eq": [
    10.218403518000287,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9948810258342662,
      "reward": null,
      "residual_heldout": 0.004572785863896207,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.218403518000287,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.218403518000287,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.994705003326541,
      "reward": null,
      "residual_heldout": 0.004584238872988687,
      "pred_coeffs": {
        "x": -3.967357290178781
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.067395204999684,
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      "wall_raw_s": 7.067395204999684,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.967357290178781
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.004309519386297323 cons=3.709511069952207e-06 wall_s=13.729 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004309519386297323,
  "conservation_residual": 3.709511069952207e-06,
  "equations": [
    "v",
    "-3*w2*x"
  ],
  "wall_s_total": 13.729095207000228,
  "wall_s_per_eq": [
    6.913899480000055,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9947017025227637,
      "reward": null,
      "residual_heldout": 0.0038808348916891874,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.913899480000055,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.913899480000055,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-3*w2*x",
      "r2_train": 0.9944972951938861,
      "reward": null,
      "residual_heldout": 0.004738203880905458,
      "pred_coeffs": {
        "x": -4.00769688641193
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 6.815195727000173,
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      "wall_raw_s": 6.815195727000173,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.3358989621373099
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5301614814040089 cons=1.0900602924779117 wall_s=17.351 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5301614814040089,
  "conservation_residual": 1.0900602924779117,
  "equations": [
    "2*v",
    "-w2*x"
  ],
  "wall_s_total": 17.350931025000136,
  "wall_s_per_eq": [
    10.158306897999864,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.0076268137247818,
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      "residual_heldout": 1.05573337393628,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 10.158306897999864,
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      "wall_raw_s": 10.158306897999864,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9949734719052555,
      "reward": null,
      "residual_heldout": 0.0045895888717376624,
      "pred_coeffs": {
        "x": -3.98904135121237
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        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.192624127000272,
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      "wall_raw_s": 7.192624127000272,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.98904135121237
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.00547409957790553 cons=6.22741460267621e-08 wall_s=14.017 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00547409957790553,
  "conservation_residual": 6.22741460267621e-08,
  "equations": [
    "v",
    "w2*x"
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  "wall_s_total": 14.016629619000014,
  "wall_s_per_eq": [
    6.990304556999945,
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9956230183212207,
      "reward": null,
      "residual_heldout": 0.005241366468132325,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.990304556999945,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.990304556999945,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9954857949587197,
      "reward": null,
      "residual_heldout": 0.0057068326876787345,
      "pred_coeffs": {
        "x": -4.000992488227647
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 7.026325062000069,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.026325062000069,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.000992488227647
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0045682443318068675 cons=9.076440049848247e-05 wall_s=17.629 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0045682443318068675,
  "conservation_residual": 9.076440049848247e-05,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 17.62857785899996,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 10.584497588999966,
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      "wall_raw_s": 10.584497588999966,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9950418147513964,
      "reward": null,
      "residual_heldout": 0.004768120417559569,
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        "x": -3.962255960489865
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.044080269999995,
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      "wall_raw_s": 7.044080269999995,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.962255960489865
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005454435556977121 cons=1.8901418012371984e-05 wall_s=14.636 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005454435556977121,
  "conservation_residual": 1.8901418012371984e-05,
  "equations": [
    "v",
    "-w2*x"
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  "wall_s_total": 14.636434446000294,
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  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.8960032810000484,
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      "wall_raw_s": 6.8960032810000484,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "structure_ok": true,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.9827073530699852
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.00457748058400006 cons=1.5633910891314912e-06 wall_s=18.379 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
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  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00457748058400006,
  "conservation_residual": 1.5633910891314912e-06,
  "equations": [
    "v",
    "w2*x"
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  "wall_s_total": 18.379137908999837,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 11.117768535999858,
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      "wall_raw_s": 11.117768535999858,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "w2*x",
      "r2_train": 0.9946205144958834,
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      "structure_ok": true,
      "wall_s": 7.2613693729999795,
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      "wall_raw_s": 7.2613693729999795,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      },
      "free_const_values": [
        -3.9950859054561936
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.005605095225954552 cons=1.1596831185897274e-05 wall_s=13.679 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
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  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005605095225954552,
  "conservation_residual": 1.1596831185897274e-05,
  "equations": [
    "v",
    "-2*w2*x"
  ],
  "wall_s_total": 13.678735527999834,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.046484770000006,
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      "wall_raw_s": 7.046484770000006,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-2*w2*x",
      "r2_train": 0.9956723186618808,
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      "structure_ok": true,
      "wall_s": 6.632250757999827,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "zero_eq_retry": 2
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      "free_const_values": [
        1.9932143946019236
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0046886870752839566 cons=2.5930404467752824e-06 wall_s=18.160 ok=True

```json
{
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  "arm": "A4_physo",
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  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0046886870752839566,
  "conservation_residual": 2.5930404467752824e-06,
  "equations": [
    "v",
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  ],
  "wall_s_total": 18.160040448000018,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "wall_s": 11.021119851000094,
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      "free_const_values": [],
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    {
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      "wall_s": 7.138920596999924,
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      "free_const_values": [
        -3.9935920078260483
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.005108696635259351 cons=4.32268019463354e-05 wall_s=13.867 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005108696635259351,
  "conservation_residual": 4.32268019463354e-05,
  "equations": [
    "v",
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  ],
  "wall_s_total": 13.866515551999782,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "structure_ok": true,
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      "free_const_values": [],
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    {
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      "structure_ok": true,
      "wall_s": 6.961434891999943,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [
        3.973973109693565
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.005077172238226815 cons=3.189468741141652e-05 wall_s=19.934 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005077172238226815,
  "conservation_residual": 3.189468741141652e-05,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 19.93437890899986,
  "wall_s_per_eq": [
    6.911550058000103,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9946865038291688,
      "reward": null,
      "residual_heldout": 0.006104534016120842,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.911550058000103,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.911550058000103,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.995347183056582,
      "reward": null,
      "residual_heldout": 0.0040498104603327876,
      "pred_coeffs": {
        "x": -3.977913989288028
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      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 13.022828850999758,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.022828850999758,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.977913989288028
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.004153618850607737 cons=6.6410368314519386e-06 wall_s=15.046 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004153618850607737,
  "conservation_residual": 6.6410368314519386e-06,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 15.045657355999992,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9947137056407495,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.6835890130000735,
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      "wall_raw_s": 7.6835890130000735,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9956154864018281,
      "reward": null,
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      "pred_coeffs": {
        "x": -3.9897755350140844
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      "true_coeffs": {
        "x": -4.0
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      "structure_ok": true,
      "wall_s": 7.362068342999919,
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      "wall_raw_s": 7.362068342999919,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.9897755350140844
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.005039660764371101 cons=4.557996831166363e-05 wall_s=20.419 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005039660764371101,
  "conservation_residual": 4.557996831166363e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 20.418544092999582,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9954797580868675,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.86375004699994,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.86375004699994,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9950189987840657,
      "reward": null,
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      "pred_coeffs": {
        "x": -3.973273966346328
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 11.554794045999643,
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      "wall_raw_s": 11.554794045999643,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.973273966346328
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.004621195473830565 cons=1.4548509693091678e-05 wall_s=14.372 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004621195473830565,
  "conservation_residual": 1.4548509693091678e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 14.371852595999826,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.224260464000054,
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      "wall_raw_s": 7.224260464000054,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9952047494103595,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.147592131999772,
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      "wall_raw_s": 7.147592131999772,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        -4.015136052140584
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.004171586906293662 cons=5.041973921802454e-06 wall_s=13.654 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004171586906293662,
  "conservation_residual": 5.041973921802454e-06,
  "equations": [
    "v",
    "-w2*x"
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  "wall_s_total": 13.65351295299979,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 6.915637274999881,
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      "wall_raw_s": 6.915637274999881,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "r2_train": 0.9952288499716104,
      "reward": null,
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        "x": -3.9912174759483383
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      "structure_ok": true,
      "wall_s": 6.737875677999909,
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      "wall_raw_s": 6.737875677999909,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.9912174759483383
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.004284543236229954 cons=2.5441415953166512e-05 wall_s=18.724 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004284543236229954,
  "conservation_residual": 2.5441415953166512e-05,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 18.724482751999858,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
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  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 11.2547469619999,
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      "wall_raw_s": 11.2547469619999,
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        "max_n_evaluations": 2500,
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        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
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      "r2_train": 0.9949962763714009,
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      "structure_ok": true,
      "wall_s": 7.469735789999959,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      "free_const_values": [
        3.9799506260620943
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.004680233670946083 cons=6.411323488761922e-07 wall_s=14.877 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004680233670946083,
  "conservation_residual": 6.411323488761922e-07,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 14.876779080999768,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "structure_ok": true,
      "wall_s": 7.248247397999876,
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        "max_n_evaluations": 2500,
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      "free_const_values": [],
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    {
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        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.9968167199003384
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.004418546030294001 cons=8.292270777247865e-05 wall_s=19.042 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004418546030294001,
  "conservation_residual": 8.292270777247865e-05,
  "equations": [
    "v",
    "-w2*x"
  ],
  "wall_s_total": 19.04203374000008,
  "wall_s_per_eq": [
    6.800497328999882,
    12.241536411000197
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9953240565193716,
      "reward": null,
      "residual_heldout": 0.00439364113340053,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.800497328999882,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.800497328999882,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-w2*x",
      "r2_train": 0.9941114835594245,
      "reward": null,
      "residual_heldout": 0.00444345092718747,
      "pred_coeffs": {
        "x": -3.9640105913685115
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 12.241536411000197,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.241536411000197,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        3.9640105913685115
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `harmonic_oscillator` / N=400 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.00460607298804298 cons=3.125991413219581e-05 wall_s=17.355 ok=True

```json
{
  "law": "harmonic_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00460607298804298,
  "conservation_residual": 3.125991413219581e-05,
  "equations": [
    "v",
    "w2*x"
  ],
  "wall_s_total": 17.354775342000266,
  "wall_s_per_eq": [
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    8.804602247000275
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9952912012386756,
      "reward": null,
      "residual_heldout": 0.004642712448540547,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.550173094999991,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.550173094999991,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "w2*x",
      "r2_train": 0.9939550444699171,
      "reward": null,
      "residual_heldout": 0.004569433527545413,
      "pred_coeffs": {
        "x": -3.97779373118787
      },
      "true_coeffs": {
        "x": -4.0
      },
      "structure_ok": true,
      "wall_s": 8.804602247000275,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.804602247000275,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -3.97779373118787
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=4.023290495065466e-16 cons=0.0 wall_s=18.862 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.023290495065466e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + x*(-4.000002) + x*1.8939802e-6 - 9.36381e-9 - 1*(-9.36381e-9) + 1.6481003e-8"
  ],
  "wall_s_total": 18.86222739699997,
  "wall_s_per_eq": [
    9.75009815600015,
    9.11212924099982
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.75009815600015,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + x*(-4.000002) + x*1.8939802e-6 - 9.36381e-9 - 1*(-9.36381e-9) + 1.6481003e-8",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 8.046580990130932e-16,
      "pred_coeffs": {
        "1": 1.6481003e-08,
        "v": -0.4,
        "x": -4.0000001060198
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.11212924099982,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=3.122151607670135e-17 cons=0.22397507968027297 wall_s=17.737 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.122151607670135e-17,
  "conservation_residual": 0.22397507968027297,
  "equations": [
    "v",
    "v*(-(-2.624511e-8)*x - 0.23056035) + v*(-0.16943966) - x - x - (x + x)"
  ],
  "wall_s_total": 17.737415643000077,
  "wall_s_per_eq": [
    9.54145706899999,
    8.195958574000088
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.54145706899999,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-(-2.624511e-8)*x - 0.23056035) + v*(-0.16943966) - x - x - (x + x)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 6.24430321534027e-17,
      "pred_coeffs": {
        "x*v": 2.624511e-08
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 8.195958574000088,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=2.134250406763496e-17 cons=0.0 wall_s=17.881 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.134250406763496e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.21505968) + v*(-0.16600561) + v*(-0.018934695) + x*(-2.2568355) + x*(-1.7431645)"
  ],
  "wall_s_total": 17.881317009999748,
  "wall_s_per_eq": [
    9.168234759999905,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.168234759999905,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.21505968) + v*(-0.16600561) + v*(-0.018934695) + x*(-2.2568355) + x*(-1.7431645)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 4.268500813526992e-17,
      "pred_coeffs": {
        "v": -0.399999985,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.713082249999843,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=1.3453908260538797e-19 cons=0.0 wall_s=16.989 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.3453908260538797e-19,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + x*(-3.8482172) + x*(-0.1517828) - 4.580701e-9 + 5.4643787e-9"
  ],
  "wall_s_total": 16.988699834999807,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.827493397000126,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + x*(-3.8482172) + x*(-0.1517828) - 4.580701e-9 + 5.4643787e-9",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.6907816521077594e-19,
      "pred_coeffs": {
        "1": 8.836777000000005e-10,
        "v": -0.4,
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      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.161206437999681,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=1.1233539701286415e-16 cons=0.0 wall_s=17.941 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.1233539701286415e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + v + x*(-4.0) - (v - 2.750281e-8) - 6.406248e-9"
  ],
  "wall_s_total": 17.941230063001058,
  "wall_s_per_eq": [
    9.72530690000076,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.72530690000076,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + v + x*(-4.0) - (v - 2.750281e-8) - 6.406248e-9",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 2.246707940257283e-16,
      "pred_coeffs": {
        "1": 2.1096562e-08,
        "v": -0.4,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.215923163000298,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=1.9371462227629465e-16 cons=0.0 wall_s=18.243 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.9371462227629465e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.27515998) + v*(-0.124840036) + x*(-4.0) + 2.163548e-8"
  ],
  "wall_s_total": 18.24346490500011,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.857709267000246,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.27515998) + v*(-0.124840036) + x*(-4.0) + 2.163548e-8",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.874292445525893e-16,
      "pred_coeffs": {
        "1": 2.163548e-08,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.385755637999864,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=1.1912741454574533e-17 cons=0.0 wall_s=18.240 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.1912741454574533e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) - 4*x + 7.39342e-9"
  ],
  "wall_s_total": 18.239997222000966,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.721627685000385,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) - 4*x + 7.39342e-9",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.3825482909149066e-17,
      "pred_coeffs": {
        "1": 7.39342e-09,
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      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.51836953700058,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=4.10295135683489e-34 cons=0.0 wall_s=17.706 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.10295135683489e-34,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.25953212) + v*(-0.14046788) + x*(-4.0)"
  ],
  "wall_s_total": 17.705751358998896,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.962529222999365,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.25953212) + v*(-0.14046788) + x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 8.20590271366978e-34,
      "pred_coeffs": {
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.743222135999531,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=1.2864636310242722e-17 cons=0.0 wall_s=19.642 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.2864636310242722e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.293663*v + v*(-0.10633699) + x*(-4.0)"
  ],
  "wall_s_total": 19.642420949000552,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.199143015000118,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.293663*v + v*(-0.10633699) + x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.5729272620485443e-17,
      "pred_coeffs": {
        "v": -0.39999999,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.443277934000434,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=4.177658659325421e-16 cons=0.0 wall_s=17.692 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.177658659325421e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(x*(-3.8977563) - (1.2612212e-8 - (-0.38977563)*v))*1.0262314"
  ],
  "wall_s_total": 17.69156841899985,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.347653211999386,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(x*(-3.8977563) - (1.2612212e-8 - (-0.38977563)*v))*1.0262314",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 8.355317318650842e-16,
      "pred_coeffs": {
        "1": -1.29430479778568e-08,
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        "x": -3.9999999046078196
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.343915207000464,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=3.06365149703917e-17 cons=0.0 wall_s=17.471 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.06365149703917e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 17.470825339999465,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 1.0,
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      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.180786797999644,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 6.12730299407834e-17,
      "pred_coeffs": {
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        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.29003854199982,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=7.528530754818706e-17 cons=0.0 wall_s=18.888 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.528530754818706e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.013093067) + x*(-4.0) + (v + 1.249519e-8)*(-0.38690692) - 1.04765165e-8 + 3.849202e-9 + 2.2971706e-8"
  ],
  "wall_s_total": 18.888143205999768,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.602825270999347,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.013093067) + x*(-4.0) + (v + 1.249519e-8)*(-0.38690692) - 1.04765165e-8 + 3.849202e-9 + 2.2971706e-8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.5057061509637411e-16,
      "pred_coeffs": {
        "1": 1.1509916022285202e-08,
        "v": -0.399999987,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.285317935000421,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=1.4299985485874246e-16 cons=0.0 wall_s=17.700 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.4299985485874246e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.4*v + x*(-3.1684463) + x*(-0.83155364) - 2.7391627e-6 - 1*(-2.7245865e-6)"
  ],
  "wall_s_total": 17.700356913999713,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.388695749999897,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.4*v + x*(-3.1684463) + x*(-0.83155364) - 2.7391627e-6 - 1*(-2.7245865e-6)",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 2.859997097174849e-16,
      "pred_coeffs": {
        "1": -1.4576200000000313e-08,
        "v": -0.4,
        "x": -3.99999994
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.311661163999815,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=8.502667569486144e-17 cons=0.0 wall_s=17.765 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 8.502667569486144e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0) + (v + 3.1883182e-8)*(-0.4) - 1*5.159432e-8 + 4.69419e-8"
  ],
  "wall_s_total": 17.764980376000494,
  "wall_s_per_eq": [
    8.879283684999791,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.879283684999791,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0) + (v + 3.1883182e-8)*(-0.4) - 1*5.159432e-8 + 4.69419e-8",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 1.7005335138972288e-16,
      "pred_coeffs": {
        "1": -1.7405692800000005e-08,
        "v": -0.4,
        "x": -4.0
      },
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        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.885696691000703,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=5.254187991851727e-18 cons=0.0 wall_s=17.933 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.254187991851727e-18,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.055709735) - (-(-0.34429026)*v + x + x + x + x)"
  ],
  "wall_s_total": 17.933258224999918,
  "wall_s_per_eq": [
    9.68793917000039,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.68793917000039,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.055709735) - (-(-0.34429026)*v + x + x + x + x)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.0508375983703454e-17,
      "pred_coeffs": {
        "v": -0.399999995,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.245319054999527,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=5.2665534056857756e-17 cons=0.0 wall_s=17.925 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.2665534056857756e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 17.925070713000423,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.375413578000007,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.0533106811371551e-16,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
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        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.549657135000416,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=3.727589571800672e-17 cons=0.0 wall_s=16.757 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.727589571800672e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*0.004807942 - 4.0*x - 0.20240396*(v + x - (-v - v + v + x))"
  ],
  "wall_s_total": 16.756858916000056,
  "wall_s_per_eq": [
    8.865129711000009,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.865129711000009,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*0.004807942 - 4.0*x - 0.20240396*(v + x - (-v - v + v + x))",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 7.455179143601343e-17,
      "pred_coeffs": {
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        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 7.891729205000047,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=1.9945430701709081e-16 cons=0.0 wall_s=18.086 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.9945430701709081e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-v + v*(-0.39999998) + v + x*(-4.0) - x + x - 1*2.009175e-8"
  ],
  "wall_s_total": 18.086160703000132,
  "wall_s_per_eq": [
    8.917461340000045,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.917461340000045,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-v + v*(-0.39999998) + v + x*(-4.0) - x + x - 1*2.009175e-8",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 3.9890861403418163e-16,
      "pred_coeffs": {
        "1": -2.009175e-08,
        "v": -0.39999998000000003,
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      },
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        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.168699363000087,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=6.5165352571466585e-18 cons=0.0 wall_s=18.096 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.5165352571466585e-18,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.4*v + x*(-3.1582186) + x - 1.8417814*(x - 4.101352e-9) - 4.101352e-9 + 4.0798898e-9"
  ],
  "wall_s_total": 18.095719447998817,
  "wall_s_per_eq": [
    9.58543810699939,
    8.510281340999427
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.58543810699939,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.4*v + x*(-3.1582186) + x - 1.8417814*(x - 4.101352e-9) - 4.101352e-9 + 4.0798898e-9",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.3033070514293317e-17,
      "pred_coeffs": {
        "1": 7.5323316284528e-09,
        "v": -0.4,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.510281340999427,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=3.2663820483731223e-16 cons=0.0 wall_s=17.460 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.2663820483731223e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(v*0.036241025 + v*0.16375896 + x + x)*(-2.0) - 1.9279316e-8"
  ],
  "wall_s_total": 17.460194099000546,
  "wall_s_per_eq": [
    9.084905737000554,
    8.375288361999992
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.084905737000554,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v*0.036241025 + v*0.16375896 + x + x)*(-2.0) - 1.9279316e-8",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 6.532764096746245e-16,
      "pred_coeffs": {
        "1": -1.9279316e-08,
        "v": -0.39999997000000004,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.375288361999992,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=8.963085397966711e-16 cons=0.16536467726658402 wall_s=17.220 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.963085397966711e-16,
  "conservation_residual": 0.16536467726658402,
  "equations": [
    "v",
    "(((w2-(w2+w2))*((-(x)+x)-(x+x)))-(gamma*v))"
  ],
  "wall_s_total": 17.219501360999857,
  "wall_s_per_eq": [
    9.12688401000014,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 6.447199627973936e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.12688401000014,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.12688401000014,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2-(w2+w2))*((-(x)+x)-(x+x)))-(gamma*v))",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 1.1478971167959484e-15,
      "pred_coeffs": {
        "v": 1.9999999995861582,
        "x": 0.8000000002669446
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 8.092617350999717,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.092617350999717,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4000000001334723,
        -1.9999999995861582
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=False residual=1.1448800472899367e-12 cons=1.4311988493035566 wall_s=25.272 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.1448800472899367e-12,
  "conservation_residual": 1.4311988493035566,
  "equations": [
    "v",
    "((gamma*((-((gamma*x))-v)+v))+((gamma*v)+-((x*w2))))"
  ],
  "wall_s_total": 25.27219340100055,
  "wall_s_per_eq": [
    15.053068144999997,
    10.219125256000552
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 6.180267568146874e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 15.053068144999997,
      "wall_pad_s": 0.0,
      "wall_raw_s": 15.053068144999997,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((gamma*((-((gamma*x))-v)+v))+((gamma*v)+-((x*w2))))",
      "r2_train": 0.9999999999967208,
      "reward": null,
      "residual_heldout": 2.2891420678230588e-12,
      "pred_coeffs": {
        "v": 3.8399940748618135,
        "x": -14.345554521265246
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 10.219125256000552,
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      "wall_raw_s": 10.219125256000552,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.3999999737085885,
        3.8399940748618135
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=False residual=6.253102104654378e-13 cons=0.7451541237156297 wall_s=17.099 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.253102104654378e-13,
  "conservation_residual": 0.7451541237156297,
  "equations": [
    "v",
    "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))"
  ],
  "wall_s_total": 17.0988672830008,
  "wall_s_per_eq": [
    7.7922603160004655,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999808,
      "reward": null,
      "residual_heldout": 2.0693777118310455e-14,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.7922603160004655,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.7922603160004655,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))",
      "r2_train": 0.9999999999990274,
      "reward": null,
      "residual_heldout": 1.229926643812565e-12,
      "pred_coeffs": {
        "v": 2.000001013071139,
        "x": 0.8000047306548779
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 9.306606967000334,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.306606967000334,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.40000236532743894,
        2.000001013071139
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5338164802752701 cons=2.6625406902316615 wall_s=23.574 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5338164802752701,
  "conservation_residual": 2.6625406902316615,
  "equations": [
    "2*v",
    "-(((-(((-(gamma)*x)*gamma))+(w2*x))-(v*gamma)))"
  ],
  "wall_s_total": 23.57385164400057,
  "wall_s_per_eq": [
    9.443851801000164,
    14.129999843000405
  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.01235400425729849,
      "reward": null,
      "residual_heldout": 1.0676329605504307,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 9.443851801000164,
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      "wall_raw_s": 9.443851801000164,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((-(((-(gamma)*x)*gamma))+(w2*x))-(v*gamma)))",
      "r2_train": 0.9999999999998888,
      "reward": null,
      "residual_heldout": 1.094432303202044e-13,
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        "v": 3.8399987074029047,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 14.129999843000405,
      "wall_pad_s": 0.0,
      "wall_raw_s": 14.129999843000405,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.39999999775190537,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=False residual=3.6456396621331795e-13 cons=12.984475065950777 wall_s=16.704 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.6456396621331795e-13,
  "conservation_residual": 12.984475065950777,
  "equations": [
    "v",
    "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))"
  ],
  "wall_s_total": 16.704030496000087,
  "wall_s_per_eq": [
    8.375441963999947,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 5.932733942627204e-16,
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        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.375441963999947,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))",
      "r2_train": 0.9999999999995652,
      "reward": null,
      "residual_heldout": 7.285346590323731e-13,
      "pred_coeffs": {
        "v": 11.946670134761307,
        "x": -15.724770072446097
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 8.32858853200014,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.32858853200014,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.1333329618647652,
        3.982223378253769
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=1.5287944792233393e-13 cons=0.0 wall_s=14.562 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.5287944792233393e-13,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))"
  ],
  "wall_s_total": 14.562158233000446,
  "wall_s_per_eq": [
    7.70819273699999,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
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      "reward": null,
      "residual_heldout": 4.0685337903540793e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.70819273699999,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.70819273699999,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))",
      "r2_train": 0.9999999999997474,
      "reward": null,
      "residual_heldout": 3.0535204246563244e-13,
      "pred_coeffs": {
        "v": -3.9999980864298075,
        "x": -0.39999956193152575
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.8539654960004555,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.8539654960004555,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.39999956193152575,
        -3.9999980864298075
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=False residual=9.672755460650896e-15 cons=4.900260292249957 wall_s=19.854 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 9.672755460650896e-15,
  "conservation_residual": 4.900260292249957,
  "equations": [
    "v",
    "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))"
  ],
  "wall_s_total": 19.853791726000054,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.059254810999846,
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      "wall_raw_s": 7.059254810999846,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))",
      "r2_train": 0.9999999999999867,
      "reward": null,
      "residual_heldout": 1.8657437087133493e-14,
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        "v": 8.079999716053958,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 12.794536915000208,
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      "wall_raw_s": 12.794536915000208,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.1999999014157862,
        -4.039999858026979
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=2.970341389091823e-15 cons=0.0 wall_s=14.512 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.970341389091823e-15,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))"
  ],
  "wall_s_total": 14.512350997000794,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.124095345000569,
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      "wall_raw_s": 7.124095345000569,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))",
      "r2_train": 0.9999999999999952,
      "reward": null,
      "residual_heldout": 5.1628105933405915e-15,
      "pred_coeffs": {
        "v": -2.0000000000036784,
        "x": -0.7999999999959633
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      "true_coeffs": {
        "x": -4.0,
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      "structure_ok": false,
      "wall_s": 7.388255652000225,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.388255652000225,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        0.39999999999798164,
        2.0000000000036784
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=3.035663868440555e-13 cons=0.0 wall_s=14.170 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.035663868440555e-13,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-(((w2*x)+(-((-(v)*gamma))+(x*w2))))"
  ],
  "wall_s_total": 14.170423184001265,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.486922155000684,
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      "wall_raw_s": 7.486922155000684,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((w2*x)+(-((-(v)*gamma))+(x*w2))))",
      "r2_train": 0.9999999999989216,
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      "residual_heldout": 6.06771224395506e-13,
      "pred_coeffs": {
        "v": -1.9999987911209973,
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      "true_coeffs": {
        "x": -4.0,
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      "wall_s": 6.683501029000581,
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      "wall_raw_s": 6.683501029000581,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      },
      "free_const_values": [
        0.4000012377602798,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=False residual=3.0412408853857015e-11 cons=1.5727823164346726 wall_s=19.335 ok=True

```json
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
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  "recovered": false,
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  "residual": 3.0412408853857015e-11,
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    "-((-((x*-(w2)))-(gamma*(v+(v-v)))))"
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  "wall_s_total": 19.334946734998994,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.895174063999548,
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      "free_const_values": [],
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-((x*-(w2)))-(gamma*(v+(v-v)))))",
      "r2_train": 0.9999999999519438,
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        "v": 4.000027282542867,
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      "wall_s": 12.439772670999446,
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      "wall_raw_s": 12.439772670999446,
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      "budget": {
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        "max_n_evaluations": 2500,
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      },
      "free_const_values": [
        -0.400008644826716,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=False residual=3.76418136385569e-11 cons=3.7212340848146273 wall_s=14.404 ok=True

```json
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  "recovered": false,
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  "residual": 3.76418136385569e-11,
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  "equations": [
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    "(-(((gamma*v)+-((w2*x))))+(v*-(gamma)))"
  ],
  "wall_s_total": 14.40350066999963,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.3762685080000665,
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        "max_n_evaluations": 2500,
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      "free_const_values": [],
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    },
    {
      "eq_i": 1,
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      "equation": "(-(((gamma*v)+-((w2*x))))+(v*-(gamma)))",
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        "v": 8.000071861827339,
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      "true_coeffs": {
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      "wall_s": 7.027232161999564,
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      "wall_raw_s": 7.027232161999564,
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=1.578908199853068e-14 cons=0.0 wall_s=13.330 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.578908199853068e-14,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "((gamma*v)+(x*w2))"
  ],
  "wall_s_total": 13.329659865999929,
  "wall_s_per_eq": [
    6.853908445999878,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 7.477081560953148e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.853908445999878,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.853908445999878,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((gamma*v)+(x*w2))",
      "r2_train": 0.9999999999999858,
      "reward": null,
      "residual_heldout": 3.0830455840966045e-14,
      "pred_coeffs": {
        "v": -3.9999998785445703,
        "x": -0.40000015307089437
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.475751420000051,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.475751420000051,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.40000015307089437,
        -3.9999998785445703
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=False residual=3.016966523244945e-13 cons=6.115099640184442 wall_s=19.651 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.016966523244945e-13,
  "conservation_residual": 6.115099640184442,
  "equations": [
    "v",
    "(-((v*-((-((gamma+-((gamma-gamma))))-gamma))))+(x*w2))"
  ],
  "wall_s_total": 19.65104415499991,
  "wall_s_per_eq": [
    6.974321313000473,
    12.676722841999435
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 1.1724437434690422e-15,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.974321313000473,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.974321313000473,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((v*-((-((gamma+-((gamma-gamma))))-gamma))))+(x*w2))",
      "r2_train": 0.9999999999995703,
      "reward": null,
      "residual_heldout": 6.022208609055199e-13,
      "pred_coeffs": {
        "v": 7.999996863759554,
        "x": 0.19999924678552283
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 12.676722841999435,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.676722841999435,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.19999924678552283,
        -3.999998431879777
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=5.060781722580556e-12 cons=0.0 wall_s=14.447 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.060781722580556e-12,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(-((((v-(v+(v+v)))*gamma)--((gamma*v))))+(x*w2))"
  ],
  "wall_s_total": 14.446500044999993,
  "wall_s_per_eq": [
    7.296243542000411,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.296243542000411,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.296243542000411,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((v-(v+(v+v)))*gamma)--((gamma*v))))+(x*w2))",
      "r2_train": 0.9999999999925776,
      "reward": null,
      "residual_heldout": 1.012090504868438e-11,
      "pred_coeffs": {
        "v": -3.9999926956843033,
        "x": -0.4000022355908321
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 7.150256502999582,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.150256502999582,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4000022355908321,
        -3.9999926956843033
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=False residual=2.0168032781938332e-11 cons=3.172076233701391 wall_s=13.331 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 2.0168032781938332e-11,
  "conservation_residual": 3.172076233701391,
  "equations": [
    "v",
    "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))"
  ],
  "wall_s_total": 13.330896773999484,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.775857362999886,
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      "wall_raw_s": 6.775857362999886,
      "wall_cap_s": 120,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))",
      "r2_train": 0.9999999999646637,
      "reward": null,
      "residual_heldout": 4.033514600184145e-11,
      "pred_coeffs": {
        "v": 3.9999758182980036,
        "x": 0.4000005794240251
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.555039410999598,
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      "wall_raw_s": 6.555039410999598,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4000005794240251,
        3.9999758182980036
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=False residual=9.486548341162053e-15 cons=3.428738581396083 wall_s=19.624 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 9.486548341162053e-15,
  "conservation_residual": 3.428738581396083,
  "equations": [
    "v",
    "(-(((-(v)*gamma)-((v*-(gamma))+-((v*gamma)))))+(w2*x))"
  ],
  "wall_s_total": 19.6240849550004,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.131272124000134,
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      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(((-(v)*gamma)-((v*-(gamma))+-((v*gamma)))))+(w2*x))",
      "r2_train": 0.9999999999999851,
      "reward": null,
      "residual_heldout": 1.828331830049289e-14,
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        "v": 3.9999995668697506,
        "x": 0.39999981066774726
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 12.492812831000265,
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      "wall_raw_s": 12.492812831000265,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.39999981066774726,
        -3.9999995668697506
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=False residual=4.124900279400104e-15 cons=2.1570337195555056 wall_s=14.467 ok=True

```json
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  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
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  "residual": 4.124900279400104e-15,
  "conservation_residual": 2.1570337195555056,
  "equations": [
    "v",
    "(-((w2*x))+(gamma*v))"
  ],
  "wall_s_total": 14.467160428999705,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.733424985000056,
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        "max_n_evaluations": 2500,
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      "free_const_values": [],
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    },
    {
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      "r2_train": 0.9999999999999907,
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        "v": 3.999999749306601,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 6.733735443999649,
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      "wall_raw_s": 6.733735443999649,
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        "max_n_evaluations": 2500,
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      },
      "free_const_values": [
        -0.4000000399320012,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=False residual=1.7049327987001282e-13 cons=3.5387892531919722 wall_s=13.290 ok=True

```json
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.7049327987001282e-13,
  "conservation_residual": 3.5387892531919722,
  "equations": [
    "v",
    "-(((v*gamma)--(((x*(gamma*(gamma-gamma)))+-((w2*x))))))"
  ],
  "wall_s_total": 13.289759548999427,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "ok": true,
  "tau": 0.2,
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        "v": 1.0
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      "wall_s": 6.672534515999359,
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      "budget": {
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        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((v*gamma)--(((x*(gamma*(gamma-gamma)))+-((w2*x))))))",
      "r2_train": 0.9999999999997591,
      "reward": null,
      "residual_heldout": 3.4008040215085143e-13,
      "pred_coeffs": {
        "v": 3.9999982445237707,
        "x": 0.39999927964788823
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.617225033000068,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.617225033000068,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.39999927964788823,
        -3.9999982445237707
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=2.809656373840705e-13 cons=0.0 wall_s=13.717 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.809656373840705e-13,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))"
  ],
  "wall_s_total": 13.716604442999596,
  "wall_s_per_eq": [
    6.909836789999645,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
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      "reward": null,
      "residual_heldout": 9.301515244611903e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.909836789999645,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.909836789999645,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))",
      "r2_train": 0.9999999999986976,
      "reward": null,
      "residual_heldout": 5.610011232436798e-13,
      "pred_coeffs": {
        "v": -8.000003289132222,
        "x": -0.20000101805859477
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.806767652999952,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.806767652999952,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.20000101805859477,
        4.000001644566111
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=False residual=2.2733795414646673e-11 cons=2.6806292186629794 wall_s=20.012 ok=True

```json
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  "n_samples": 50,
  "arm": "A4_physo",
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  "recovered": false,
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  "residual": 2.2733795414646673e-11,
  "conservation_residual": 2.6806292186629794,
  "equations": [
    "v",
    "-(((gamma*v)+(w2*-(x))))"
  ],
  "wall_s_total": 20.012385715000164,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 13.29562915600036,
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      "wall_raw_s": 13.29562915600036,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*v)+(w2*-(x))))",
      "r2_train": 0.9999999999574374,
      "reward": null,
      "residual_heldout": 4.546694533524323e-11,
      "pred_coeffs": {
        "v": 4.000026266698885,
        "x": 0.3999993597232698
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      "true_coeffs": {
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        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.716756558999805,
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      "wall_raw_s": 6.716756558999805,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3999993597232698,
        -4.000026266698885
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=8.751220499954001e-17 cons=0.0 wall_s=16.660 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A0_pysr",
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  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 8.751220499954001e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(v + 3.9157324e-8)*(-0.39999998) - (x + x) - (x + x)"
  ],
  "wall_s_total": 16.659564097999464,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.954257662999225,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v + 3.9157324e-8)*(-0.39999998) - (x + x) - (x + x)",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 1.7502440999908002e-16,
      "pred_coeffs": {
        "1": -1.566292881685352e-08,
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 7.705306435000239,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=2.441390850224139e-17 cons=0.0 wall_s=16.836 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.441390850224139e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.4304973*v + v*0.030497285 + x*(-4.0)"
  ],
  "wall_s_total": 16.836430550999467,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.819646599999942,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.4304973*v + v*0.030497285 + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 4.882781700448278e-17,
      "pred_coeffs": {
        "v": -0.40000001500000004,
        "x": -4.0
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        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.016783950999525,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=5.176478146088909e-17 cons=0.0 wall_s=16.748 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.176478146088909e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.2177011) + v*(-0.18229888) + x*(-4.0)"
  ],
  "wall_s_total": 16.748447976000534,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.022709324000061,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.2177011) + v*(-0.18229888) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.0352956292177818e-16,
      "pred_coeffs": {
        "v": -0.39999998000000003,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 7.725738652000473,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=1.608534489082127e-16 cons=0.0 wall_s=15.820 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.608534489082127e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) - (-5.0910977e-8)*x*(-x - x + 0.96437514) + x*(-4.0)"
  ],
  "wall_s_total": 15.820300264000252,
  "wall_s_per_eq": [
    8.106099966000329,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.106099966000329,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) - (-5.0910977e-8)*x*(-x - x + 0.96437514) + x*(-4.0)",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.217068978164254e-16,
      "pred_coeffs": {
        "x^2": -1.01821954e-07,
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        "x": -3.9999999509027195
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": true,
      "wall_s": 7.714200297999923,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=8.513395384797096e-17 cons=0.0 wall_s=16.802 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 8.513395384797096e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + x*(-3.708952) + x*(-0.29104805)"
  ],
  "wall_s_total": 16.802232156000173,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.645480559000134,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + x*(-3.708952) + x*(-0.29104805)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.7026790769594192e-16,
      "pred_coeffs": {
        "v": -0.4,
        "x": -4.00000005
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.156751597000039,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=3.889635621982033e-17 cons=0.0 wall_s=17.450 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.889635621982033e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 17.44965879299889,
  "wall_s_per_eq": [
    9.373789542999475,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.373789542999475,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 7.779271243964066e-17,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.075869249999414,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=1.002221028490126e-33 cons=0.0 wall_s=16.405 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.002221028490126e-33,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.33797908) - 0.06202092*v + x*(-4.0)"
  ],
  "wall_s_total": 16.405028479000066,
  "wall_s_per_eq": [
    8.62251739200019,
    7.782511086999875
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.62251739200019,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.33797908) - 0.06202092*v + x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.004442056980252e-33,
      "pred_coeffs": {
        "v": -0.39999999999999997,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 7.782511086999875,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=2.9169743863820924e-16 cons=0.0 wall_s=17.737 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.9169743863820924e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(-3.791335e-8*v*x + v*(-0.099999994) - x)*4.0"
  ],
  "wall_s_total": 17.737371504999828,
  "wall_s_per_eq": [
    8.931401269000162,
    8.805970235999666
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.931401269000162,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-3.791335e-8*v*x + v*(-0.099999994) - x)*4.0",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 5.833948772764185e-16,
      "pred_coeffs": {
        "x*v": -1.516534e-07
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 8.805970235999666,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=1.3631562303821526e-15 cons=0.0 wall_s=17.878 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.3631562303821526e-15,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + x*(-4.331578) + x*0.3315778"
  ],
  "wall_s_total": 17.878455927000687,
  "wall_s_per_eq": [
    9.632382974000393,
    8.246072953000294
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.632382974000393,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + x*(-4.331578) + x*0.3315778",
      "r2_train": 0.9999999999999974,
      "reward": null,
      "residual_heldout": 2.726312460764305e-15,
      "pred_coeffs": {
        "v": -0.4,
        "x": -4.000000200000001
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.246072953000294,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=5.256759853078605e-17 cons=0.0 wall_s=17.250 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.256759853078605e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.24431464) + v*(-0.15568534) + x*(-4.0)"
  ],
  "wall_s_total": 17.250470668000162,
  "wall_s_per_eq": [
    8.727053481999974,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
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      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.727053481999974,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.24431464) + v*(-0.15568534) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.051351970615721e-16,
      "pred_coeffs": {
        "v": -0.39999998000000003,
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      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.523417186000188,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=1.0682705560466896e-16 cons=0.0 wall_s=17.972 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.0682705560466896e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.25512394) + v*(-0.18000945) + v*0.035133418 + x*(-4.0) - 8.623388e-9"
  ],
  "wall_s_total": 17.97189054899991,
  "wall_s_per_eq": [
    9.030896842999937,
    8.940993705999972
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.030896842999937,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.25512394) + v*(-0.18000945) + v*0.035133418 + x*(-4.0) - 8.623388e-9",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 2.1365411120933792e-16,
      "pred_coeffs": {
        "1": -8.623388e-09,
        "v": -0.3999999719999999,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.940993705999972,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=1.538402721459798e-16 cons=0.0 wall_s=16.967 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.538402721459798e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999992) - 1.0687532e-7*v + x*(-4.0)"
  ],
  "wall_s_total": 16.9666721349995,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.474365719999696,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999992) - 1.0687532e-7*v + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 3.076805442919596e-16,
      "pred_coeffs": {
        "v": -0.40000002687532,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.492306414999803,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=1.7164937792390565e-16 cons=0.0 wall_s=16.293 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.7164937792390565e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.3473896) + v*(-0.052610364) + x*(-4.0)"
  ],
  "wall_s_total": 16.293145091000042,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.285286543999973,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.3473896) + v*(-0.052610364) + x*(-4.0)",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 3.432987558478113e-16,
      "pred_coeffs": {
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      "true_coeffs": {
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        "v": -0.4
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      "wall_s": 8.007858547000069,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=3.0320023191001002e-19 cons=0.0 wall_s=17.106 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.0320023191001002e-19,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.21605992*v + x*(-1.67009) + (x - 3.912705e-9)*(-2.32991) - (v*0.18394008 - 1*(-7.82541e-9))"
  ],
  "wall_s_total": 17.106051330999435,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "pred_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.873023196999384,
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.21605992*v + x*(-1.67009) + (x - 3.912705e-9)*(-2.32991) - (v*0.18394008 - 1*(-7.82541e-9))",
      "r2_train": 1.0,
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      "wall_s": 8.233028134000051,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=2.3907637744610807e-33 cons=0.0 wall_s=16.600 ok=True

```json
{
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  "n_samples": 100,
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  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.3907637744610807e-33,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + x*(-2.2386065) + x*(-1.7613935)"
  ],
  "wall_s_total": 16.60043292699993,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
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      "r2_train": 1.0,
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      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.76134746200023,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + x*(-2.2386065) + x*(-1.7613935)",
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      "reward": null,
      "residual_heldout": 4.7815275489221615e-33,
      "pred_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.839085464999698,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.739 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A0_pysr",
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  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) - 4.0*x"
  ],
  "wall_s_total": 17.73867097799939,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 1.0,
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      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 9.111925117999817,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) - 4.0*x",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": -0.4,
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      "structure_ok": true,
      "wall_s": 8.626745859999573,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=5.025010510553668e-17 cons=0.0 wall_s=17.205 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.025010510553668e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-3.738681e-8*v + x*(-4.0) - 0.19999999*(v + v)"
  ],
  "wall_s_total": 17.20499675100018,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "structure_ok": true,
      "wall_s": 9.125981311999567,
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
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      "equation": "-3.738681e-8*v + x*(-4.0) - 0.19999999*(v + v)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.0050021021107336e-16,
      "pred_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.079015439000614,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=3.669095401198146e-17 cons=0.0 wall_s=16.934 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.669095401198146e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.05356942*v + x*(-4.0) - (v*0.34643057 - 1.0859921e-8)"
  ],
  "wall_s_total": 16.9340490099994,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "structure_ok": true,
      "wall_s": 9.108680123999875,
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    {
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      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=1.9740339443387697e-17 cons=0.0 wall_s=17.069 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.9740339443387697e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.65674937) - (-0.25674936)*v + x*(-4.0)"
  ],
  "wall_s_total": 17.068800327000645,
  "wall_s_per_eq": [
    8.843508433999887,
    8.225291893000758
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.843508433999887,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.65674937) - (-0.25674936)*v + x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.9480678886775394e-17,
      "pred_coeffs": {
        "v": -0.40000001,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.225291893000758,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=1.890295967479381e-16 cons=0.0 wall_s=17.337 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.890295967479381e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "x*(-4.0) + (v + (-(-4.0)*x - 0.4)*x*5.0916917e-8)*(-0.4) - 1.2729229e-8"
  ],
  "wall_s_total": 17.336767437999697,
  "wall_s_per_eq": [
    8.593085825999879,
    8.743681611999818
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.593085825999879,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*(-4.0) + (v + (-(-4.0)*x - 0.4)*x*5.0916917e-8)*(-0.4) - 1.2729229e-8",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.780591934958762e-16,
      "pred_coeffs": {
        "x^2": -8.14670672e-08,
        "1": -1.2729229e-08,
        "v": -0.4,
        "x": -3.999999991853293
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.743681611999818,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=False residual=9.484496233014386e-16 cons=0.6269967603761919 wall_s=14.538 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 9.484496233014386e-16,
  "conservation_residual": 0.6269967603761919,
  "equations": [
    "v",
    "(((w2-((-(w2)+w2)-w2))*(-(x)-x))+(gamma*v))"
  ],
  "wall_s_total": 14.538064371000473,
  "wall_s_per_eq": [
    7.668638885999826,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 4.930866897285691e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.668638885999826,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.668638885999826,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2-((-(w2)+w2)-w2))*(-(x)-x))+(gamma*v))",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 1.403812556874308e-15,
      "pred_coeffs": {
        "v": 1.0000000000223024,
        "x": 1.5999999998352659
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.869425485000647,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.869425485000647,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.39999999995881647,
        1.0000000000223024
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=False residual=1.8730074373931572e-12 cons=1.618838526336511 wall_s=13.879 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.8730074373931572e-12,
  "conservation_residual": 1.618838526336511,
  "equations": [
    "v",
    "((v*(((-(gamma)+-((gamma-gamma)))+gamma)-gamma))+(x*w2))"
  ],
  "wall_s_total": 13.878612442999838,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 3.436465570856896e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.129335186999924,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.129335186999924,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((v*(((-(gamma)+-((gamma-gamma)))+gamma)-gamma))+(x*w2))",
      "r2_train": 0.999999999996164,
      "reward": null,
      "residual_heldout": 3.745671228229229e-12,
      "pred_coeffs": {
        "v": 3.9999936388718855,
        "x": 0.399997093243776
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.749277255999914,
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      "wall_raw_s": 6.749277255999914,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.399997093243776,
        -3.9999936388718855
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=False residual=3.287405323269676e-14 cons=0.9976790556644539 wall_s=20.602 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.287405323269676e-14,
  "conservation_residual": 0.9976790556644539,
  "equations": [
    "v",
    "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))"
  ],
  "wall_s_total": 20.601791102999414,
  "wall_s_per_eq": [
    6.714278892999573,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999788,
      "reward": null,
      "residual_heldout": 2.963874878967826e-14,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.714278892999573,
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      "wall_raw_s": 6.714278892999573,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))",
      "r2_train": 0.9999999999999711,
      "reward": null,
      "residual_heldout": 3.610935767571527e-14,
      "pred_coeffs": {
        "v": 2.000000280746967,
        "x": 0.8000005260244604
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 13.88751220999984,
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      "wall_raw_s": 13.88751220999984,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4000002630122302,
        2.000000280746967
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5572698053501458 cons=0.0 wall_s=14.702 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5572698053501458,
  "conservation_residual": 0.0,
  "equations": [
    "2*v",
    "-(((gamma*v)+(x*((((-(w2)+w2)+w2)+w2)+w2))))"
  ],
  "wall_s_total": 14.701627083999483,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.05444541728836194,
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        "v": 2.0
      },
      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 7.509216317999744,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*v)+(x*((((-(w2)+w2)+w2)+w2)+w2))))",
      "r2_train": 0.9999999999995556,
      "reward": null,
      "residual_heldout": 6.628542202056971e-13,
      "pred_coeffs": {
        "v": -1.333334028352904,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 7.192410765999739,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.192410765999739,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4000011248820397,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=False residual=7.918166242754627e-16 cons=6.000370271234437 wall_s=14.916 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 7.918166242754627e-16,
  "conservation_residual": 6.000370271234437,
  "equations": [
    "v",
    "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))"
  ],
  "wall_s_total": 14.915650748999724,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 5.141789541645118e-16,
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        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.126475862000007,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.126475862000007,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))",
      "r2_train": 0.9999999999999962,
      "reward": null,
      "residual_heldout": 1.0694542943864136e-15,
      "pred_coeffs": {
        "v": 11.946666723440552,
        "x": -15.724760625489107
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.789174886999717,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.789174886999717,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.13333335239553945,
        3.9822222411468506
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=3.485679387696367e-11 cons=0.0 wall_s=14.107 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.485679387696367e-11,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))"
  ],
  "wall_s_total": 14.107098236999263,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.814807404000021,
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      "wall_raw_s": 6.814807404000021,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))",
      "r2_train": 0.9999999999319551,
      "reward": null,
      "residual_heldout": 6.971316502914691e-11,
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        "v": -4.000032540298272,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.292290832999242,
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      "wall_raw_s": 7.292290832999242,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.4000065053993404,
        -4.000032540298272
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=1.1618106251639329e-13 cons=0.0 wall_s=21.497 ok=True

```json
{
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  "n_samples": 100,
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  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.1618106251639329e-13,
  "conservation_residual": 0.0,
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    "v",
    "((-((((x+x)--((x-x)))*w2))+-((v*gamma)))-(w2*x))"
  ],
  "wall_s_total": 21.497073219999947,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "wall_s": 14.269582590000027,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((-((((x+x)--((x-x)))*w2))+-((v*gamma)))-(w2*x))",
      "r2_train": 0.9999999999997834,
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      "true_coeffs": {
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      "wall_s": 7.22749062999992,
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      "wall_raw_s": 7.22749062999992,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      "free_const_values": [
        0.4000006879355067,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=4.445069321532955e-15 cons=0.0 wall_s=14.307 ok=True

```json
{
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  "seed": 7,
  "recovered": false,
  "structure_ok": false,
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  "residual": 4.445069321532955e-15,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))"
  ],
  "wall_s_total": 14.306575209001494,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.123394669000845,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [],
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))",
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      "residual_heldout": 8.010229584839853e-15,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.183180540000649,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=1.195693810338888e-15 cons=0.0 wall_s=15.220 ok=True

```json
{
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  "n_samples": 100,
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  "recovered": false,
  "structure_ok": false,
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  "residual": 1.195693810338888e-15,
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    "v",
    "-(((w2*x)+(-((-(v)*gamma))+(x*w2))))"
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  "wall_s_total": 15.220199981000405,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "pred_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.404042799999843,
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      "free_const_values": [],
      "zero_eq": false,
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    {
      "eq_i": 1,
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      "equation": "-(((w2*x)+(-((-(v)*gamma))+(x*w2))))",
      "r2_train": 0.999999999999998,
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        "v": -2.00000003013215,
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        "max_n_evaluations": 2500,
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      "free_const_values": [
        0.3999999799043372,
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      "zero_eq": false,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=False residual=3.1683999035905444e-11 cons=2.316703913017492 wall_s=15.797 ok=True

```json
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  "residual": 3.1683999035905444e-11,
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    "v",
    "-((-((x*-(w2)))-(gamma*(v+(v-v)))))"
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  "wall_s_total": 15.797118090999902,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "free_const_values": [],
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    {
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=False residual=2.3821315295329664e-15 cons=4.722386816000213 wall_s=21.772 ok=True

```json
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    "(-(((gamma*v)+-((w2*x))))+(v*-(gamma)))"
  ],
  "wall_s_total": 21.771550791000664,
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  "wall_pad_s_total": 0.0,
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  ],
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    {
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        0.20000003661607973,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=1.190681862475906e-15 cons=0.0 wall_s=13.828 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.190681862475906e-15,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "((gamma*v)+(x*w2))"
  ],
  "wall_s_total": 13.828151391000574,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.218674366999949,
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      "wall_raw_s": 7.218674366999949,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((gamma*v)+(x*w2))",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 1.7816563551938717e-15,
      "pred_coeffs": {
        "v": -4.000000002767525,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 6.6094770240006255,
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      "wall_raw_s": 6.6094770240006255,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4000000007435082,
        -4.000000002767525
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=4.699161906274664e-13 cons=0.0 wall_s=14.524 ok=True

```json
{
  "law": "damped_oscillator",
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.699161906274664e-13,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "((w2*(-(((-(((x--(x))-x))-x)+x))+x))+(gamma*v))"
  ],
  "wall_s_total": 14.523900099000457,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.615701534999971,
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      "wall_raw_s": 7.615701534999971,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((w2*(-(((-(((x--(x))-x))-x)+x))+x))+(gamma*v))",
      "r2_train": 0.9999999999994738,
      "reward": null,
      "residual_heldout": 9.392444694882291e-13,
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        "v": -1.9999990741136953,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.908198564000486,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.908198564000486,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.3999981785657037,
        -1.9999990741136953
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=4.886780666178404e-13 cons=0.0 wall_s=14.226 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.886780666178404e-13,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(-((((v-(v+(v+v)))*gamma)--((gamma*v))))+(x*w2))"
  ],
  "wall_s_total": 14.225956899000266,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.136989317999905,
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      "wall_raw_s": 7.136989317999905,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((v-(v+(v+v)))*gamma)--((gamma*v))))+(x*w2))",
      "r2_train": 0.9999999999989598,
      "reward": null,
      "residual_heldout": 9.76691633050187e-13,
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        "v": -3.999997209766142,
        "x": -0.40000107279872427
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      "true_coeffs": {
        "x": -4.0,
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      "structure_ok": false,
      "wall_s": 7.088967581000361,
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      "wall_raw_s": 7.088967581000361,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.40000107279872427,
        -3.999997209766142
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=False residual=5.163433190102506e-12 cons=2.8140126967268957 wall_s=22.360 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 5.163433190102506e-12,
  "conservation_residual": 2.8140126967268957,
  "equations": [
    "v",
    "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))"
  ],
  "wall_s_total": 22.360495246000937,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 15.389470523000455,
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        "batch_size": 32,
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        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))",
      "r2_train": 0.9999999999909476,
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      "pred_coeffs": {
        "v": 3.999988396201289,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 6.9710247230004825,
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      "wall_raw_s": 6.9710247230004825,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.3999998593033733,
        3.999988396201289
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=False residual=6.462292701588487e-14 cons=2.5695542612454343 wall_s=17.718 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
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  "residual": 6.462292701588487e-14,
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  "equations": [
    "v",
    "(-(((-(v)*gamma)-((v*-(gamma))+-((v*gamma)))))+(w2*x))"
  ],
  "wall_s_total": 17.717894094000258,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "wall_s": 8.576394890000302,
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      "free_const_values": [],
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
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      "equation": "(-(((-(v)*gamma)-((v*-(gamma))+-((v*gamma)))))+(w2*x))",
      "r2_train": 0.9999999999998621,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.141499203999956,
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      "wall_raw_s": 9.141499203999956,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      },
      "free_const_values": [
        0.39999937114487577,
        -3.999999054458302
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    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=False residual=1.930114033872747e-13 cons=1.954401135626732 wall_s=30.044 ok=True

```json
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  "recovered": false,
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  "residual": 1.930114033872747e-13,
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    "v",
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  "wall_s_total": 30.04415276600048,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "free_const_values": [],
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    {
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        "max_n_evaluations": 2500,
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        -0.40000053883809966,
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=1.0041652671457586e-12 cons=0.0 wall_s=64.351 ok=True

```json
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  "arm": "A4_physo",
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  "recovered": false,
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  "residual": 1.0041652671457586e-12,
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    "v",
    "((-(x)*w2)+(v*-((gamma+gamma))))"
  ],
  "wall_s_total": 64.35141237899916,
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  "wall_pad_s_total": 0.0,
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  ],
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  "tau": 0.2,
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  "eq_results": [
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      "structure_ok": true,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((-(x)*w2)+(v*-((gamma+gamma))))",
      "r2_train": 0.9999999999983329,
      "reward": null,
      "residual_heldout": 2.0076810356494596e-12,
      "pred_coeffs": {
        "v": -8.000004082802125,
        "x": -0.20000127003971885
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 50.38640199599922,
      "wall_pad_s": 0.0,
      "wall_raw_s": 50.38640199599922,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.20000127003971885,
        4.000002041401062
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=2.1813978927705895e-13 cons=0.0 wall_s=115.866 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.1813978927705895e-13,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))"
  ],
  "wall_s_total": 115.86568660400008,
  "wall_s_per_eq": [
    53.69016824699975,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 5.138734228216416e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 53.69016824699975,
      "wall_pad_s": 0.0,
      "wall_raw_s": 53.69016824699975,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))",
      "r2_train": 0.9999999999997289,
      "reward": null,
      "residual_heldout": 4.3576570513129625e-13,
      "pred_coeffs": {
        "v": -8.00000150205388,
        "x": -0.20000056249739895
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 62.17551835700033,
      "wall_pad_s": 0.0,
      "wall_raw_s": 62.17551835700033,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.20000056249739895,
        4.00000075102694
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=False residual=6.100972628883505e-13 cons=2.5716551412139648 wall_s=135.751 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.100972628883505e-13,
  "conservation_residual": 2.5716551412139648,
  "equations": [
    "v",
    "-(((gamma*v)+(w2*-(x))))"
  ],
  "wall_s_total": 135.75115388299946,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 42.43870568799957,
      "wall_pad_s": 0.0,
      "wall_raw_s": 42.43870568799957,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*v)+(w2*-(x))))",
      "r2_train": 0.9999999999988776,
      "reward": null,
      "residual_heldout": 1.2195948568047822e-12,
      "pred_coeffs": {
        "v": 3.999996233150229,
        "x": 0.4000006540064823
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 93.31244819499989,
      "wall_pad_s": 0.0,
      "wall_raw_s": 93.31244819499989,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4000006540064823,
        -3.999996233150229
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=4.4072921533408484e-17 cons=0.0 wall_s=41.244 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.4072921533408484e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 41.24375737800074,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 31.856061223000324,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 8.814584306681697e-17,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.387696155000413,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.617 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) - 4.0*x"
  ],
  "wall_s_total": 19.61704789400028,
  "wall_s_per_eq": [
    10.026604622999912,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.026604622999912,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) - 4.0*x",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": -0.4,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.590443271000368,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=7.827214136291753e-17 cons=0.0 wall_s=19.586 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.827214136291753e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(-(-0.099999994)*v + x)*(-4.0)"
  ],
  "wall_s_total": 19.58568547899995,
  "wall_s_per_eq": [
    10.290853814000002,
    9.294831664999947
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.290853814000002,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(-0.099999994)*v + x)*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.5654428272583507e-16,
      "pred_coeffs": {
        "v": -0.399999976,
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      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.294831664999947,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.938 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + x*(-4.0)"
  ],
  "wall_s_total": 18.937781920000816,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.691024725000716,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": -0.4,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.2467571950001,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.720 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + x*(-4.0)"
  ],
  "wall_s_total": 17.719512239999858,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.769567682999877,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": -0.4,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.94994455699998,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=6.33245824486266e-17 cons=0.0 wall_s=18.162 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.33245824486266e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.39999998*v + x*(-4.0)"
  ],
  "wall_s_total": 18.162148024998714,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.26609429599921,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.39999998*v + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.266491648972532e-16,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.896053728999505,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=4.33271019215976e-17 cons=0.0 wall_s=18.023 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.33271019215976e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 18.023391491999973,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.025834410999778,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 8.66542038431952e-17,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.997557081000195,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=5.442432916617985e-17 cons=0.0 wall_s=18.345 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.442432916617985e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 18.344692919999943,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.022839104000013,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.088486583323597e-16,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.32185381599993,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.034 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(v*0.1 + x)*(-4.0)"
  ],
  "wall_s_total": 19.034472110000934,
  "wall_s_per_eq": [
    10.000960469000347,
    9.033511641000587
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.000960469000347,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v*0.1 + x)*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": -0.4,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.033511641000587,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=4.371040091165101e-17 cons=0.0 wall_s=18.000 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.371040091165101e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 17.999767073999465,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.899884309999834,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 8.742080182330202e-17,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.09988276399963,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=5.757524001757587e-17 cons=0.0 wall_s=17.695 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.757524001757587e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 17.695381628999712,
  "wall_s_per_eq": [
    9.403835240000262,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 1.0,
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      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 9.403835240000262,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.1515048003515174e-16,
      "pred_coeffs": {
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        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.29154638899945,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.987 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.4*v + x*(-4.0)"
  ],
  "wall_s_total": 18.987482168000497,
  "wall_s_per_eq": [
    10.02997667300042,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.02997667300042,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.4*v + x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": -0.4,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.957505495000078,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.685 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.4) + x*(-4.0)"
  ],
  "wall_s_total": 17.68454287700024,
  "wall_s_per_eq": [
    9.005147392000254,
    8.679395484999986
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.005147392000254,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4) + x*(-4.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": -0.4,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.679395484999986,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=6.901539263435666e-17 cons=0.0 wall_s=19.826 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.901539263435666e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.39999998*v + x*(-4.0)"
  ],
  "wall_s_total": 19.825542376000158,
  "wall_s_per_eq": [
    9.993348212000456,
    9.832194163999702
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.993348212000456,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.39999998*v + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.3803078526871332e-16,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.832194163999702,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=4.3557468115949774e-17 cons=0.0 wall_s=18.553 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.3557468115949774e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 18.552951125999243,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.821196090999365,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 8.711493623189955e-17,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.731755034999878,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=3.8731798123872545e-17 cons=0.0 wall_s=18.777 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.8731798123872545e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 18.777416640999945,
  "wall_s_per_eq": [
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    8.985279155000171
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.792137485999774,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 7.746359624774509e-17,
      "pred_coeffs": {
        "v": -0.39999998,
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      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.985279155000171,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=6.817565752968146e-17 cons=0.0 wall_s=18.465 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.817565752968146e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(v*0.099999994 + x)*(-4.0)"
  ],
  "wall_s_total": 18.464620606999233,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.471515977999843,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v*0.099999994 + x)*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.3635131505936291e-16,
      "pred_coeffs": {
        "v": -0.399999976,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.99310462899939,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=4.4254484667055244e-17 cons=0.0 wall_s=18.577 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.4254484667055244e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 18.576967386000433,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
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      },
      "structure_ok": true,
      "wall_s": 9.565223350000451,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 8.850896933411049e-17,
      "pred_coeffs": {
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        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.011744035999982,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=5.1897966350887383e-17 cons=0.0 wall_s=17.242 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.1897966350887383e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-0.39999998*v + x*(-4.0)"
  ],
  "wall_s_total": 17.24180195000008,
  "wall_s_per_eq": [
    8.461187470999903,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.461187470999903,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.39999998*v + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.0379593270177477e-16,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.780614479000178,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=3.803709221461632e-17 cons=0.0 wall_s=16.881 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.803709221461632e-17,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "v*(-0.39999998) + x*(-4.0)"
  ],
  "wall_s_total": 16.880791556000986,
  "wall_s_per_eq": [
    8.90330694900058,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.90330694900058,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39999998) + x*(-4.0)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 7.607418442923264e-17,
      "pred_coeffs": {
        "v": -0.39999998,
        "x": -4.0
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 7.977484607000406,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=1.0574462907490121e-15 cons=0.3466431753722546 wall_s=15.469 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.0574462907490121e-15,
  "conservation_residual": 0.3466431753722546,
  "equations": [
    "v",
    "(((w2-((-(w2)+w2)-w2))*(-(x)-x))+(gamma*v))"
  ],
  "wall_s_total": 15.469323329000872,
  "wall_s_per_eq": [
    8.738050784000734,
    6.731272545000138
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 7.780912047733613e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.738050784000734,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.738050784000734,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2-((-(w2)+w2)-w2))*(-(x)-x))+(gamma*v))",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 1.336801376724663e-15,
      "pred_coeffs": {
        "v": 1.0000000001555671,
        "x": 1.5999999986855478
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.731272545000138,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.731272545000138,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.39999999967138694,
        1.0000000001555671
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=False residual=1.6278615965136467e-13 cons=1.6137229294690083 wall_s=14.576 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.6278615965136467e-13,
  "conservation_residual": 1.6137229294690083,
  "equations": [
    "v",
    "((v*(((-(gamma)+-((gamma-gamma)))+gamma)-gamma))+(x*w2))"
  ],
  "wall_s_total": 14.575688802000514,
  "wall_s_per_eq": [
    7.52812560700022,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 4.822659698107653e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.52812560700022,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.52812560700022,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((v*(((-(gamma)+-((gamma-gamma)))+gamma)-gamma))+(x*w2))",
      "r2_train": 0.9999999999996404,
      "reward": null,
      "residual_heldout": 3.2509005333291855e-13,
      "pred_coeffs": {
        "v": 3.9999978374817062,
        "x": 0.3999993609383754
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.0475631950002935,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.0475631950002935,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3999993609383754,
        -3.9999978374817062
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=False residual=1.4061813670433104e-14 cons=0.9082432972697444 wall_s=14.701 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.4061813670433104e-14,
  "conservation_residual": 0.9082432972697444,
  "equations": [
    "v",
    "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))"
  ],
  "wall_s_total": 14.701260089000243,
  "wall_s_per_eq": [
    7.275956636000046,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999819,
      "reward": null,
      "residual_heldout": 2.4853664133766878e-14,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.275956636000046,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.275956636000046,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))",
      "r2_train": 0.9999999999999964,
      "reward": null,
      "residual_heldout": 3.2699632070993295e-15,
      "pred_coeffs": {
        "v": 2.0000000682320884,
        "x": 0.8000001998784138
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.425303453000197,
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      "wall_raw_s": 7.425303453000197,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4000000999392069,
        2.0000000682320884
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.552908806921434 cons=0.0 wall_s=14.894 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.552908806921434,
  "conservation_residual": 0.0,
  "equations": [
    "2*v",
    "-(((x*w2)+(-(((gamma+gamma)*-((v-v))))--((v*gamma)))))"
  ],
  "wall_s_total": 14.893747537999843,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.01268219705764162,
      "reward": null,
      "residual_heldout": 1.1058176138326008,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 7.558627694999814,
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      "wall_raw_s": 7.558627694999814,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((x*w2)+(-(((gamma+gamma)*-((v-v))))--((v*gamma)))))",
      "r2_train": 0.9999999999891878,
      "reward": null,
      "residual_heldout": 1.0267179977158308e-11,
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        "v": -3.9999873695882284,
        "x": -0.399997198891162
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 7.3351198430000295,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.3351198430000295,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        0.399997198891162,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=False residual=3.274477689753793e-14 cons=7.805792075053101 wall_s=15.100 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.274477689753793e-14,
  "conservation_residual": 7.805792075053101,
  "equations": [
    "v",
    "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))"
  ],
  "wall_s_total": 15.099622815000657,
  "wall_s_per_eq": [
    7.639935330000299,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
      },
      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 7.639935330000299,
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      "wall_raw_s": 7.639935330000299,
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      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))",
      "r2_train": 0.9999999999999327,
      "reward": null,
      "residual_heldout": 6.497954553015146e-14,
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        "v": 11.94666912584908,
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      "true_coeffs": {
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        "v": -0.4
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      "structure_ok": false,
      "wall_s": 7.459687485000359,
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      "wall_raw_s": 7.459687485000359,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.13333331765051162,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=1.642968175521709e-11 cons=0.0 wall_s=14.464 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.642968175521709e-11,
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    "v",
    "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))"
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  "wall_s_total": 14.463963241999409,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.520673451999755,
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      "wall_raw_s": 7.520673451999755,
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        "wall_cap_s": 120,
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))",
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        "v": -3.999978183462284,
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      "true_coeffs": {
        "x": -4.0,
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      "structure_ok": false,
      "wall_s": 6.943289789999653,
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      "wall_raw_s": 6.943289789999653,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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      "free_const_values": [
        -0.3999947043893291,
        -3.999978183462284
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=False residual=1.4137465341171646e-12 cons=4.042025814615776 wall_s=15.185 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.4137465341171646e-12,
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    "v",
    "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))"
  ],
  "wall_s_total": 15.18450773099994,
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  "tau": 0.2,
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  "eq_results": [
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.744864764999875,
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        "device": "cpu",
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))",
      "r2_train": 0.9999999999965158,
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      "true_coeffs": {
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      "wall_s": 7.439642966000065,
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      "wall_raw_s": 7.439642966000065,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "device": "cpu",
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=8.590908583407737e-15 cons=0.0 wall_s=16.241 ok=True

```json
{
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  "seed": 7,
  "recovered": false,
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  "accepted": true,
  "residual": 8.590908583407737e-15,
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    "v",
    "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))"
  ],
  "wall_s_total": 16.24053841500063,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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    {
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      "wall_raw_s": 7.905940851000196,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=1.285645730874847e-15 cons=0.0 wall_s=14.390 ok=True

```json
{
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  "residual": 1.285645730874847e-15,
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    "-(((w2*x)+(-((-(v)*gamma))+(x*w2))))"
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  "wall_s_total": 14.389527408000504,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "structure_ok": true,
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      "free_const_values": [],
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    {
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}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=False residual=9.572761489142236e-14 cons=2.0158494555450863 wall_s=15.183 ok=True

```json
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  "residual": 9.572761489142236e-14,
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  "wall_s_total": 15.183423586999197,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "free_const_values": [],
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    {
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        "max_n_evaluations": 2500,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=False residual=3.2681534824302325e-11 cons=4.950353664885032 wall_s=14.571 ok=True

```json
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  "wall_s_total": 14.571280691999164,
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    {
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=1.0888019543427009e-15 cons=0.0 wall_s=15.936 ok=True

```json
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  "residual": 1.0888019543427009e-15,
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  "wall_s_total": 15.935502376999466,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((gamma*v)+(x*w2))",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 1.4093650690370223e-15,
      "pred_coeffs": {
        "v": -4.00000002253405,
        "x": -0.39999998945637494
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 8.062372558999414,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.062372558999414,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.39999998945637494,
        -4.00000002253405
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=9.78789597629604e-16 cons=0.0 wall_s=14.849 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.78789597629604e-16,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "((w2*(-(((-(((x--(x))-x))-x)+x))+x))+(gamma*v))"
  ],
  "wall_s_total": 14.849077326999577,
  "wall_s_per_eq": [
    7.0003845499995805,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
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      "reward": null,
      "residual_heldout": 6.626352483395515e-16,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.0003845499995805,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.0003845499995805,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((w2*(-(((-(((x--(x))-x))-x)+x))+x))+(gamma*v))",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 1.2949439469196567e-15,
      "pred_coeffs": {
        "v": -1.9999999990151336,
        "x": -0.7999999993753972
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.848692776999997,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.848692776999997,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.3999999996876986,
        -1.9999999990151336
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=1.2116709178361714e-11 cons=0.0 wall_s=14.756 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.2116709178361714e-11,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-(((x*w2)+(gamma*v)))"
  ],
  "wall_s_total": 14.7555436370003,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.161518818999866,
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      "wall_raw_s": 8.161518818999866,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((x*w2)+(gamma*v)))",
      "r2_train": 0.9999999999752188,
      "reward": null,
      "residual_heldout": 2.4232849011188164e-11,
      "pred_coeffs": {
        "v": -3.999980660163958,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.594024818000435,
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      "wall_raw_s": 6.594024818000435,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3999956739351042,
        3.999980660163958
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=False residual=2.207260376005831e-13 cons=1.906679441336306 wall_s=14.907 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 2.207260376005831e-13,
  "conservation_residual": 1.906679441336306,
  "equations": [
    "v",
    "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))"
  ],
  "wall_s_total": 14.906717066000056,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.159727242000372,
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      "wall_raw_s": 8.159727242000372,
      "wall_cap_s": 120,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))",
      "r2_train": 0.9999999999994921,
      "reward": null,
      "residual_heldout": 4.4074042083632115e-13,
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        "v": 3.999997736558313,
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      "true_coeffs": {
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        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.746989823999684,
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      "wall_raw_s": 6.746989823999684,
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      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.4000006639351001,
        3.999997736558313
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=5.455444003861505e-14 cons=0.0 wall_s=16.589 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.455444003861505e-14,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(-(((x+(x+-(((x+-(x))+x))))*w2))+-((v*gamma)))"
  ],
  "wall_s_total": 16.589148507999198,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.401928528999633,
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      "wall_raw_s": 9.401928528999633,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(((x+(x+-(((x+-(x))+x))))*w2))+-((v*gamma)))",
      "r2_train": 0.9999999999998802,
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      "residual_heldout": 1.0854805834868894e-13,
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        "v": -3.99999909986545,
        "x": -0.3999994134544138
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 7.187219978999565,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.187219978999565,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3999994134544138,
        3.99999909986545
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=False residual=1.0317077933543465e-13 cons=2.096847984556182 wall_s=15.033 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
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  "residual": 1.0317077933543465e-13,
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  "equations": [
    "v",
    "(-((w2*x))+(gamma*v))"
  ],
  "wall_s_total": 15.033101971001088,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
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      "wall_s": 8.377728233000198,
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        "max_n_evaluations": 2500,
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      "free_const_values": [],
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
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      "r2_train": 0.9999999999997834,
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        "v": 3.9999985529548354,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 6.65537373800089,
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      "wall_raw_s": 6.65537373800089,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
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        "parallel_mode": false,
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      },
      "free_const_values": [
        -0.40000046723344823,
        3.9999985529548354
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=False residual=2.6059128735254555e-13 cons=1.8994491279850247 wall_s=16.590 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
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  "residual": 2.6059128735254555e-13,
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  "equations": [
    "v",
    "-(((v*gamma)--(((x*(gamma*(gamma-gamma)))+-((w2*x))))))"
  ],
  "wall_s_total": 16.589653255000485,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "structure_ok": true,
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      "budget": {
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      "free_const_values": [],
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((v*gamma)--(((x*(gamma*(gamma-gamma)))+-((w2*x))))))",
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      "true_coeffs": {
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      "wall_s": 6.981330027000695,
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      "wall_raw_s": 6.981330027000695,
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        "max_n_evaluations": 2500,
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        0.3999991591092379,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=3.3473126948023823e-14 cons=0.0 wall_s=15.178 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.3473126948023823e-14,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))"
  ],
  "wall_s_total": 15.177671639999971,
  "wall_s_per_eq": [
    8.548989003000315,
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 6.356075069853336e-16,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.548989003000315,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.548989003000315,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))",
      "r2_train": 0.9999999999999353,
      "reward": null,
      "residual_heldout": 6.631064638906232e-14,
      "pred_coeffs": {
        "v": -8.000000574077646,
        "x": -0.2000002513408721
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.628682636999656,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.628682636999656,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.2000002513408721,
        4.000000287038823
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=False residual=9.6185608122097e-13 cons=1.8317699066446387 wall_s=16.048 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 9.6185608122097e-13,
  "conservation_residual": 1.8317699066446387,
  "equations": [
    "v",
    "-(((gamma*v)+(w2*-(x))))"
  ],
  "wall_s_total": 16.04842423899845,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.816420630999346,
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      "wall_raw_s": 8.816420630999346,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*v)+(w2*-(x))))",
      "r2_train": 0.9999999999979349,
      "reward": null,
      "residual_heldout": 1.923027823316284e-12,
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        "v": 3.9999958771363104,
        "x": 0.3999976361094648
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.232003607999104,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.232003607999104,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        0.3999976361094648,
        -3.9999958771363104
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.006372925177172016 cons=0.0 wall_s=17.072 ok=True

```json
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006372925177172016,
  "conservation_residual": 0.0,
  "equations": [
    "x*(x - 0.3537587)*v*0.1751461 + v - 1*(-0.017350392)",
    "-0.39012066*v + x*(-3.9952197)"
  ],
  "wall_s_total": 17.07243678299892,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "reward": null,
      "residual_heldout": 0.005161082383660427,
      "pred_coeffs": {
        "x*v": -0.06195945664607,
        "1": 0.017350392
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.471890645999338,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.39012066*v + x*(-3.9952197)",
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      "reward": null,
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        "x": -3.9952197
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.600546136999583,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0048609705242976115 cons=0.0 wall_s=15.836 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0048609705242976115,
  "conservation_residual": 0.0,
  "equations": [
    "v - 1*0.020247072",
    "v*(-0.44119716) + x*(-4.0205684)"
  ],
  "wall_s_total": 15.836337553999329,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 1*0.020247072",
      "r2_train": 0.9952031281281778,
      "reward": null,
      "residual_heldout": 0.005602588814340387,
      "pred_coeffs": {
        "1": -0.020247072,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.707258083999477,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.44119716) + x*(-4.0205684)",
      "r2_train": 0.9963957684650656,
      "reward": null,
      "residual_heldout": 0.004119352234254835,
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        "x": -4.0205684
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      "true_coeffs": {
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        "v": -0.4
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      "structure_ok": true,
      "wall_s": 8.129079469999851,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.007949949485966282 cons=0.0 wall_s=16.133 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007949949485966282,
  "conservation_residual": 0.0,
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    "v*0.9834944",
    "v*(-0.39847282) + x*(-3.9487536)"
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  "wall_s_total": 16.132814792999852,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*0.9834944",
      "r2_train": 0.9913225308717952,
      "reward": null,
      "residual_heldout": 0.005349930300960467,
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        "v": 0.9834944
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.905333394000081,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
      "eq_i": 1,
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      "equation": "v*(-0.39847282) + x*(-3.9487536)",
      "r2_train": 0.9954106179217125,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.227481398999771,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.004298311646560028 cons=0.0 wall_s=16.009 ok=True

```json
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
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  "recovered": true,
  "structure_ok": true,
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  "residual": 0.004298311646560028,
  "conservation_residual": 0.0,
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    "v*0.9872055",
    "v*(-0.40422785) + x*(-4.00676)"
  ],
  "wall_s_total": 16.00903137200021,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "structure_ok": true,
      "wall_s": 8.290278966999722,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
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    {
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      "equation": "v*(-0.40422785) + x*(-4.00676)",
      "r2_train": 0.996831433572046,
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      "structure_ok": true,
      "wall_s": 7.718752405000487,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.008103415288060883 cons=0.0 wall_s=16.206 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008103415288060883,
  "conservation_residual": 0.0,
  "equations": [
    "v - 0.25661698*(x + 0.21493044)*(x*x - 1*0.5041854)",
    "v*(-0.39031118) + x*(-3.9288979)"
  ],
  "wall_s_total": 16.20647211799951,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "structure_ok": true,
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        "x": -3.9288979
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 7.950224088999676,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.0042501935270150195 cons=0.40633904986422176 wall_s=16.954 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0042501935270150195,
  "conservation_residual": 0.40633904986422176,
  "equations": [
    "v + (0.37801018 - (v*v + x))*(-1*v*0.016348233 - 1*0.030279566)",
    "v*(-0.38334522) + x*(-3.9298003)"
  ],
  "wall_s_total": 16.954344097000103,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + (0.37801018 - (v*v + x))*(-1*v*0.016348233 - 1*0.030279566)",
      "r2_train": 0.9963547696167033,
      "reward": null,
      "residual_heldout": 0.0035215753135393376,
      "pred_coeffs": {
        "v^2": 0.030279566,
        "x*v": 0.016348233,
        "1": -0.01144598419398188
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.508957783000369,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.38334522) + x*(-3.9298003)",
      "r2_train": 0.9948763064136454,
      "reward": null,
      "residual_heldout": 0.0049788117404907005,
      "pred_coeffs": {
        "v": -0.38334522,
        "x": -3.9298003
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.445386313999734,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.00552217405452608 cons=0.0 wall_s=16.429 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00552217405452608,
  "conservation_residual": 0.0,
  "equations": [
    "v*0.97940135",
    "v*(-0.3815613) + x*(-3.9492238)"
  ],
  "wall_s_total": 16.429141739999977,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v*0.97940135",
      "r2_train": 0.9970532429336636,
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      "residual_heldout": 0.006635199396835092,
      "pred_coeffs": {
        "v": 0.97940135
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.281119246999879,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.3815613) + x*(-3.9492238)",
      "r2_train": 0.9940568140219802,
      "reward": null,
      "residual_heldout": 0.004409148712217068,
      "pred_coeffs": {
        "v": -0.3815613,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.148022493000099,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.007459868868031825 cons=0.3410862557253728 wall_s=16.907 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007459868868031825,
  "conservation_residual": 0.3410862557253728,
  "equations": [
    "v - 0.11688359*x*x*(v + x) + 0.011882923",
    "-0.3818289*v + x*(-3.9779716)"
  ],
  "wall_s_total": 16.906587439999385,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 0.11688359*x*x*(v + x) + 0.011882923",
      "r2_train": 0.9951762262210293,
      "reward": null,
      "residual_heldout": 0.003970443190066087,
      "pred_coeffs": {
        "1": 0.011882923
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.148803287000192,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.3818289*v + x*(-3.9779716)",
      "r2_train": 0.9955354688494227,
      "reward": null,
      "residual_heldout": 0.010949294545997563,
      "pred_coeffs": {
        "v": -0.3818289,
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        "x": -4.0,
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      },
      "structure_ok": true,
      "wall_s": 8.757784152999193,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.004046822552898458 cons=0.0 wall_s=16.373 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004046822552898458,
  "conservation_residual": 0.0,
  "equations": [
    "v + x*(x*(v*v - 1*0.48354337)*0.14801414 - 0.04934892)",
    "v*(-0.42237905) + x*(-3.9760506)"
  ],
  "wall_s_total": 16.372781800000666,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + x*(x*(v*v - 1*0.48354337)*0.14801414 - 0.04934892)",
      "r2_train": 0.9983257865908785,
      "reward": null,
      "residual_heldout": 0.005904707320746732,
      "pred_coeffs": {
        "v": 1.0,
        "x": -0.04934892
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.09125965200019,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.42237905) + x*(-3.9760506)",
      "r2_train": 0.9942585791812436,
      "reward": null,
      "residual_heldout": 0.0021889377850501848,
      "pred_coeffs": {
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": true,
      "wall_s": 8.281522148000477,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.007931194140429728 cons=0.0 wall_s=16.042 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007931194140429728,
  "conservation_residual": 0.0,
  "equations": [
    "v*(0.97576785 + v*(-0.025551671))",
    "v*(-0.3955753) + x*(-4.0448656)"
  ],
  "wall_s_total": 16.042401812001117,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(0.97576785 + v*(-0.025551671))",
      "r2_train": 0.9953747128855492,
      "reward": null,
      "residual_heldout": 0.008312637771779001,
      "pred_coeffs": {
        "v^2": -0.025551671,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.6374057990005895,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.3955753) + x*(-4.0448656)",
      "r2_train": 0.9944421988733995,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.404996013000527,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.00751739127993999 cons=0.0 wall_s=16.798 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00751739127993999,
  "conservation_residual": 0.0,
  "equations": [
    "v*0.9781017",
    "v*(-0.4037948) - 4.0402827*x"
  ],
  "wall_s_total": 16.79796440499922,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*0.9781017",
      "r2_train": 0.9912640117144506,
      "reward": null,
      "residual_heldout": 0.008160230190355078,
      "pred_coeffs": {
        "v": 0.9781017
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.063990785999522,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4037948) - 4.0402827*x",
      "r2_train": 0.9971476735512754,
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      "pred_coeffs": {
        "v": -0.4037948,
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        "x": -4.0,
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      "structure_ok": true,
      "wall_s": 8.733973618999698,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.004706993624123882 cons=0.008494148900001981 wall_s=16.421 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004706993624123882,
  "conservation_residual": 0.008494148900001981,
  "equations": [
    "v + (v + 0.45998347)*(x*x*0.20275553 + (v + x)*0.05479831) - 0.045130536",
    "(-(-0.108298756)*v + x)*(-3.9527721)"
  ],
  "wall_s_total": 16.42134894100036,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v + (v + 0.45998347)*(x*x*0.20275553 + (v + x)*0.05479831) - 0.045130536",
      "r2_train": 0.9963860305859621,
      "reward": null,
      "residual_heldout": 0.0061723048587638265,
      "pred_coeffs": {
        "v^2": 0.05479831,
        "x*v": 0.05479831,
        "1": -0.045130536
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.354828651000389,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(-0.108298756)*v + x)*(-3.9527721)",
      "r2_train": 0.9957064377275313,
      "reward": null,
      "residual_heldout": 0.0032416823894839387,
      "pred_coeffs": {
        "v": -0.4280803011815076,
        "x": -3.9527721
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": true,
      "wall_s": 8.066520289999971,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.01067048318484149 cons=0.0 wall_s=16.019 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01067048318484149,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.44963205)*v*x*x*x + v",
    "v*(-0.44449693) + x*(-3.9795644)"
  ],
  "wall_s_total": 16.019448471000942,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-(-0.44963205)*v*x*x*x + v",
      "r2_train": 0.9947786306839864,
      "reward": null,
      "residual_heldout": 0.015271273514512016,
      "pred_coeffs": {
        "1": -0.002635381874421723,
        "v": 1.0057520551588104,
        "x": -0.0040469558488960625,
        "v^2": 0.011537931183941972,
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        "x^2": 0.003220455359348033,
        "v^3": 0.005848542631047294,
        "x*v^2": 0.02862520573769674,
        "x^2*v": -0.14899255956652027,
        "x^3": 0.0017332087424165935
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.846801702000448,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.44449693) + x*(-3.9795644)",
      "r2_train": 0.9953661563364292,
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      "structure_ok": true,
      "wall_s": 8.172646769000494,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.0038636219196594743 cons=0.0 wall_s=16.533 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0038636219196594743,
  "conservation_residual": 0.0,
  "equations": [
    "(x - 0.90312827)*v*0.20929945*(x*x - 0.15112472) + v",
    "-0.4020142*v + x*(-3.8745444)"
  ],
  "wall_s_total": 16.53290854199986,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "reward": null,
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      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.172337768000034,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.4020142*v + x*(-3.8745444)",
      "r2_train": 0.9938871815568237,
      "reward": null,
      "residual_heldout": 0.0033597525519200077,
      "pred_coeffs": {
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      "true_coeffs": {
        "x": -4.0,
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      "structure_ok": true,
      "wall_s": 8.360570773999825,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.008654633055447421 cons=0.0 wall_s=16.471 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008654633055447421,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.13598181)*v*v*x*(v + 1.2144916)*(v - x) + v",
    "-0.36176905*v + x*(-4.0067735)"
  ],
  "wall_s_total": 16.47130530999948,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-(-0.13598181)*v*v*x*(v + 1.2144916)*(v - x) + v",
      "r2_train": 0.9960313541802621,
      "reward": null,
      "residual_heldout": 0.007849706387976737,
      "pred_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.021616334999635,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.36176905*v + x*(-4.0067735)",
      "r2_train": 0.9958557557978295,
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      "structure_ok": true,
      "wall_s": 8.449688974999845,
      "wall_pad_s": 0.0,
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      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.011532565157008193 cons=0.3659801747601271 wall_s=16.058 ok=True

```json
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  "n_samples": 50,
  "arm": "A0_pysr",
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  "recovered": false,
  "structure_ok": false,
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  "residual": 0.011532565157008193,
  "conservation_residual": 0.3659801747601271,
  "equations": [
    "v*(x*(x - 0.45123506)*(x*x - 1*0.2278492) + 0.9953569)",
    "v*(-0.39484778) + x*(-3.9530678)"
  ],
  "wall_s_total": 16.057532821999303,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(x*(x - 0.45123506)*(x*x - 1*0.2278492) + 0.9953569)",
      "r2_train": 0.9958873784578416,
      "reward": null,
      "residual_heldout": 0.01172561027475366,
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        "x*v": 0.102813547432952
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      "structure_ok": false,
      "wall_s": 7.749088649999976,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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    },
    {
      "eq_i": 1,
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      "equation": "v*(-0.39484778) + x*(-3.9530678)",
      "r2_train": 0.9944951436623796,
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      "structure_ok": true,
      "wall_s": 8.308444171999326,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.007993576320459392 cons=0.0 wall_s=15.605 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007993576320459392,
  "conservation_residual": 0.0,
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    "v + x*0.04616727",
    "-0.4094292*v + x*(-3.9810636)"
  ],
  "wall_s_total": 15.605404246000035,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "structure_ok": true,
      "wall_s": 7.7941576880002685,
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      "free_const_values": null,
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    {
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      "target": "dv/dt",
      "equation": "-0.4094292*v + x*(-3.9810636)",
      "r2_train": 0.9960697630758851,
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      "wall_s": 7.811246557999766,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.005628897723299627 cons=0.22682440077741123 wall_s=15.765 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.005628897723299627,
  "conservation_residual": 0.22682440077741123,
  "equations": [
    "v + x*(v*(-0.05282625) - 0.05294716)",
    "v*(-0.42956886) + x*(-4.0141935)"
  ],
  "wall_s_total": 15.764867756000058,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.222706446000302,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0039006781990905052 cons=0.0 wall_s=16.357 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0039006781990905052,
  "conservation_residual": 0.0,
  "equations": [
    "v*(1.0180142 - v*(-0.025635319)) - 0.017742112",
    "(v*0.09786955 + x)*(-3.9672549)"
  ],
  "wall_s_total": 16.357323156000348,
  "wall_s_per_eq": [
    8.043587633000243,
    8.313735523000105
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(1.0180142 - v*(-0.025635319)) - 0.017742112",
      "r2_train": 0.9951705942484047,
      "reward": null,
      "residual_heldout": 0.003353466161481444,
      "pred_coeffs": {
        "v^2": 0.025635319,
        "1": -0.017742112,
        "v": 1.0180142
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.043587633000243,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v*0.09786955 + x)*(-3.9672549)",
      "r2_train": 0.9961737726322706,
      "reward": null,
      "residual_heldout": 0.0044478902366995665,
      "pred_coeffs": {
        "v": -0.388273451798295,
        "x": -3.9672549
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.313735523000105,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=50 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.005635887349401545 cons=0.0 wall_s=15.944 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005635887349401545,
  "conservation_residual": 0.0,
  "equations": [
    "v + (v*v*(v*(-x)*x - 0.16354913) - 1*(-0.18057466))*(-0.10030394)",
    "v*(-0.39581928) + x*(-3.93368)"
  ],
  "wall_s_total": 15.944383381999614,
  "wall_s_per_eq": [
    8.065583427000092,
    7.878799954999522
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + (v*v*(v*(-x)*x - 0.16354913) - 1*(-0.18057466))*(-0.10030394)",
      "r2_train": 0.99564198647872,
      "reward": null,
      "residual_heldout": 0.004723102716360316,
      "pred_coeffs": {
        "v^2": 0.016404622122572196,
        "1": -0.0181123498621604,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.065583427000092,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39581928) + x*(-3.93368)",
      "r2_train": 0.9941218617173255,
      "reward": null,
      "residual_heldout": 0.006548671982442774,
      "pred_coeffs": {
        "v": -0.39581928,
        "x": -3.93368
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 7.878799954999522,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=False residual=0.0054458974862525746 cons=1.2416848738947404 wall_s=16.817 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.0054458974862525746,
  "conservation_residual": 1.2416848738947404,
  "equations": [
    "v",
    "(((w2-(w2+w2))*((-(x)+x)-(x+x)))-(gamma*v))"
  ],
  "wall_s_total": 16.816525708999507,
  "wall_s_per_eq": [
    9.74837785499949,
    7.068147854000017
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9946662315879548,
      "reward": null,
      "residual_heldout": 0.003305084539400007,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.74837785499949,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.74837785499949,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2-(w2+w2))*((-(x)+x)-(x+x)))-(gamma*v))",
      "r2_train": 0.9958251078545229,
      "reward": null,
      "residual_heldout": 0.007586710433105142,
      "pred_coeffs": {
        "v": 1.997623921528036,
        "x": 0.7802037156925438
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.068147854000017,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.068147854000017,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3901018578462719,
        -1.997623921528036
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=False residual=0.004784658767463709 cons=2.992611336022128 wall_s=15.565 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.004784658767463709,
  "conservation_residual": 2.992611336022128,
  "equations": [
    "v",
    "((v*(((-(gamma)+-((gamma-gamma)))+gamma)-gamma))+(x*w2))"
  ],
  "wall_s_total": 15.564587478000249,
  "wall_s_per_eq": [
    6.950824450000255,
    8.613763027999994
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9943273659888515,
      "reward": null,
      "residual_heldout": 0.005449690129765435,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.950824450000255,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.950824450000255,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((v*(((-(gamma)+-((gamma-gamma)))+gamma)-gamma))+(x*w2))",
      "r2_train": 0.9963957687241726,
      "reward": null,
      "residual_heldout": 0.004119627405161983,
      "pred_coeffs": {
        "v": 4.020544578266896,
        "x": 0.4412087639687615
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 8.613763027999994,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.613763027999994,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4412087639687615,
        -4.020544578266896
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=False residual=0.0075363202505479504 cons=1.514396089795319 wall_s=16.587 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.0075363202505479504,
  "conservation_residual": 1.514396089795319,
  "equations": [
    "v",
    "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))"
  ],
  "wall_s_total": 16.586775818000206,
  "wall_s_per_eq": [
    6.997624702999929,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9909203438789138,
      "reward": null,
      "residual_heldout": 0.004523148606904743,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.997624702999929,
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      "wall_raw_s": 6.997624702999929,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))",
      "r2_train": 0.9954106180057503,
      "reward": null,
      "residual_heldout": 0.010549491894191158,
      "pred_coeffs": {
        "v": 1.9743809035421562,
        "x": 0.7969985923181618
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 9.589151115000277,
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      "wall_raw_s": 9.589151115000277,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.3984992961590809,
        1.9743809035421562
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.7677277925444869 cons=3.5861664424514017 wall_s=14.007 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.7677277925444869,
  "conservation_residual": 3.5861664424514017,
  "equations": [
    "2*v",
    "-(((-(((-(gamma)*x)*gamma))+(w2*x))-(v*gamma)))"
  ],
  "wall_s_total": 14.007090015000358,
  "wall_s_per_eq": [
    7.226875965000545,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.3477140514954502,
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        "v": 2.0
      },
      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 7.226875965000545,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((-(((-(gamma)*x)*gamma))+(w2*x))-(v*gamma)))",
      "r2_train": 0.9968314338025569,
      "reward": null,
      "residual_heldout": 0.002283291719194803,
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        "v": 3.843365104323538,
        "x": -14.36723227403612
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      "true_coeffs": {
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        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.780214049999813,
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      "wall_raw_s": 6.780214049999813,
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      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.40422305109576206,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=False residual=0.003655895045430125 cons=6.823063404299005 wall_s=15.739 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.003655895045430125,
  "conservation_residual": 6.823063404299005,
  "equations": [
    "v",
    "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))"
  ],
  "wall_s_total": 15.73929329800012,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
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      "wall_raw_s": 9.187302309999723,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))",
      "r2_train": 0.9966307212051142,
      "reward": null,
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        "v": 11.735888128697937,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.551990988000398,
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      "wall_raw_s": 6.551990988000398,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.13010487742032997,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.004215706126737474 cons=0.0 wall_s=16.179 ok=True

```json
{
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  "n_samples": 50,
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  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004215706126737474,
  "conservation_residual": 0.0,
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    "v",
    "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))"
  ],
  "wall_s_total": 16.178730875999463,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.972027618999164,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))",
      "r2_train": 0.9948763064749405,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.206703257000299,
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      "wall_raw_s": 7.206703257000299,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      "free_const_values": [
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        -3.929738507747893
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=False residual=0.00528288205101524 cons=3.907732965612894 wall_s=16.333 ok=True

```json
{
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  "n_samples": 50,
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  "recovered": false,
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  "residual": 0.00528288205101524,
  "conservation_residual": 3.907732965612894,
  "equations": [
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    "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))"
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  "wall_s_total": 16.332733424000253,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "free_const_values": [],
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    {
      "eq_i": 1,
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      "equation": "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))",
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      "wall_raw_s": 9.147944524000195,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      "free_const_values": [
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        -3.9856654078599907
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.007269169464981673 cons=0.0 wall_s=14.306 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
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  "recovered": false,
  "structure_ok": false,
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  "residual": 0.007269169464981673,
  "conservation_residual": 0.0,
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    "v",
    "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))"
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  "wall_s_total": 14.305804933999752,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "structure_ok": true,
      "wall_s": 7.270905923999635,
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        "max_n_evaluations": 2500,
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      "free_const_values": [],
      "zero_eq": false,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))",
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      "wall_raw_s": 7.034899010000117,
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        "max_n_evaluations": 2500,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.0036147375937998823 cons=0.0 wall_s=16.449 ok=True

```json
{
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  "n_samples": 50,
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  "seed": 8,
  "recovered": false,
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  "residual": 0.0036147375937998823,
  "conservation_residual": 0.0,
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  "wall_s_total": 16.44947444099944,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 9.58873130899974,
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      "free_const_values": [],
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((w2*x)+(-((-(v)*gamma))+(x*w2))))",
      "r2_train": 0.9942585787285819,
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      "wall_s": 6.860743131999698,
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      "wall_raw_s": 6.860743131999698,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=False residual=0.006833619128060446 cons=1.0773045137147317 wall_s=16.555 ok=True

```json
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  "wall_s_total": 16.555206545000146,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "wall_s": 7.364094157000181,
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      "free_const_values": [],
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    {
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      "equation": "-((-((x*-(w2)))-(gamma*(v+(v-v)))))",
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      "wall_s": 9.191112387999965,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=False residual=0.007328991112591163 cons=3.0335145892105926 wall_s=14.002 ok=True

```json
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  "n_samples": 50,
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  "recovered": false,
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  "residual": 0.007328991112591163,
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    "(-(((gamma*v)+-((w2*x))))+(v*-(gamma)))"
  ],
  "wall_s_total": 14.002136683999197,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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    {
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        "v": 8.08060795944457,
        "x": 0.20190030461121766
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.0272308029998385,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.0272308029998385,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.20190030461121766,
        -4.040303979722285
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.003732533530245913 cons=0.0 wall_s=16.321 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003732533530245913,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "((gamma*v)+(x*w2))"
  ],
  "wall_s_total": 16.320820968999215,
  "wall_s_per_eq": [
    6.891464654999254,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9935276705141778,
      "reward": null,
      "residual_heldout": 0.004223888528650065,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.891464654999254,
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      "wall_raw_s": 6.891464654999254,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((gamma*v)+(x*w2))",
      "r2_train": 0.9957064369135559,
      "reward": null,
      "residual_heldout": 0.0032411785318417607,
      "pred_coeffs": {
        "v": -3.9527478140944985,
        "x": -0.42806701952610227
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      "true_coeffs": {
        "x": -4.0,
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      "structure_ok": false,
      "wall_s": 9.42935631399996,
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      "wall_raw_s": 9.42935631399996,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.42806701952610227,
        -3.9527478140944985
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=False residual=0.007173698130983149 cons=3.5039934472059686 wall_s=13.944 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.007173698130983149,
  "conservation_residual": 3.5039934472059686,
  "equations": [
    "v",
    "(-((v*-((-((gamma+-((gamma-gamma))))-gamma))))+(x*w2))"
  ],
  "wall_s_total": 13.943623003000539,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.1233258150004986,
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      "wall_raw_s": 7.1233258150004986,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((v*-((-((gamma+-((gamma-gamma))))-gamma))))+(x*w2))",
      "r2_train": 0.9953661569228737,
      "reward": null,
      "residual_heldout": 0.00606953664793868,
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        "v": 7.959100731225223,
        "x": 0.22224935391707248
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.8202971880000405,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.8202971880000405,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.22224935391707248,
        -3.9795503656126114
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.003211474899962564 cons=0.0 wall_s=16.620 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003211474899962564,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(-((((v-(v+(v+v)))*gamma)--((gamma*v))))+(x*w2))"
  ],
  "wall_s_total": 16.620233088999157,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.845023023999602,
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      "wall_raw_s": 9.845023023999602,
      "wall_cap_s": 120,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((v-(v+(v+v)))*gamma)--((gamma*v))))+(x*w2))",
      "r2_train": 0.9938871815331993,
      "reward": null,
      "residual_heldout": 0.0033602751165427423,
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        "v": -3.8745138641663814,
        "x": -0.40201318679406045
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 6.7752100649995555,
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      "wall_raw_s": 6.7752100649995555,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.40201318679406045,
        -3.8745138641663814
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=False residual=0.006528225766405559 cons=2.9274581506919497 wall_s=13.956 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.006528225766405559,
  "conservation_residual": 2.9274581506919497,
  "equations": [
    "v",
    "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))"
  ],
  "wall_s_total": 13.956368297999688,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.8965475959994365,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))",
      "r2_train": 0.9958557547395049,
      "reward": null,
      "residual_heldout": 0.009459737117729948,
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        "v": 4.006762530462315,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.059820702000252,
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      "wall_raw_s": 7.059820702000252,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.3617639056662492,
        4.006762530462315
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.010017639577815957 cons=0.0 wall_s=16.905 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.010017639577815957,
  "conservation_residual": 0.0,
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    "v",
    "-((-((-(v)*(-((gamma--(gamma)))-gamma)))-(x*w2)))"
  ],
  "wall_s_total": 16.90521986300064,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 9.881189805000758,
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        "max_n_evaluations": 2500,
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        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-((-(v)*(-((gamma--(gamma)))-gamma)))-(x*w2)))",
      "r2_train": 0.9944951441933017,
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        "v": -11.859118662221736,
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      "structure_ok": false,
      "wall_s": 7.02403005799988,
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      "wall_raw_s": 7.02403005799988,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "device": "cpu",
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      },
      "free_const_values": [
        -0.13161146643848817,
        -3.953039554073912
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      "zero_eq": false,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=False residual=0.007459676357844993 cons=1.4748967050681283 wall_s=16.982 ok=True

```json
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  "n_samples": 50,
  "arm": "A4_physo",
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  "recovered": false,
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  "residual": 0.007459676357844993,
  "conservation_residual": 1.4748967050681283,
  "equations": [
    "v",
    "(-(((gamma*v)--((-((w2-w2))*x))))+(w2*x))"
  ],
  "wall_s_total": 16.982057421000718,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.085039813000549,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [],
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(((gamma*v)--((-((w2-w2))*x))))+(w2*x))",
      "r2_train": 0.9960697638279715,
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        "v": 3.9810144939539276,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.89701760800017,
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      "wall_raw_s": 9.89701760800017,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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      "free_const_values": [
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=False residual=0.00402403832629902 cons=2.2365166837391053 wall_s=13.766 ok=True

```json
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.00402403832629902,
  "conservation_residual": 2.2365166837391053,
  "equations": [
    "v",
    "-(((v*gamma)--(((x*(gamma*(gamma-gamma)))+-((w2*x))))))"
  ],
  "wall_s_total": 13.766017261000343,
  "wall_s_per_eq": [
    7.080052627999976,
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9958064883726113,
      "reward": null,
      "residual_heldout": 0.005024429377043939,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.080052627999976,
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      "wall_raw_s": 7.080052627999976,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((v*gamma)--(((x*(gamma*(gamma-gamma)))+-((w2*x))))))",
      "r2_train": 0.9955400247696714,
      "reward": null,
      "residual_heldout": 0.003023647275554101,
      "pred_coeffs": {
        "v": 4.01413167828822,
        "x": 0.42954451558533296
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.685964633000367,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.685964633000367,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.42954451558533296,
        -4.01413167828822
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.0036927443059822547 cons=0.0 wall_s=17.257 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0036927443059822547,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))"
  ],
  "wall_s_total": 17.256911575999766,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.817730193999523,
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      "wall_raw_s": 6.817730193999523,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))",
      "r2_train": 0.9961737721743689,
      "reward": null,
      "residual_heldout": 0.004447891057324028,
      "pred_coeffs": {
        "v": -7.934508439368046,
        "x": -0.19413605218155447
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      "true_coeffs": {
        "x": -4.0,
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      "structure_ok": false,
      "wall_s": 10.439181382000243,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.439181382000243,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.19413605218155447,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=50 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=False residual=0.005305134758491114 cons=2.3550737475985932 wall_s=14.057 ok=True

```json
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.005305134758491114,
  "conservation_residual": 2.3550737475985932,
  "equations": [
    "v",
    "-(((gamma*v)+(w2*-(x))))"
  ],
  "wall_s_total": 14.057174836999366,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": true,
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      "wall_raw_s": 7.272965778999605,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
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      "structure_ok": false,
      "wall_s": 6.78420905799976,
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      "wall_raw_s": 6.78420905799976,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.39583197138353987,
        -3.933750937635076
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.007049025320150988 cons=0.0 wall_s=16.513 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007049025320150988,
  "conservation_residual": 0.0,
  "equations": [
    "(v - x*x*(v*(v + 0.44669485)*x*(-0.25182915) + 0.036507666))*1.0097737",
    "v*(-0.40111157) + x*(-3.9865181)"
  ],
  "wall_s_total": 16.51264785500007,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(v - x*x*(v*(v + 0.44669485)*x*(-0.25182915) + 0.036507666))*1.0097737",
      "r2_train": 0.9933529598123805,
      "reward": null,
      "residual_heldout": 0.004781547642504839,
      "pred_coeffs": {
        "x^2": -0.0368644809751842
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 7.981155800000124,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.40111157) + x*(-3.9865181)",
      "r2_train": 0.9965875759230427,
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        "x": -3.9865181
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.531492054999944,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.007699236825431071 cons=0.0 wall_s=18.964 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
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  "residual": 0.007699236825431071,
  "conservation_residual": 0.0,
  "equations": [
    "v - (-0.22598325)*x*x*(v + 0.23529081)*(v*x + x)",
    "(v*(-0.11327574) - x)*4.046225"
  ],
  "wall_s_total": 18.964453304000017,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v - (-0.22598325)*x*x*(v + 0.23529081)*(v*x + x)",
      "r2_train": 0.9948249566941733,
      "reward": null,
      "residual_heldout": 0.008336866519171225,
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        "x": 0.010099764873933086,
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        "x*v": 0.054514729339813314,
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        "v^3": -0.004335806708609754,
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        "x^2*v": -0.03723893093097791,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.580565819000185,
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      "wall_raw_s": null,
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        "wall_cap_s": 120,
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      "free_const_values": null,
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    {
      "eq_i": 1,
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        "v": -0.4
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      "wall_s": 10.383887484999832,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.004935834821801766 cons=0.0 wall_s=18.343 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004935834821801766,
  "conservation_residual": 0.0,
  "equations": [
    "v - (-1)*0.025941946*x",
    "v*(-0.39839894) + x*(-3.977722)"
  ],
  "wall_s_total": 18.34279038600016,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "target": "dx/dt",
      "equation": "v - (-1)*0.025941946*x",
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      "structure_ok": true,
      "wall_s": 8.605622066000251,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39839894) + x*(-3.977722)",
      "r2_train": 0.9949146735169325,
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      "structure_ok": true,
      "wall_s": 9.73716831999991,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.004133964493848814 cons=0.0 wall_s=18.106 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004133964493848814,
  "conservation_residual": 0.0,
  "equations": [
    "v*(x*x*0.116610765 + 0.97861755)",
    "v*(-0.4024355) + x*(-4.010909)"
  ],
  "wall_s_total": 18.106210554000427,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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        "v": 0.9786175499999996,
        "x^2*v": 0.11661076500000048
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      "structure_ok": true,
      "wall_s": 8.851193188000252,
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      "wall_raw_s": null,
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        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4024355) + x*(-4.010909)",
      "r2_train": 0.9962089927213136,
      "reward": null,
      "residual_heldout": 0.003824159361946268,
      "pred_coeffs": {
        "v": -0.4024355,
        "x": -4.010909
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.255017366000175,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0055552377888182305 cons=0.0 wall_s=17.684 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0055552377888182305,
  "conservation_residual": 0.0,
  "equations": [
    "v*(0.97851354 - (-0.09245941)*x*x)",
    "(-(-0.10604619)*v + x)*(-4.020515)"
  ],
  "wall_s_total": 17.68396016800034,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(0.97851354 - (-0.09245941)*x*x)",
      "r2_train": 0.9958391937020954,
      "reward": null,
      "residual_heldout": 0.003748261734645247,
      "pred_coeffs": {
        "v": 0.9785135399999998,
        "x^2*v": 0.0924594100000009
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.794681761999527,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(-0.10604619)*v + x)*(-4.020515)",
      "r2_train": 0.9953913265297666,
      "reward": null,
      "residual_heldout": 0.0073622138429912136,
      "pred_coeffs": {
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": true,
      "wall_s": 8.889278406000813,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.003911005524948696 cons=0.0 wall_s=17.779 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003911005524948696,
  "conservation_residual": 0.0,
  "equations": [
    "v*0.9904022",
    "v*(-0.42184594) + x*(-3.9524684)"
  ],
  "wall_s_total": 17.7785258670001,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v*0.9904022",
      "r2_train": 0.9955637912244611,
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      "residual_heldout": 0.004178921532980457,
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        "v": 0.9904022
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.562265016999845,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.42184594) + x*(-3.9524684)",
      "r2_train": 0.9948235396866236,
      "reward": null,
      "residual_heldout": 0.003643089516916935,
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        "v": -0.42184594,
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      "structure_ok": true,
      "wall_s": 9.216260850000253,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.006760798884550773 cons=0.08285047573763514 wall_s=17.314 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006760798884550773,
  "conservation_residual": 0.08285047573763514,
  "equations": [
    "(v - (x + 0.1405202)*(v*(-0.19303259)*(0.3286266 - v) - 0.046091303))*0.97696054",
    "(v*(-0.098832764) - x)*4.039716"
  ],
  "wall_s_total": 17.31417966599929,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(v - (x + 0.1405202)*(v*(-0.19303259)*(0.3286266 - v) - 0.046091303))*0.97696054",
      "r2_train": 0.9943828726958707,
      "reward": null,
      "residual_heldout": 0.010120850467775751,
      "pred_coeffs": {
        "x*v": 0.06197412076435142,
        "1": 0.006327538083242016
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.28507252199961,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v*(-0.098832764) - x)*4.039716",
      "r2_train": 0.9946104947219884,
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      "true_coeffs": {
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        "v": -0.4
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      "structure_ok": true,
      "wall_s": 9.029107143999681,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.008512865861678352 cons=0.0 wall_s=17.444 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008512865861678352,
  "conservation_residual": 0.0,
  "equations": [
    "v - 1*0.007913558",
    "v*(-0.43690902) + x*(-4.0475125)"
  ],
  "wall_s_total": 17.443867646999024,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 1*0.007913558",
      "r2_train": 0.9954189540332249,
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      "residual_heldout": 0.004244006781409012,
      "pred_coeffs": {
        "1": -0.007913558,
        "v": 1.0
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.257941597999888,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.43690902) + x*(-4.0475125)",
      "r2_train": 0.9938697977306679,
      "reward": null,
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      "structure_ok": true,
      "wall_s": 9.185926048999136,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.007322800683158416 cons=0.0 wall_s=17.721 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007322800683158416,
  "conservation_residual": 0.0,
  "equations": [
    "v*(1.0142232 - 0.14431989*x*x)",
    "-0.41290092*v + x*(-3.9761298)"
  ],
  "wall_s_total": 17.7212811039999,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v*(1.0142232 - 0.14431989*x*x)",
      "r2_train": 0.9958775268913235,
      "reward": null,
      "residual_heldout": 0.006481208154210104,
      "pred_coeffs": {
        "v": 1.0142232000000002,
        "x^2*v": -0.14431989000000012
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      "wall_s": 8.956080663999273,
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        "wall_cap_s": 120,
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      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.41290092*v + x*(-3.9761298)",
      "r2_train": 0.9961616828720102,
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      "structure_ok": true,
      "wall_s": 8.765200440000626,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.006001961178674794 cons=0.0 wall_s=17.459 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006001961178674794,
  "conservation_residual": 0.0,
  "equations": [
    "v - 1*0.015138202",
    "v*(-0.40533778) - 3.9604123*x"
  ],
  "wall_s_total": 17.458613929999956,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "equation": "v - 1*0.015138202",
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        "1": -0.015138202,
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      "structure_ok": true,
      "wall_s": 8.09760123399974,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.40533778) - 3.9604123*x",
      "r2_train": 0.9942169887648523,
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      "structure_ok": true,
      "wall_s": 9.361012696000216,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.006292260232494786 cons=0.0 wall_s=17.415 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006292260232494786,
  "conservation_residual": 0.0,
  "equations": [
    "v*(v*v*x*(x*(-0.21579906)*x + 0.06848774) + 1.0191082)",
    "v*(-0.41324696) + x*(-3.9792717)"
  ],
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  "wall_pad_s_total": 0.0,
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    0.0,
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v*(v*v*x*(x*(-0.21579906)*x + 0.06848774) + 1.0191082)",
      "r2_train": 0.9965108822427137,
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.55970581299971,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.41324696) + x*(-3.9792717)",
      "r2_train": 0.9951195894209344,
      "reward": null,
      "residual_heldout": 0.006550435332345241,
      "pred_coeffs": {
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.85576680000031,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.00586423644357538 cons=0.05642528772379207 wall_s=17.672 ok=True

```json
{
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  "residual": 0.00586423644357538,
  "conservation_residual": 0.05642528772379207,
  "equations": [
    "v + (x - (v*(-x*(-v + x)) - x))*(v*0.06695319 + 0.015505814)",
    "v*(-0.40233234) + x*(-3.9916992)"
  ],
  "wall_s_total": 17.671927702000175,
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  "wall_pad_s_total": 0.0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
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      "wall_s": 8.595833719999973,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.006199304747152171 cons=0.0 wall_s=17.622 ok=True

```json
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  "residual": 0.006199304747152171,
  "conservation_residual": 0.0,
  "equations": [
    "v*(v*v*(-0.02589191) - 1*(-1.0217804))",
    "v*(-0.3715947) - 3.9939091*x"
  ],
  "wall_s_total": 17.62238789300045,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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    {
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0059641585727069745 cons=0.0 wall_s=17.509 ok=True

```json
{
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  "seed": 13,
  "recovered": true,
  "structure_ok": true,
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  "residual": 0.0059641585727069745,
  "conservation_residual": 0.0,
  "equations": [
    "v + ((-v)*v + 0.74634856)*(x - 0.2784739)*x*0.098912634",
    "-0.39036658*v + x*(-4.039331)"
  ],
  "wall_s_total": 17.50862835299995,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "equation": "v + ((-v)*v + 0.74634856)*(x - 0.2784739)*x*0.098912634",
      "r2_train": 0.9958746232323169,
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      "wall_s": 8.735841468999752,
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      "free_const_values": null,
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    {
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      "r2_train": 0.9948395227199522,
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      "wall_s": 8.772786884000197,
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}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.00492301763612313 cons=0.0 wall_s=16.234 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
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  "residual": 0.00492301763612313,
  "conservation_residual": 0.0,
  "equations": [
    "v - x*(x*x*0.12643129 - 0.0581252)",
    "v*(-0.40200862) - 4.0230513*x"
  ],
  "wall_s_total": 16.234351824999976,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "equation": "v - x*(x*x*0.12643129 - 0.0581252)",
      "r2_train": 0.9946007290729876,
      "reward": null,
      "residual_heldout": 0.005102213692926862,
      "pred_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.374340336000387,
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.40200862) - 4.0230513*x",
      "r2_train": 0.9947300600577386,
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      "structure_ok": true,
      "wall_s": 7.860011488999589,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.005044180865086139 cons=0.0 wall_s=16.339 ok=True

```json
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  "seed": 15,
  "recovered": true,
  "structure_ok": true,
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  "residual": 0.005044180865086139,
  "conservation_residual": 0.0,
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    "v + x*(v + x)*x*0.07448362",
    "-0.39597145*v + x*(-3.9526289)"
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  "wall_s_total": 16.3389747049996,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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        "v": 1.0000000000000004,
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      "free_const_values": null,
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    {
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      "r2_train": 0.9955067684719692,
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      "structure_ok": true,
      "wall_s": 8.331837712999913,
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        "timeout_in_seconds": 100,
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  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.008896190456048518 cons=0.19222937510797833 wall_s=16.385 ok=True

```json
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  "n_samples": 100,
  "arm": "A0_pysr",
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  "recovered": false,
  "structure_ok": false,
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  "residual": 0.008896190456048518,
  "conservation_residual": 0.19222937510797833,
  "equations": [
    "(-v + x)*x*v*0.103164*(x - 1*0.3693303) + v + 0.008583157",
    "-0.42083946*v + x*(-3.9763355)"
  ],
  "wall_s_total": 16.385233811000035,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "equation": "(-v + x)*x*v*0.103164*(x - 1*0.3693303) + v + 0.008583157",
      "r2_train": 0.9957640185126935,
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      "free_const_values": null,
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    {
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      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.389755793999939,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.0049233917415784055 cons=0.0454587595971159 wall_s=17.781 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0049233917415784055,
  "conservation_residual": 0.0454587595971159,
  "equations": [
    "v + (v*(-0.11114793) - 0.056221526)*(x*x - 0.11876457) + 0.0058893124",
    "v*(-0.38027498) + x*(-3.9041727)"
  ],
  "wall_s_total": 17.78059359799954,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + (v*(-0.11114793) - 0.056221526)*(x*x - 0.11876457) + 0.0058893124",
      "r2_train": 0.9956224845482353,
      "reward": null,
      "residual_heldout": 0.0043630717932189745,
      "pred_coeffs": {
        "1": 0.01256643776013382
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.402280530999633,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.38027498) + x*(-3.9041727)",
      "r2_train": 0.9937920187940363,
      "reward": null,
      "residual_heldout": 0.005483711689937836,
      "pred_coeffs": {
        "v": -0.38027498,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.378313066999908,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.005539829389180008 cons=0.0 wall_s=18.090 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005539829389180008,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.016977016)*v*v + v - 0.015375461",
    "v*(-0.41867927) + x*(-3.96264)"
  ],
  "wall_s_total": 18.090322658000332,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-(-0.016977016)*v*v + v - 0.015375461",
      "r2_train": 0.9968669662968844,
      "reward": null,
      "residual_heldout": 0.0046017215727633225,
      "pred_coeffs": {
        "v^2": 0.016977016,
        "1": -0.015375461,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.26778291500068,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.41867927) + x*(-3.96264)",
      "r2_train": 0.9935551758535948,
      "reward": null,
      "residual_heldout": 0.006477937205596694,
      "pred_coeffs": {
        "v": -0.41867927,
        "x": -3.96264
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.822539742999652,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.006725522371298269 cons=0.0498452625480197 wall_s=18.486 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006725522371298269,
  "conservation_residual": 0.0498452625480197,
  "equations": [
    "-(-0.045166362)*v*x + v - 1*(-0.011359147)",
    "v*(-0.39300063) + x*(-3.9516084)"
  ],
  "wall_s_total": 18.486122038000758,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-(-0.045166362)*v*x + v - 1*(-0.011359147)",
      "r2_train": 0.9970726922980382,
      "reward": null,
      "residual_heldout": 0.006497761545062851,
      "pred_coeffs": {
        "x*v": 0.045166362,
        "1": 0.011359147
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 9.029473153000254,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39300063) + x*(-3.9516084)",
      "r2_train": 0.9936615741516868,
      "reward": null,
      "residual_heldout": 0.006953283197533687,
      "pred_coeffs": {
        "v": -0.39300063,
        "x": -3.9516084
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.456648885000504,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.007226998420624022 cons=0.33561534954177663 wall_s=21.815 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007226998420624022,
  "conservation_residual": 0.33561534954177663,
  "equations": [
    "v",
    "(((w2-((-(w2)+w2)-w2))*(-(x)-x))+(gamma*v))"
  ],
  "wall_s_total": 21.81473597599961,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9926532297968749,
      "reward": null,
      "residual_heldout": 0.0051374064040195415,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.030425461999585,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.030425461999585,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2-((-(w2)+w2)-w2))*(-(x)-x))+(gamma*v))",
      "r2_train": 0.9965875750850642,
      "reward": null,
      "residual_heldout": 0.009316590437228501,
      "pred_coeffs": {
        "v": 0.996629308959449,
        "x": 1.604464243288942
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 12.784310514000026,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.784310514000026,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4011160608222355,
        0.996629308959449
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=False residual=0.007281141305145827 cons=2.0551066934847313 wall_s=15.542 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.007281141305145827,
  "conservation_residual": 2.0551066934847313,
  "equations": [
    "v",
    "((gamma*((-((gamma*x))-v)+v))+((gamma*v)+-((x*w2))))"
  ],
  "wall_s_total": 15.541583877999983,
  "wall_s_per_eq": [
    8.112354154000059,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9943672424014042,
      "reward": null,
      "residual_heldout": 0.007500102381527847,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.112354154000059,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.112354154000059,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((gamma*((-((gamma*x))-v)+v))+((gamma*v)+-((x*w2))))",
      "r2_train": 0.9959117397966839,
      "reward": null,
      "residual_heldout": 0.007062180228763807,
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        "v": 3.8361364440236887,
        "x": -14.25758070627096
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.429229723999924,
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      "wall_raw_s": 7.429229723999924,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4583621108957498,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=False residual=0.005038656765714888 cons=0.9242806732045152 wall_s=18.000 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.005038656765714888,
  "conservation_residual": 0.9242806732045152,
  "equations": [
    "v",
    "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))"
  ],
  "wall_s_total": 17.999870911999096,
  "wall_s_per_eq": [
    6.990613651999411,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9955665169510293,
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        "v": 1.0
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 6.990613651999411,
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      "wall_raw_s": 6.990613651999411,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))",
      "r2_train": 0.994914673437477,
      "reward": null,
      "residual_heldout": 0.0047760102831161805,
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        "v": 1.988862235103326,
        "x": 0.7968206334418296
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 11.009257259999686,
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      "wall_raw_s": 11.009257259999686,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.3984103167209148,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5631787854465793 cons=0.0 wall_s=14.878 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5631787854465793,
  "conservation_residual": 0.0,
  "equations": [
    "2*v",
    "-(((gamma*v)+(x*((((-(w2)+w2)+w2)+w2)+w2))))"
  ],
  "wall_s_total": 14.878444957998909,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.07394252011700653,
      "reward": null,
      "residual_heldout": 1.1225335881805303,
      "pred_coeffs": {
        "v": 2.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 7.3970905649994165,
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      "wall_raw_s": 7.3970905649994165,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*v)+(x*((((-(w2)+w2)+w2)+w2)+w2))))",
      "r2_train": 0.9962089932478811,
      "reward": null,
      "residual_heldout": 0.003823982712628292,
      "pred_coeffs": {
        "v": -1.3369849451435944,
        "x": -1.2072855585495554
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.481354392999492,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.481354392999492,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4024285195165185,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=False residual=0.00542112888728165 cons=6.797778331443093 wall_s=13.880 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.00542112888728165,
  "conservation_residual": 6.797778331443093,
  "equations": [
    "v",
    "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))"
  ],
  "wall_s_total": 13.880274295999698,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.113342740000007,
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      "wall_raw_s": 7.113342740000007,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))",
      "r2_train": 0.9953913264781682,
      "reward": null,
      "residual_heldout": 0.0073621995760457665,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 6.76693155599969,
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      "wall_raw_s": 6.76693155599969,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.14212092438343166,
        4.000311747729432
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.0038875842560486145 cons=0.0 wall_s=14.939 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0038875842560486145,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))"
  ],
  "wall_s_total": 14.93914504300028,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": true,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      "free_const_values": [],
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))",
      "r2_train": 0.994823539503294,
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      "wall_raw_s": 7.507765416999973,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      },
      "free_const_values": [
        -0.4218425299065743,
        -3.9524690542863716
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=False residual=0.003449370412631189 cons=3.093484209349725 wall_s=14.607 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.003449370412631189,
  "conservation_residual": 3.093484209349725,
  "equations": [
    "v",
    "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))"
  ],
  "wall_s_total": 14.606535936,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.065752491000239,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "device": "cpu",
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))",
      "r2_train": 0.9946104955167993,
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      "true_coeffs": {
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      "wall_raw_s": 7.540783444999761,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "parallel_mode": false,
        "device": "cpu",
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      "free_const_values": [
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.008630266034531677 cons=0.0 wall_s=18.443 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
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  "recovered": false,
  "structure_ok": false,
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  "residual": 0.008630266034531677,
  "conservation_residual": 0.0,
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    "v",
    "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))"
  ],
  "wall_s_total": 18.44295457500084,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 11.358197707000727,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [],
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((-(((x--((x+x)))-x))*-(w2)))-(gamma*v))",
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      "wall_s": 7.084756868000113,
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=False residual=0.007519286755612567 cons=1.8884760694075124 wall_s=14.205 ok=True

```json
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  "wall_s_total": 14.204730115999155,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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    {
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      "zero_eq": false,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=False residual=0.005783197081930181 cons=1.8722296386604327 wall_s=18.011 ok=True

```json
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  "arm": "A4_physo",
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  "recovered": false,
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  "residual": 0.005783197081930181,
  "conservation_residual": 1.8722296386604327,
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  ],
  "wall_s_total": 18.01097801100059,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 10.93222342900026,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.93222342900026,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4053373803057749,
        3.960400525030623
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=False residual=0.00581392474895768 cons=4.6641146661715975 wall_s=14.725 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.00581392474895768,
  "conservation_residual": 4.6641146661715975,
  "equations": [
    "v",
    "(-(((gamma*v)+-((w2*x))))+(v*-(gamma)))"
  ],
  "wall_s_total": 14.725354590998904,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9954129481069964,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 6.921582889999627,
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      "wall_raw_s": 6.921582889999627,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(((gamma*v)+-((w2*x))))+(v*-(gamma)))",
      "r2_train": 0.9951195891257383,
      "reward": null,
      "residual_heldout": 0.006550472995756938,
      "pred_coeffs": {
        "v": 7.958560583227294,
        "x": 0.2066258014727074
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      "true_coeffs": {
        "x": -4.0,
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      "structure_ok": false,
      "wall_s": 7.8037717009992775,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.8037717009992775,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.2066258014727074,
        -3.979280291613647
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.005371192614187665 cons=0.0 wall_s=14.010 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005371192614187665,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "((gamma*v)+(x*w2))"
  ],
  "wall_s_total": 14.010060061000331,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.218926372000169,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((gamma*v)+(x*w2))",
      "r2_train": 0.9939280989387395,
      "reward": null,
      "residual_heldout": 0.00462845318046746,
      "pred_coeffs": {
        "v": -3.9917047546196023,
        "x": -0.4023130925323715
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 6.791133689000162,
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      "wall_raw_s": 6.791133689000162,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4023130925323715,
        -3.9917047546196023
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=False residual=0.0052314159052557 cons=4.6453098230775876 wall_s=19.079 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.0052314159052557,
  "conservation_residual": 4.6453098230775876,
  "equations": [
    "v",
    "(-((v*-((-((gamma+-((gamma-gamma))))-gamma))))+(x*w2))"
  ],
  "wall_s_total": 19.079466153000794,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 11.771763730000202,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((v*-((-((gamma+-((gamma-gamma))))-gamma))))+(x*w2))",
      "r2_train": 0.9946592610612103,
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      "residual_heldout": 0.0050892630078510125,
      "pred_coeffs": {
        "v": 7.987827554224047,
        "x": 0.1857988528884344
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      "true_coeffs": {
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        "v": -0.4
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      "structure_ok": false,
      "wall_s": 7.307702423000592,
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      "wall_raw_s": 7.307702423000592,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.1857988528884344,
        -3.9939137771120237
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.005572909366271545 cons=0.0 wall_s=14.521 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005572909366271545,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-(((x*w2)+(gamma*v)))"
  ],
  "wall_s_total": 14.520696115001556,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.674581333001697,
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      "wall_raw_s": 7.674581333001697,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((x*w2)+(gamma*v)))",
      "r2_train": 0.9948395231830568,
      "reward": null,
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        "v": -4.03932617431742,
        "x": -0.3903634505260036
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.846114781999859,
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      "wall_raw_s": 6.846114781999859,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      },
      "free_const_values": [
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      "zero_eq": false,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=False residual=0.004292942893586674 cons=1.6932547373634752 wall_s=19.848 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.004292942893586674,
  "conservation_residual": 1.6932547373634752,
  "equations": [
    "v",
    "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))"
  ],
  "wall_s_total": 19.84792361500149,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9942975660116562,
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.488559453000562,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "parallel_mode": false,
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        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))",
      "r2_train": 0.9947300595575688,
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        "v": 4.023048964936847,
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      "true_coeffs": {
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      "wall_s": 12.35936416200093,
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      "wall_raw_s": 12.35936416200093,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.402009280411553,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.004856247900996888 cons=0.0 wall_s=14.245 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.004856247900996888,
  "conservation_residual": 0.0,
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    "v",
    "-((-((-(v)*(-((gamma--(gamma)))-gamma)))-(x*w2)))"
  ],
  "wall_s_total": 14.245170920999954,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.3489478219999,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [],
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-((-(v)*(-((gamma--(gamma)))-gamma)))-(x*w2)))",
      "r2_train": 0.9955067688625554,
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        "v": -11.857919657331248,
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      "true_coeffs": {
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      "wall_s": 6.8962230990000535,
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      "wall_raw_s": 6.8962230990000535,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [
        -0.1319952379125486,
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=False residual=0.008704344050705819 cons=1.1213638543659996 wall_s=13.873 ok=True

```json
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.008704344050705819,
  "conservation_residual": 1.1213638543659996,
  "equations": [
    "v",
    "(-(((gamma*v)--((-((w2-w2))*x))))+(w2*x))"
  ],
  "wall_s_total": 13.873186769000313,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9951873227955819,
      "reward": null,
      "residual_heldout": 0.009075996463469247,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.059005966000768,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.059005966000768,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(((gamma*v)--((-((w2-w2))*x))))+(w2*x))",
      "r2_train": 0.994853084523936,
      "reward": null,
      "residual_heldout": 0.008332691637942391,
      "pred_coeffs": {
        "v": 3.9763354447707977,
        "x": 0.42083893246966714
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.8141808029995445,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.8141808029995445,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.42083893246966714,
        -3.9763354447707977
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=False residual=0.0048203902251040135 cons=2.5934974175411227 wall_s=19.054 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.0048203902251040135,
  "conservation_residual": 2.5934974175411227,
  "equations": [
    "v",
    "-(((v*gamma)--(((x*(gamma*(gamma-gamma)))+-((w2*x))))))"
  ],
  "wall_s_total": 19.054137854000146,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 12.016120726999361,
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      "wall_raw_s": 12.016120726999361,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((v*gamma)--(((x*(gamma*(gamma-gamma)))+-((w2*x))))))",
      "r2_train": 0.9937920189736499,
      "reward": null,
      "residual_heldout": 0.005484088517958021,
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        "v": 3.9041570243915102,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.038017127000785,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.038017127000785,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.38026990764370006,
        -3.9041570243915102
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.005443557495273548 cons=0.0 wall_s=14.017 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
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  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005443557495273548,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))"
  ],
  "wall_s_total": 14.017447941001592,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.132920165000542,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))",
      "r2_train": 0.9935551752459175,
      "reward": null,
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        "x": -0.2093406617114581
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 6.88452777600105,
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      "wall_raw_s": 6.88452777600105,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.2093406617114581,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=False residual=0.0057616076463937425 cons=1.7908100105321425 wall_s=13.785 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.0057616076463937425,
  "conservation_residual": 1.7908100105321425,
  "equations": [
    "v",
    "-(((gamma*v)+(w2*-(x))))"
  ],
  "wall_s_total": 13.784834578998925,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 6.97414692899838,
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      "wall_raw_s": 6.97414692899838,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*v)+(w2*-(x))))",
      "r2_train": 0.993661574184099,
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      "residual_heldout": 0.006953272974230971,
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      "structure_ok": false,
      "wall_s": 6.8106876500005455,
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      "wall_raw_s": 6.8106876500005455,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3929946725302184,
        -3.95160085225
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.005248480495022488 cons=0.0 wall_s=21.104 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005248480495022488,
  "conservation_residual": 0.0,
  "equations": [
    "v + (v - 1*(-1.6318938))*(-(-0.010100594)*v*v - 0.0048410157)",
    "v*(-0.40144542) + x*(-3.9566317)"
  ],
  "wall_s_total": 21.104267403999984,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + (v - 1*(-1.6318938))*(-(-0.010100594)*v*v - 0.0048410157)",
      "r2_train": 0.9949562849620267,
      "reward": null,
      "residual_heldout": 0.005696470845576404,
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        "v^2": 0.0164830967249172,
        "1": -0.00790002350653266,
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.541250537000451,
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      "wall_raw_s": null,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.40144542) + x*(-3.9566317)",
      "r2_train": 0.9954199442566601,
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        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 10.563016866999533,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.005109707816835557 cons=0.0 wall_s=17.776 ok=True

```json
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  "structure_ok": false,
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  "residual": 0.005109707816835557,
  "conservation_residual": 0.0,
  "equations": [
    "-0.037026405*v*x + v",
    "(v*(-0.10378303) - x)*4.002941"
  ],
  "wall_s_total": 17.776329218999308,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
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  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "equation": "-0.037026405*v*x + v",
      "r2_train": 0.9954002603634551,
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        "x*v": -0.037026405
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      "structure_ok": false,
      "wall_s": 8.623153344999082,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v*(-0.10378303) - x)*4.002941",
      "r2_train": 0.9944538200527233,
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      "structure_ok": true,
      "wall_s": 9.153175874000226,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.005635115304084873 cons=0.0 wall_s=17.645 ok=True

```json
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  "noise": 0.05,
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  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005635115304084873,
  "conservation_residual": 0.0,
  "equations": [
    "v*v*0.01134716 + v - 0.009088079",
    "-0.40437892*v + x*(-3.9951215)"
  ],
  "wall_s_total": 17.645155947000603,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "equation": "v*v*0.01134716 + v - 0.009088079",
      "r2_train": 0.9958296147524353,
      "reward": null,
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        "v^2": 0.01134716,
        "1": -0.009088079,
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      "structure_ok": true,
      "wall_s": 8.517237285999727,
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      "wall_raw_s": null,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
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      "equation": "-0.40437892*v + x*(-3.9951215)",
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      "wall_s": 9.127918661000876,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.004469465904799947 cons=0.0 wall_s=18.651 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004469465904799947,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.991715)*v + x*x*(-0.028099239)",
    "v*(-0.40429407) + x*(-4.006716)"
  ],
  "wall_s_total": 18.65129970199996,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-(-0.991715)*v + x*x*(-0.028099239)",
      "r2_train": 0.9949500862939525,
      "reward": null,
      "residual_heldout": 0.00494073309354292,
      "pred_coeffs": {
        "x^2": -0.028099239,
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.86514384200018,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.40429407) + x*(-4.006716)",
      "r2_train": 0.9940761933848976,
      "reward": null,
      "residual_heldout": 0.003998198716056974,
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        "v": -0.4
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      "structure_ok": true,
      "wall_s": 9.78615585999978,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.005578966771527305 cons=0.0 wall_s=18.558 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A0_pysr",
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  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005578966771527305,
  "conservation_residual": 0.0,
  "equations": [
    "v - 0.0037005432",
    "v*(-0.40253246) + x*(-4.0107956)"
  ],
  "wall_s_total": 18.557852049001667,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 0.0037005432",
      "r2_train": 0.9960179668104218,
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      "residual_heldout": 0.0058079193483998245,
      "pred_coeffs": {
        "1": -0.0037005432,
        "v": 1.0
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        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.675288864000322,
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      "wall_raw_s": null,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.40253246) + x*(-4.0107956)",
      "r2_train": 0.9955157435442161,
      "reward": null,
      "residual_heldout": 0.005350014194654785,
      "pred_coeffs": {
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        "x": -4.0107956
      },
      "true_coeffs": {
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        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.882563185001345,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.005033273936737066 cons=0.0 wall_s=19.971 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005033273936737066,
  "conservation_residual": 0.0,
  "equations": [
    "v - 1*0.0048228083",
    "(v*0.103533596 + x)*(-3.986189)"
  ],
  "wall_s_total": 19.971367296999233,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 1*0.0048228083",
      "r2_train": 0.9961370329212377,
      "reward": null,
      "residual_heldout": 0.005001484850709937,
      "pred_coeffs": {
        "1": -0.0048228083,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.025963899999624,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v*0.103533596 + x)*(-3.986189)",
      "r2_train": 0.9948769163186275,
      "reward": null,
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      "pred_coeffs": {
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        "x": -3.986189
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 9.945403396999609,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005621027958686809 cons=0.0 wall_s=18.804 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005621027958686809,
  "conservation_residual": 0.0,
  "equations": [
    "v*0.9878118",
    "v*(-0.38829195) + x*(-3.9925137)"
  ],
  "wall_s_total": 18.804119160999107,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*0.9878118",
      "r2_train": 0.9951701632381842,
      "reward": null,
      "residual_heldout": 0.0050068043602196225,
      "pred_coeffs": {
        "v": 0.9878118
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.048794579999594,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.38829195) + x*(-3.9925137)",
      "r2_train": 0.9954324701696651,
      "reward": null,
      "residual_heldout": 0.006235251557153996,
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        "v": -0.38829195,
        "x": -3.9925137
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": true,
      "wall_s": 9.755324580999513,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.004863838427848119 cons=0.0 wall_s=17.880 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004863838427848119,
  "conservation_residual": 0.0,
  "equations": [
    "v - 1*0.0058391974",
    "(v*0.099841624 + x)*(-3.9929526)"
  ],
  "wall_s_total": 17.879730974000267,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 1*0.0058391974",
      "r2_train": 0.9953730064276479,
      "reward": null,
      "residual_heldout": 0.004497887964983155,
      "pred_coeffs": {
        "1": -0.0058391974,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.669399914999303,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v*0.099841624 + x)*(-3.9929526)",
      "r2_train": 0.994501283966987,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 9.210331059000964,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.004659818465654296 cons=0.0 wall_s=18.191 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004659818465654296,
  "conservation_residual": 0.0,
  "equations": [
    "v*(x*0.012434889 + 1.0050527) + 0.0047251424",
    "-0.41355097*v + x*(-3.9998193)"
  ],
  "wall_s_total": 18.19100713899934,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9951485806920687,
      "reward": null,
      "residual_heldout": 0.0045416708796866545,
      "pred_coeffs": {
        "x*v": 0.012434889,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 9.246032989000014,
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      "wall_cap_s": 120,
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      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.41355097*v + x*(-3.9998193)",
      "r2_train": 0.9953271149043328,
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      "pred_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.944974149999325,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004850745456395958 cons=0.0 wall_s=17.595 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004850745456395958,
  "conservation_residual": 0.0,
  "equations": [
    "x*v*(-0.021803766)*(v + x) + v",
    "v*(-0.4173471) + x*(-3.9965396)"
  ],
  "wall_s_total": 17.595356028001333,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9947742125004144,
      "reward": null,
      "residual_heldout": 0.004367828840411095,
      "pred_coeffs": {
        "v": 1.0000000000000004,
        "x*v^2": -0.021803765999999964,
        "x^2*v": -0.02180376599999962
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.921703451000212,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4173471) + x*(-3.9965396)",
      "r2_train": 0.9945567922269499,
      "reward": null,
      "residual_heldout": 0.005333662072380822,
      "pred_coeffs": {
        "v": -0.4173471,
        "x": -3.9965396
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 8.673652577001121,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.005382044051865555 cons=0.0 wall_s=17.662 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005382044051865555,
  "conservation_residual": 0.0,
  "equations": [
    "v*(0.99429494 + v*(-0.010867933)) + 0.007911734",
    "v*(-0.38236788) - 3.9792478*x"
  ],
  "wall_s_total": 17.66249477999918,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "reward": null,
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      "pred_coeffs": {
        "v^2": -0.010867933,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 9.060277463000602,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.38236788) - 3.9792478*x",
      "r2_train": 0.9944076988960204,
      "reward": null,
      "residual_heldout": 0.005171612125484538,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.602217316998576,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.00684001113084064 cons=0.0 wall_s=18.649 ok=True

```json
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  "n_samples": 400,
  "arm": "A0_pysr",
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  "structure_ok": true,
  "accepted": true,
  "residual": 0.00684001113084064,
  "conservation_residual": 0.0,
  "equations": [
    "v + x*(v*(-0.028160248)*v - 1*(-0.017012876)) + 0.006972718",
    "v*(-0.3918711) + x*(-3.996201)"
  ],
  "wall_s_total": 18.64911385599953,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "r2_train": 0.9946678849204817,
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      "structure_ok": true,
      "wall_s": 9.353532564000488,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
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      "equation": "v*(-0.3918711) + x*(-3.996201)",
      "r2_train": 0.9954986700158013,
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      "structure_ok": true,
      "wall_s": 9.295581291999042,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.005302542031669518 cons=0.0 wall_s=18.388 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005302542031669518,
  "conservation_residual": 0.0,
  "equations": [
    "v + x*(-0.016511055)",
    "-0.39452648*v + x*(-4.015664)"
  ],
  "wall_s_total": 18.388154953001504,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "x": -0.016511055
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      "structure_ok": true,
      "wall_s": 8.958947939001519,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.39452648*v + x*(-4.015664)",
      "r2_train": 0.9953826297418593,
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      "structure_ok": true,
      "wall_s": 9.429207013999985,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.004399484712854015 cons=0.0 wall_s=17.557 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004399484712854015,
  "conservation_residual": 0.0,
  "equations": [
    "v - x*x*(x*0.041337933 - 1*0.033437215)",
    "v*(-0.39887136) + x*(-3.977389)"
  ],
  "wall_s_total": 17.557346953999513,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - x*x*(x*0.041337933 - 1*0.033437215)",
      "r2_train": 0.994889319572788,
      "reward": null,
      "residual_heldout": 0.004881226980547849,
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      "structure_ok": true,
      "wall_s": 8.474875838999651,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39887136) + x*(-3.977389)",
      "r2_train": 0.9945410709446768,
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        "v": -0.39887136,
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      "structure_ok": true,
      "wall_s": 9.082471114999862,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.0038308689897563137 cons=0.10511956531855723 wall_s=20.156 ok=True

```json
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0038308689897563137,
  "conservation_residual": 0.10511956531855723,
  "equations": [
    "v*(0.9978922 - (-0.031392284)*x)",
    "(v + x*10.045334)*(-0.39758655)"
  ],
  "wall_s_total": 20.156294553000407,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "r2_train": 0.9946825373947966,
      "reward": null,
      "residual_heldout": 0.0032776761107220897,
      "pred_coeffs": {
        "x*v": 0.031392284
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      "structure_ok": false,
      "wall_s": 10.900406606000615,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(v + x*10.045334)*(-0.39758655)",
      "r2_train": 0.9947995158844684,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 9.255887946999792,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.004814579603799869 cons=0.0 wall_s=20.439 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004814579603799869,
  "conservation_residual": 0.0,
  "equations": [
    "v + x*(x*(0.31267583 - x) + 0.31267583)*(-0.06738968)",
    "(v*(-0.101380855) - x)*4.0077534"
  ],
  "wall_s_total": 20.439144501000555,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v + x*(x*(0.31267583 - x) + 0.31267583)*(-0.06738968)",
      "r2_train": 0.994891175238362,
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      "structure_ok": true,
      "wall_s": 10.211938637999992,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
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      "equation": "(v*(-0.101380855) - x)*4.0077534",
      "r2_train": 0.9949753974760271,
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 10.227205863000563,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.005164304184885197 cons=0.0 wall_s=19.649 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005164304184885197,
  "conservation_residual": 0.0,
  "equations": [
    "v - 1*0.00456959",
    "-0.4021676*v + x*(-3.9910507)"
  ],
  "wall_s_total": 19.64886426799967,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 1*0.00456959",
      "r2_train": 0.9950094725333057,
      "reward": null,
      "residual_heldout": 0.005213913343737774,
      "pred_coeffs": {
        "1": -0.00456959,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.263673506000487,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.4021676*v + x*(-3.9910507)",
      "r2_train": 0.9950401127048948,
      "reward": null,
      "residual_heldout": 0.0051146950260326195,
      "pred_coeffs": {
        "v": -0.4021676,
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": true,
      "wall_s": 10.385190761999183,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.007155986736763067 cons=0.0 wall_s=18.478 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007155986736763067,
  "conservation_residual": 0.0,
  "equations": [
    "v + 0.0047943555",
    "v*(-0.39920476) + x*(-3.9261165)"
  ],
  "wall_s_total": 18.47762152100222,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v + 0.0047943555",
      "r2_train": 0.9954073795783145,
      "reward": null,
      "residual_heldout": 0.006076492383692394,
      "pred_coeffs": {
        "1": 0.0047943555,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.943563910001103,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.39920476) + x*(-3.9261165)",
      "r2_train": 0.9948277101510123,
      "reward": null,
      "residual_heldout": 0.008235481089833739,
      "pred_coeffs": {
        "v": -0.39920476,
        "x": -3.9261165
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        "v": -0.4
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      "structure_ok": true,
      "wall_s": 9.534057611001117,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.004626414583216736 cons=0.0 wall_s=18.924 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004626414583216736,
  "conservation_residual": 0.0,
  "equations": [
    "v*(v*(-0.02373203*v + (-1*v*0.013659214*v + 0.015161642)) - 1*(-1.0278667))",
    "v*(-0.4015635) + x*(-3.986577)"
  ],
  "wall_s_total": 18.92350951899971,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(v*(-0.02373203*v + (-1*v*0.013659214*v + 0.015161642)) - 1*(-1.0278667))",
      "r2_train": 0.9952483439368158,
      "reward": null,
      "residual_heldout": 0.004823010649048176,
      "pred_coeffs": {
        "v^2": 0.015161642,
        "v": 1.0278667
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.000563259998671,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(-0.4015635) + x*(-3.986577)",
      "r2_train": 0.9949769130100871,
      "reward": null,
      "residual_heldout": 0.004429818517385295,
      "pred_coeffs": {
        "v": -0.4015635,
        "x": -3.986577
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.922946259001037,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `damped_oscillator` / N=400 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.005921723164130227 cons=0.0 wall_s=17.905 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005921723164130227,
  "conservation_residual": 0.0,
  "equations": [
    "v - (v*v + x)*(x*(-(-0.041748185)*x - 0.011947602) - 0.0077471086)",
    "-0.39355373*v + x*(-3.970415)"
  ],
  "wall_s_total": 17.904548961998444,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - (v*v + x)*(x*(-(-0.041748185)*x - 0.011947602) - 0.0077471086)",
      "r2_train": 0.9955555109511235,
      "reward": null,
      "residual_heldout": 0.004735437158674003,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.600246246998722,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-0.39355373*v + x*(-3.970415)",
      "r2_train": 0.9942564085617565,
      "reward": null,
      "residual_heldout": 0.007108009169586451,
      "pred_coeffs": {
        "v": -0.39355373,
        "x": -3.970415
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": true,
      "wall_s": 9.304302714999722,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.00509789847614508 cons=0.04267315314445425 wall_s=20.541 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00509789847614508,
  "conservation_residual": 0.04267315314445425,
  "equations": [
    "v",
    "(((w2-((-(w2)+w2)-w2))*(-(x)-x))+(gamma*v))"
  ],
  "wall_s_total": 20.540688445998967,
  "wall_s_per_eq": [
    13.112554707999152,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9948368925289822,
      "reward": null,
      "residual_heldout": 0.005395386018375402,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 13.112554707999152,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.112554707999152,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2-((-(w2)+w2)-w2))*(-(x)-x))+(gamma*v))",
      "r2_train": 0.995419944731739,
      "reward": null,
      "residual_heldout": 0.004800410933914759,
      "pred_coeffs": {
        "v": 0.989159175608947,
        "x": 1.605774365187189
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.428133737999815,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.428133737999815,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.40144359129679724,
        0.989159175608947
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=False residual=0.004818413527822505 cons=2.50277760974217 wall_s=14.236 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.004818413527822505,
  "conservation_residual": 2.50277760974217,
  "equations": [
    "v",
    "((v*(((-(gamma)+-((gamma-gamma)))+gamma)-gamma))+(x*w2))"
  ],
  "wall_s_total": 14.235899298997538,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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        "v": 1.0
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      "structure_ok": true,
      "wall_s": 7.292143621998548,
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      "wall_raw_s": 7.292143621998548,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((v*(((-(gamma)+-((gamma-gamma)))+gamma)-gamma))+(x*w2))",
      "r2_train": 0.9944538195561972,
      "reward": null,
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        "x": 0.4154374371788688
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      "true_coeffs": {
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      "wall_s": 6.94375567699899,
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      "wall_raw_s": 6.94375567699899,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        0.4154374371788688,
        -4.002942774258687
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=False residual=0.005562305513315645 cons=0.9464449536153179 wall_s=14.407 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.005562305513315645,
  "conservation_residual": 0.9464449536153179,
  "equations": [
    "v",
    "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))"
  ],
  "wall_s_total": 14.406569276998198,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.1926730449995375,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((w2--(((-((w2+(w2-w2)))-w2)-w2)))*x)+(v*gamma))",
      "r2_train": 0.9952417421701816,
      "reward": null,
      "residual_heldout": 0.005940681916692585,
      "pred_coeffs": {
        "v": 1.9975640698312864,
        "x": 0.8087667201559949
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.21389623199866,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.21389623199866,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.40438336007799747,
        1.9975640698312864
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.5472018118789308 cons=3.0064543807457733 wall_s=20.504 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5472018118789308,
  "conservation_residual": 3.0064543807457733,
  "equations": [
    "2*v",
    "-(((-(((-(gamma)*x)*gamma))+(w2*x))-(v*gamma)))"
  ],
  "wall_s_total": 20.5044862550003,
  "wall_s_per_eq": [
    13.12017590600044,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.053887636125671046,
      "reward": null,
      "residual_heldout": 1.0904055550452492,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 13.12017590600044,
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      "wall_raw_s": 13.12017590600044,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((-(((-(gamma)*x)*gamma))+(w2*x))-(v*gamma)))",
      "r2_train": 0.994076193614845,
      "reward": null,
      "residual_heldout": 0.003998068712612386,
      "pred_coeffs": {
        "v": 3.8432485519044377,
        "x": -14.366273201636247
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.384310348999861,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.384310348999861,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4042862300793108,
        3.8432485519044377
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=False residual=0.0055425984305649935 cons=7.394548753536693 wall_s=14.041 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.0055425984305649935,
  "conservation_residual": 7.394548753536693,
  "equations": [
    "v",
    "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))"
  ],
  "wall_s_total": 14.04103734599812,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.2229316009998,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.2229316009998,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-(((gamma+gamma)*v))+((x*((gamma*gamma)+w2))-(gamma*v))))",
      "r2_train": 0.9955157429452995,
      "reward": null,
      "residual_heldout": 0.005349979320852878,
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        "v": 11.978348670641447,
        "x": -15.80813883810201
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      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.81810574499832,
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      "wall_raw_s": 6.81810574499832,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.13417637028218082,
        3.9927828902138156
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.004990105697244869 cons=0.0 wall_s=14.204 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004990105697244869,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))"
  ],
  "wall_s_total": 14.203591333000077,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.411266611999963,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*-((((v+v)-(-(v)+v))-v)))-(x*w2)))",
      "r2_train": 0.9948769165747828,
      "reward": null,
      "residual_heldout": 0.005064858058807422,
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        "v": -3.986142210018795,
        "x": -0.4127111521137258
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      "true_coeffs": {
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        "v": -0.4
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      "structure_ok": false,
      "wall_s": 6.792324721000114,
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      "wall_raw_s": 6.792324721000114,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4127111521137258,
        -3.986142210018795
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=False residual=0.005446870132609352 cons=3.3280139200741754 wall_s=21.492 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.005446870132609352,
  "conservation_residual": 3.3280139200741754,
  "equations": [
    "v",
    "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))"
  ],
  "wall_s_total": 21.492404460001126,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 13.8085540330012,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "device": "cpu",
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      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((x*(gamma*gamma))-(v*gamma))+-(((v*gamma)+-((x*w2)))))",
      "r2_train": 0.9954324696958293,
      "reward": null,
      "residual_heldout": 0.006235254089937315,
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        "x": 16.436765579526213
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.683850426999925,
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      "wall_raw_s": 7.683850426999925,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.19414531490898904,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=False residual=0.004853204849870139 cons=1.8845716531830095 wall_s=15.175 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.004853204849870139,
  "conservation_residual": 1.8845716531830095,
  "equations": [
    "v",
    "((gamma*(v+(((v+v)-v)-v)))-(w2*x))"
  ],
  "wall_s_total": 15.174700304001817,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 8.0539701530015,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((gamma*(v+(((v+v)-v)-v)))-(w2*x))",
      "r2_train": 0.9945012837637193,
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      "wall_s": 7.120730151000316,
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      "wall_raw_s": 7.120730151000316,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      },
      "free_const_values": [
        -0.39866409619266974,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=False residual=0.004545375408845753 cons=2.4078648107762444 wall_s=14.478 ok=True

```json
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.004545375408845753,
  "conservation_residual": 2.4078648107762444,
  "equations": [
    "v",
    "((v*-(gamma))+(w2*x))"
  ],
  "wall_s_total": 14.478340838000804,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.460735736000061,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [],
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((v*-(gamma))+(w2*x))",
      "r2_train": 0.9953271146083794,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.0176051020007435,
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      "wall_raw_s": 7.0176051020007435,
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      "budget": {
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        "max_n_evaluations": 2500,
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      },
      "free_const_values": [
        0.4135463786504626,
        -3.999814390590076
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=False residual=0.004801260160708178 cons=2.2369575437533387 wall_s=21.243 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
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  "structure_ok": false,
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  "residual": 0.004801260160708178,
  "conservation_residual": 2.2369575437533387,
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    "v",
    "-((-((x*-(w2)))-(gamma*(v+(v-v)))))"
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  "wall_s_total": 21.243353087000287,
  "wall_s_per_eq": [
    13.713156608000645,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "v": 1.0
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      "true_coeffs": {
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        "max_n_evaluations": 2500,
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        "device": "cpu",
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      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-((x*-(w2)))-(gamma*(v+(v-v)))))",
      "r2_train": 0.9945567929432961,
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      "residual_heldout": 0.0053336335056589045,
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        "v": 3.996543236863237,
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      "true_coeffs": {
        "x": -4.0,
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      "structure_ok": false,
      "wall_s": 7.530196478999642,
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      "wall_raw_s": 7.530196478999642,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      "free_const_values": [
        -0.4173448236207395,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=False residual=0.00541912214893447 cons=4.190569152935331 wall_s=14.773 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.00541912214893447,
  "conservation_residual": 4.190569152935331,
  "equations": [
    "v",
    "(-(((gamma*v)+-((w2*x))))+(v*-(gamma)))"
  ],
  "wall_s_total": 14.773497615999077,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.411705905999042,
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      "wall_raw_s": 7.411705905999042,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-(((gamma*v)+-((w2*x))))+(v*-(gamma)))",
      "r2_train": 0.9944076983989181,
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      "residual_heldout": 0.005171606826890114,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.361791710000034,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.361791710000034,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
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        -3.979248006568747
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.0066192250053830615 cons=0.0 wall_s=14.338 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
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  "residual": 0.0066192250053830615,
  "conservation_residual": 0.0,
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  ],
  "wall_s_total": 14.338419404999513,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "free_const_values": [],
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    {
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      "wall_raw_s": 7.068760090000069,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "device": "cpu",
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      "free_const_values": [
        -0.39187089068648784,
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=False residual=0.0051866499167797855 cons=4.653217442480828 wall_s=22.181 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
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  "residual": 0.0051866499167797855,
  "conservation_residual": 4.653217442480828,
  "equations": [
    "v",
    "(-((v*-((-((gamma+-((gamma-gamma))))-gamma))))+(x*w2))"
  ],
  "wall_s_total": 22.180836133999037,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.202949479999006,
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      "free_const_values": [],
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    {
      "eq_i": 1,
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      "true_coeffs": {
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        "max_n_evaluations": 2500,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.004237862550474569 cons=0.0 wall_s=14.222 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
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  "recovered": false,
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  "residual": 0.004237862550474569,
  "conservation_residual": 0.0,
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    "v",
    "(-((((v-(v+(v+v)))*gamma)--((gamma*v))))+(x*w2))"
  ],
  "wall_s_total": 14.221944734999852,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": true,
      "wall_s": 7.324463146000198,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [],
      "zero_eq": false,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((((v-(v+(v+v)))*gamma)--((gamma*v))))+(x*w2))",
      "r2_train": 0.9945410714622627,
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      "wall_s": 6.8974815889996535,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [
        -0.39887471529220614,
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  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=False residual=0.003778401581535992 cons=2.291111027667391 wall_s=14.256 ok=True

```json
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  "wall_s_total": 14.25582530200154,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "free_const_values": [],
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    {
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      "equation": "(-((((x-x)*-((gamma*-(gamma))))-(gamma*v)))-(x*w2))",
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      "wall_s": 6.926109431000441,
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        "max_n_evaluations": 2500,
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.004750346973015545 cons=0.0 wall_s=13.909 ok=True

```json
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  "recovered": false,
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  "residual": 0.004750346973015545,
  "conservation_residual": 0.0,
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    "v",
    "-((-((-(v)*(-((gamma--(gamma)))-gamma)))-(x*w2)))"
  ],
  "wall_s_total": 13.908974472999034,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-((-((-(v)*(-((gamma--(gamma)))-gamma)))-(x*w2)))",
      "r2_train": 0.9949753977625635,
      "reward": null,
      "residual_heldout": 0.004988762588177104,
      "pred_coeffs": {
        "v": -12.023248235508326,
        "x": -0.13543616822553534
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.786147254999378,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.786147254999378,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.13543616822553534,
        -4.007749411836109
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=False residual=0.0051434658323061926 cons=2.0814849009303757 wall_s=21.967 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.0051434658323061926,
  "conservation_residual": 2.0814849009303757,
  "equations": [
    "v",
    "(-((w2*x))+(gamma*v))"
  ],
  "wall_s_total": 21.966940203001286,
  "wall_s_per_eq": [
    14.612935790000847,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9949716604106132,
      "reward": null,
      "residual_heldout": 0.005172236800927969,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 14.612935790000847,
      "wall_pad_s": 0.0,
      "wall_raw_s": 14.612935790000847,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(-((w2*x))+(gamma*v))",
      "r2_train": 0.9950401137719296,
      "reward": null,
      "residual_heldout": 0.005114694863684415,
      "pred_coeffs": {
        "v": 3.991050297425884,
        "x": 0.40216754891048584
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.354004413000439,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.354004413000439,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.40216754891048584,
        3.991050297425884
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.007106752773393215 cons=0.0 wall_s=14.973 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007106752773393215,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "((-(x)*w2)+(v*-((gamma+gamma))))"
  ],
  "wall_s_total": 14.97334078899803,
  "wall_s_per_eq": [
    7.439413663998494,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9953705522643261,
      "reward": null,
      "residual_heldout": 0.005978010164600506,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.439413663998494,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.439413663998494,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((-(x)*w2)+(v*-((gamma+gamma))))",
      "r2_train": 0.9948277103779624,
      "reward": null,
      "residual_heldout": 0.008235495382185924,
      "pred_coeffs": {
        "v": -7.852225317807627,
        "x": -0.19960179888673504
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 7.533927124999536,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.533927124999536,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.19960179888673504,
        3.9261126589038136
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.004514538946687126 cons=0.0 wall_s=14.094 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004514538946687126,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))"
  ],
  "wall_s_total": 14.094424884000546,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9951116527768538,
      "reward": null,
      "residual_heldout": 0.004599251915541002,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.390704227000242,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.390704227000242,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "(((v*gamma)--(((v*(-(gamma)-gamma))+-((v*gamma)))))-(w2*x))",
      "r2_train": 0.9949769129269186,
      "reward": null,
      "residual_heldout": 0.004429825977833249,
      "pred_coeffs": {
        "v": -7.973203588079649,
        "x": -0.20078685430325105
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.703720657000304,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.703720657000304,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.20078685430325105,
        3.9866017940398244
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `damped_oscillator` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=False residual=0.005888866984415808 cons=2.1287467003179072 wall_s=13.975 ok=True

```json
{
  "law": "damped_oscillator",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.005888866984415808,
  "conservation_residual": 2.1287467003179072,
  "equations": [
    "v",
    "-(((gamma*v)+(w2*-(x))))"
  ],
  "wall_s_total": 13.975012245999096,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9954434397509544,
      "reward": null,
      "residual_heldout": 0.004669618804965747,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.044106845998613,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.044106845998613,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-(((gamma*v)+(w2*-(x))))",
      "r2_train": 0.9942564079275515,
      "reward": null,
      "residual_heldout": 0.007108115163865869,
      "pred_coeffs": {
        "v": 3.970388242524981,
        "x": 0.3935478865339002
      },
      "true_coeffs": {
        "x": -4.0,
        "v": -0.4
      },
      "structure_ok": false,
      "wall_s": 6.9309054000004835,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.9309054000004835,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3935478865339002,
        -3.970388242524981
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=8.73109281164483e-33 cons=0.2642619914941399 wall_s=17.695 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.73109281164483e-33,
  "conservation_residual": 0.2642619914941399,
  "equations": [
    "x*(2.0 - y)*0.5",
    "y*(x*0.5 - 1*1.0)"
  ],
  "wall_s_total": 17.69540596400111,
  "wall_s_per_eq": [
    9.528898055999889,
    8.166507908001222
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(2.0 - y)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 8.577233724676933e-33,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.528898055999889,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1*1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 8.884951898612726e-33,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.166507908001222,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=1.6714020959177898e-16 cons=0.25495068178708336 wall_s=16.975 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.6714020959177898e-16,
  "conservation_residual": 0.25495068178708336,
  "equations": [
    "x*(-0.45465305)*(2.0 - y)*(-1.0997397)",
    "(x - 2.0)*y*0.5"
  ],
  "wall_s_total": 16.97472838700014,
  "wall_s_per_eq": [
    8.270569737000187,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-0.45465305)*(2.0 - y)*(-1.0997397)",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.342804191835579e-16,
      "pred_coeffs": {
        "x*y": -0.500000008811085
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.270569737000187,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.0461380637308897e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.704158649999954,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=2.451556743830708e-15 cons=0.24445038417042086 wall_s=17.433 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.451556743830708e-15,
  "conservation_residual": 0.24445038417042086,
  "equations": [
    "(y + y + y + y + y + y + y - 11.456229 - 2.5437708)*(-0.071428575)*x",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 17.432907046000764,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(y + y + y + y + y + y + y - 11.456229 - 2.5437708)*(-0.071428575)*x",
      "r2_train": 0.9999999999999949,
      "reward": null,
      "residual_heldout": 4.903113487661416e-15,
      "pred_coeffs": {
        "x*y": -0.500000025
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.092860541999471,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.354947289942254e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.340046504001293,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=7.560798571882226e-33 cons=0.2937381976800653 wall_s=17.677 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.560798571882226e-33,
  "conservation_residual": 0.2937381976800653,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*(-(-0.5)*x - 1.0)"
  ],
  "wall_s_total": 17.676924933999544,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "residual_heldout": 4.3406140782607315e-33,
      "pred_coeffs": {
        "x*y": -0.5
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 9.221178247998978,
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      "wall_raw_s": null,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-(-0.5)*x - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.078098306550372e-32,
      "pred_coeffs": {
        "x*y": 0.5
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        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.455746686000566,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=4.049741077052833e-15 cons=0.327640872048906 wall_s=18.373 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.049741077052833e-15,
  "conservation_residual": 0.327640872048906,
  "equations": [
    "x*(y*(-0.5) - 1*0.020781765 + 1.0207818)",
    "(x - 2.0)*y*0.5"
  ],
  "wall_s_total": 18.37346973899912,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "x*(y*(-0.5) - 1*0.020781765 + 1.0207818)",
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      "residual_heldout": 8.099482154105666e-15,
      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.850363133999053,
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      "wall_raw_s": null,
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      "budget": {
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        "target_mean_wall_s": 0
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      "free_const_values": null,
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    },
    {
      "eq_i": 1,
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      "r2_train": 1.0,
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      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.523106605000066,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=5.336743666780905e-15 cons=0.3794700322145239 wall_s=15.233 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.336743666780905e-15,
  "conservation_residual": 0.3794700322145239,
  "equations": [
    "x*(0.8888705 + y*(-0.5)) + x*0.11112953",
    "(2.0 - x)*y*(-0.5)"
  ],
  "wall_s_total": 15.233332849998988,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.8888705 + y*(-0.5)) + x*0.11112953",
      "r2_train": 0.999999999999995,
      "reward": null,
      "residual_heldout": 1.067348733356181e-14,
      "pred_coeffs": {
        "x*y": -0.5
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      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.444954354999936,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(2.0 - x)*y*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.2581624848816962e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 7.788378494999051,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=6.19674638990694e-15 cons=0.2979807800122004 wall_s=15.989 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.19674638990694e-15,
  "conservation_residual": 0.2979807800122004,
  "equations": [
    "(2.0 - y)*x*0.5",
    "(x*0.09378359 - 0.18756717)*y*5.3314233"
  ],
  "wall_s_total": 15.988505276001888,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(2.0 - y)*x*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.572304455761614e-32,
      "pred_coeffs": {
        "x*y": -0.5
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      "true_coeffs": {
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        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.958640267001101,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x*0.09378359 - 0.18756717)*y*5.3314233",
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      "reward": null,
      "residual_heldout": 1.239349277981388e-14,
      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.029865009000787,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=6.093819000069215e-17 cons=0.28406100145097274 wall_s=18.253 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
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  "recovered": false,
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  "residual": 6.093819000069215e-17,
  "conservation_residual": 0.28406100145097274,
  "equations": [
    "x*(1.0 - 0.5*y)",
    "y*3.0539834*(2.0 - x)*(-0.1637206)"
  ],
  "wall_s_total": 18.253021632001037,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "pred_coeffs": {
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      "wall_s": 8.013316542001121,
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      "free_const_values": null,
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    {
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      "equation": "y*3.0539834*(2.0 - x)*(-0.1637206)",
      "r2_train": 0.9999999999999999,
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      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 10.239705089999916,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=8.778911619539555e-33 cons=0.231553479946365 wall_s=16.822 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
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  "residual": 8.778911619539555e-33,
  "conservation_residual": 0.231553479946365,
  "equations": [
    "x*(-0.5)*(y - 1*2.0)",
    "(x - 1*2.0)*y*0.5"
  ],
  "wall_s_total": 16.82214739400115,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=3.831996759278684e-15 cons=0.1459875527754313 wall_s=18.413 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.831996759278684e-15,
  "conservation_residual": 0.1459875527754313,
  "equations": [
    "(y*0.46036714 - 0.9207343)*(-1.0860897)*(x + y*(-3.2794443e-8))",
    "((x - 1.9999998) - 1.5269929e-7)*y*0.5 + (1.3217006e-8 - 1.5776934e-8*y)*(x + 1.9412551)"
  ],
  "wall_s_total": 18.41320019900013,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(y*0.46036714 - 0.9207343)*(-1.0860897)*(x + y*(-3.2794443e-8))",
      "r2_train": 0.9999999999999938,
      "reward": null,
      "residual_heldout": 4.6171768703678936e-15,
      "pred_coeffs": {
        "x*y": -0.500000008972458,
        "y^2": 1.6397221794246763e-08
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.580349018999186,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "((x - 1.9999998) - 1.5269929e-7)*y*0.5 + (1.3217006e-8 - 1.5776934e-8*y)*(x + 1.9412551)",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 3.046816648189475e-15,
      "pred_coeffs": {
        "x*y": 0.499999984223066,
        "1": 2.56575803042306e-08
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.832851180000944,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=2.597214243853152e-15 cons=0.30875393290751385 wall_s=15.726 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.597214243853152e-15,
  "conservation_residual": 0.30875393290751385,
  "equations": [
    "(0.42081365 + y*(-0.21040682))*x*2.3763487",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 15.72648837899942,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(0.42081365 + y*(-0.21040682))*x*2.3763487",
      "r2_train": 0.9999999999999919,
      "reward": null,
      "residual_heldout": 5.194428487706304e-15,
      "pred_coeffs": {
        "x*y": -0.49999997317813394
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      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.592961798000033,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 5.281908699572063e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.133526580999387,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=1.1834486776862676e-15 cons=0.17729118675307254 wall_s=17.385 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.1834486776862676e-15,
  "conservation_residual": 0.17729118675307254,
  "equations": [
    "(y - 2.0)*(-0.21717909*x + x)*(-0.6387157)",
    "(x - 1.6642547)*y*0.5 + y*(-0.16787267)"
  ],
  "wall_s_total": 17.38495202100239,
  "wall_s_per_eq": [
    8.729070189001504,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(y - 2.0)*(-0.21717909*x + x)*(-0.6387157)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.2326417159431702e-16,
      "pred_coeffs": {
        "x*y": -0.500000005505287
      },
      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.729070189001504,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1.6642547)*y*0.5 + y*(-0.16787267)",
      "r2_train": 0.9999999999999979,
      "reward": null,
      "residual_heldout": 2.243633183778218e-15,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.655881832000887,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=9.476527324293978e-16 cons=0.1387722974828953 wall_s=16.221 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.476527324293978e-16,
  "conservation_residual": 0.1387722974828953,
  "equations": [
    "x*(-2.1495373)*((y - 1.3941416)*0.2326082 - 1*0.14092764)",
    "(x - 2.0)*0.5*y"
  ],
  "wall_s_total": 16.221375653001814,
  "wall_s_per_eq": [
    7.875375596000595,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-2.1495373)*((y - 1.3941416)*0.2326082 - 1*0.14092764)",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 1.8953054648587955e-15,
      "pred_coeffs": {
        "x*y": -0.5000000021858599
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.875375596000595,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*0.5*y",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.977248542154781e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.34600005700122,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=3.267440035798103e-16 cons=0.15225022323489804 wall_s=15.376 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.267440035798103e-16,
  "conservation_residual": 0.15225022323489804,
  "equations": [
    "(1.2551367 - y)*x*0.5 - (-0.37243164)*x",
    "(x - 2.0)*0.60358936*(-0.17162225*y + y)"
  ],
  "wall_s_total": 15.376032129999658,
  "wall_s_per_eq": [
    8.066422849999071,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(1.2551367 - y)*x*0.5 - (-0.37243164)*x",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 5.879477630386408e-16,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.066422849999071,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*0.60358936*(-0.17162225*y + y)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 6.554024412097983e-17,
      "pred_coeffs": {
        "x*y": 0.49999999596073996
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.309609280000586,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=4.692867874993869e-16 cons=0.1665227615775846 wall_s=17.710 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.692867874993869e-16,
  "conservation_residual": 0.1665227615775846,
  "equations": [
    "(2.0 - y)*0.5*x",
    "y*(x*y*(-4.3212465e-9) + x - 1.3618567)*0.5 + y*(-0.31907165)"
  ],
  "wall_s_total": 17.710099111998716,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(2.0 - y)*0.5*x",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.224604371145397e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
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        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.451588505999098,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*y*(-4.3212465e-9) + x - 1.3618567)*0.5 + y*(-0.31907165)",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 9.385735749987738e-16,
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        "x*y": 0.5
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.258510605999618,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=1.3128746143542696e-15 cons=0.27532726511164235 wall_s=16.960 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.3128746143542696e-15,
  "conservation_residual": 0.27532726511164235,
  "equations": [
    "(y - 1*2.0)*x*(-0.5)",
    "y*(2.1628532 - x)*(-0.5) - (-0.08142662)*y"
  ],
  "wall_s_total": 16.959520067000994,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(y - 1*2.0)*x*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.4652985634230523e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.338636505000977,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(2.1628532 - x)*(-0.5) - (-0.08142662)*y",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 2.625749228708539e-15,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.620883562000017,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=2.389641237606611e-32 cons=0.4592616888222142 wall_s=17.270 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.389641237606611e-32,
  "conservation_residual": 0.4592616888222142,
  "equations": [
    "x*(y - 2.0)*(-0.5)",
    "y*(x*0.5 - 1*1.0)"
  ],
  "wall_s_total": 17.270190288998492,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(y - 2.0)*(-0.5)",
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      "reward": null,
      "residual_heldout": 1.524098285313967e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.889481193999018,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1*1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.2551841898992553e-32,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.380709094999474,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=1.148231748663333e-32 cons=0.24572734350774034 wall_s=17.495 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.148231748663333e-32,
  "conservation_residual": 0.24572734350774034,
  "equations": [
    "(y - 1*2.0)*(-0.5)*x",
    "(x - 2.0)*y*0.5"
  ],
  "wall_s_total": 17.49516782000137,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "(y - 1*2.0)*(-0.5)*x",
      "r2_train": 1.0,
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      "residual_heldout": 1.1049007227897156e-32,
      "pred_coeffs": {
        "x*y": -0.5
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.02049318399986,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
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      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.47467463600151,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=3.109347250897775e-32 cons=0.46426439177578605 wall_s=15.924 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.109347250897775e-32,
  "conservation_residual": 0.46426439177578605,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*0.5*(x - 2.0)"
  ],
  "wall_s_total": 15.923574267999356,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.0412614487200414e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.505694964000213,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*0.5*(x - 2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.177433053075509e-32,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
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        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.417879303999143,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=2.1723768968783667e-15 cons=0.2291640779824771 wall_s=16.600 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.1723768968783667e-15,
  "conservation_residual": 0.2291640779824771,
  "equations": [
    "(y - 1*2.0)*(-0.49999997)*x",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 16.600493286001438,
  "wall_s_per_eq": [
    7.703794499000651,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 1*2.0)*(-0.49999997)*x",
      "r2_train": 0.9999999999999962,
      "reward": null,
      "residual_heldout": 4.3447537937567335e-15,
      "pred_coeffs": {
        "x*y": -0.49999997
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.703794499000651,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 9.324354944163135e-33,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.896698787000787,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.048148776097248484 cons=0.20429492711052577 wall_s=17.681 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.048148776097248484,
  "conservation_residual": 0.20429492711052577,
  "equations": [
    "x*(2*a - b*y)",
    "-x*(c*x + 3*d)"
  ],
  "wall_s_total": 17.681207408000773,
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    10.049287671999991,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(2*a - b*y)",
      "r2_train": 0.9999999999999947,
      "reward": null,
      "residual_heldout": 1.1313840686798245e-14,
      "pred_coeffs": {
        "x*y": -0.4999999999999997
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 10.049287671999991,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.049287671999991,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4999999999999996,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + 3*d)",
      "r2_train": 0.84726432079522,
      "reward": null,
      "residual_heldout": 0.09629755219448566,
      "pred_coeffs": {
        "x^2": 0.45148308813619004,
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.631919736000782,
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      "wall_raw_s": 7.631919736000782,
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      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.45148308813619004,
        0.3549775991610373
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.10777633168092617 cons=0.19110495319148235 wall_s=15.962 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.10777633168092617,
  "conservation_residual": 0.19110495319148235,
  "equations": [
    "x*(-a - 3*b*y)",
    "x*(-c*x - d)"
  ],
  "wall_s_total": 15.9622397309995,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 1.84922180833601e-10,
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        "x*y": -0.5000067256676852
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 7.940542092999749,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
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      "equation": "x*(-c*x - d)",
      "r2_train": 0.812377921870843,
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      "wall_s": 8.02169763799975,
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      "wall_raw_s": 8.02169763799975,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.43015981747748855,
        0.9824197499280996
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.171796482560312 cons=0.018273146797980613 wall_s=16.178 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.171796482560312,
  "conservation_residual": 0.018273146797980613,
  "equations": [
    "y*(-a + b*y)",
    "x*(c*x - d)"
  ],
  "wall_s_total": 16.17818041099963,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "y*(-a + b*y)",
      "r2_train": 0.8437147632713919,
      "reward": null,
      "residual_heldout": 0.1757496125616524,
      "pred_coeffs": {
        "y^2": -0.5052239663659475,
        "y": 1.1651876203788962
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.06665717299984,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.06665717299984,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.1651876203788962,
        -0.5052239663659475
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(c*x - d)",
      "r2_train": 0.8492951417490995,
      "reward": null,
      "residual_heldout": 0.16784335255897162,
      "pred_coeffs": {
        "x^2": 0.3810677966844757,
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      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.11152323799979,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.11152323799979,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3810677966844757,
        0.8506819896067257
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.14386503600644676 cons=0.42494970086748884 wall_s=16.700 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.14386503600644676,
  "conservation_residual": 0.42494970086748884,
  "equations": [
    "y*(a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 16.700015570999312,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "y*(a + b*y)",
      "r2_train": 0.8005696112093265,
      "reward": null,
      "residual_heldout": 0.2877300719290788,
      "pred_coeffs": {
        "y^2": -0.41278354440673515,
        "y": 0.944798729477798
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.532008971998948,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.532008971998948,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.944798729477798,
        -0.41278354440673515
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + d)",
      "r2_train": 0.9999999998759013,
      "reward": null,
      "residual_heldout": 8.381470818749493e-11,
      "pred_coeffs": {
        "x*y": 0.5000040829938787
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.168006599000364,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.168006599000364,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000040829938787,
        -1.0000118005829932
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=1.5012432129665248e-12 cons=0.44316017311374034 wall_s=16.449 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.5012432129665248e-12,
  "conservation_residual": 0.44316017311374034,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(2*c*x + d)"
  ],
  "wall_s_total": 16.449363751999044,
  "wall_s_per_eq": [
    8.548941844999717,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(-2*a + b*y)",
      "r2_train": 0.9999999999999939,
      "reward": null,
      "residual_heldout": 5.601608583399434e-15,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 8.548941844999717,
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      "wall_raw_s": 8.548941844999717,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000000000000001,
        -0.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(2*c*x + d)",
      "r2_train": 0.9999999999970656,
      "reward": null,
      "residual_heldout": 2.99688481734965e-12,
      "pred_coeffs": {
        "x*y": 0.5000008486630215
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.900421906999327,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.900421906999327,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.25000042433151076,
        -1.0000017347307226
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.11370822882939562 cons=0.13171347801770492 wall_s=15.893 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.11370822882939562,
  "conservation_residual": 0.13171347801770492,
  "equations": [
    "-x*(a + b*y)",
    "2*c*x*(x + y) + d*y"
  ],
  "wall_s_total": 15.892555714999617,
  "wall_s_per_eq": [
    8.031474721999984,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-x*(a + b*y)",
      "r2_train": 0.9999999998957936,
      "reward": null,
      "residual_heldout": 6.526720819015621e-11,
      "pred_coeffs": {
        "x*y": -0.5000040738241138
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.031474721999984,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.031474721999984,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0000096624524633,
        0.5000040738241138
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "2*c*x*(x + y) + d*y",
      "r2_train": 0.9042777018989675,
      "reward": null,
      "residual_heldout": 0.22741645759352402,
      "pred_coeffs": {
        "x*y": 0.12931509225131038,
        "x^2": 0.12931509225131038
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.861080992999632,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.861080992999632,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.06465754612565519,
        -0.5773394408314925
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=1.6353217846354003e-13 cons=0.18073980629151037 wall_s=17.103 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.6353217846354003e-13,
  "conservation_residual": 0.18073980629151037,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x - d)"
  ],
  "wall_s_total": 17.102507112998865,
  "wall_s_per_eq": [
    8.545114569000361,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9999999999997985,
      "reward": null,
      "residual_heldout": 2.5757323009850494e-13,
      "pred_coeffs": {
        "x*y": -0.5000001631853669
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.545114569000361,
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      "wall_raw_s": 8.545114569000361,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0000002739514358,
        -0.5000001631853669
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.9999999999999674,
      "reward": null,
      "residual_heldout": 6.94911268285751e-14,
      "pred_coeffs": {
        "x*y": 0.5000000020502278
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.557392543998503,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.557392543998503,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000000020502278,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=5.91158328251214e-14 cons=0.2304244444878385 wall_s=17.455 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.91158328251214e-14,
  "conservation_residual": 0.2304244444878385,
  "equations": [
    "x*(-3*a - b*y)",
    "y*(c*x + 3*d)"
  ],
  "wall_s_total": 17.455113780999454,
  "wall_s_per_eq": [
    8.922774544000276,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-3*a - b*y)",
      "r2_train": 0.9999999999999577,
      "reward": null,
      "residual_heldout": 2.705890375382283e-14,
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        "x*y": -0.49999999910234794
      },
      "true_coeffs": {
        "x": 1.0,
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      },
      "structure_ok": false,
      "wall_s": 8.922774544000276,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.922774544000276,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.33333333554389644,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + 3*d)",
      "r2_train": 0.9999999999999346,
      "reward": null,
      "residual_heldout": 9.117276189641997e-14,
      "pred_coeffs": {
        "x*y": 0.49999999054036676
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.532339236999178,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.532339236999178,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49999999054036676,
        -0.3333333750542191
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.060824252744785666 cons=0.1474433173368413 wall_s=16.363 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.060824252744785666,
  "conservation_residual": 0.1474433173368413,
  "equations": [
    "-x*(a + 2*b*y)",
    "x*(-c*x + 2*d)"
  ],
  "wall_s_total": 16.362967179999032,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-x*(a + 2*b*y)",
      "r2_train": 0.9999999999937895,
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      "residual_heldout": 6.291192897929954e-12,
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        "x*y": -0.5000012777693839
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 8.110683158998654,
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      "wall_raw_s": 8.110683158998654,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0000028664446612,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + 2*d)",
      "r2_train": 0.8403621961098761,
      "reward": null,
      "residual_heldout": 0.12164850548328014,
      "pred_coeffs": {
        "x^2": 0.48043608886184186,
        "x": -1.0850456030435975
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.252284021000378,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.252284021000378,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.48043608886184186,
        -0.5425228015217988
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=7.317614211941255e-15 cons=0.17910131177800076 wall_s=16.815 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.317614211941255e-15,
  "conservation_residual": 0.17910131177800076,
  "equations": [
    "x*(2*a - b*y)",
    "-y*(c*x + d)"
  ],
  "wall_s_total": 16.815402528998675,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(2*a - b*y)",
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      "residual_heldout": 9.133961174121613e-15,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.527046286999393,
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      "wall_raw_s": 8.527046286999393,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.9999999999999921,
      "reward": null,
      "residual_heldout": 5.501267249760896e-15,
      "pred_coeffs": {
        "x*y": 0.5000000030138849
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.288356241999281,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.288356241999281,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000000030138849,
        0.9999999992119506
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=4.213419068890631e-10 cons=0.45141925490154033 wall_s=17.156 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.213419068890631e-10,
  "conservation_residual": 0.45141925490154033,
  "equations": [
    "-x*(a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 17.155736744000023,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "max_n_evaluations": 2500,
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        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
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      "equation": "y*(c*x + d)",
      "r2_train": 0.9999999999187608,
      "reward": null,
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        "x*y": 0.5000033393631153
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      "structure_ok": false,
      "wall_s": 8.324484798000412,
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      "wall_raw_s": 8.324484798000412,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000033393631153,
        -1.0000096893844133
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.12811804508973032 cons=0.1667955907329465 wall_s=16.152 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.12811804508973032,
  "conservation_residual": 0.1667955907329465,
  "equations": [
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    "-x*(c*x + d)"
  ],
  "wall_s_total": 16.152298205999614,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-(a + 2*b*y)*(x + y)",
      "r2_train": 0.9436301178847649,
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        "x*y": -0.24834249388044552,
        "y^2": -0.24834249388044552
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        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.3231114159989374,
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      "wall_raw_s": 7.3231114159989374,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -0.5407459785352173,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + d)",
      "r2_train": 0.8903940396861796,
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        "x^2": 0.4102371836156859,
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      "structure_ok": false,
      "wall_s": 8.829186790000676,
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      "wall_raw_s": 8.829186790000676,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4102371836156859,
        0.9672594472564882
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=6.236062718731408e-14 cons=0.4007787172799806 wall_s=15.506 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.236062718731408e-14,
  "conservation_residual": 0.4007787172799806,
  "equations": [
    "x*(-3*a + b*y)",
    "-y*(c*x + d)"
  ],
  "wall_s_total": 15.506191159000082,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "residual_heldout": 2.3077044662448277e-14,
      "pred_coeffs": {
        "x*y": -0.4999999999999991
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.180066771999918,
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      "wall_raw_s": 8.180066771999918,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.33333333333333276,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.9999999999998471,
      "reward": null,
      "residual_heldout": 1.0164420971217989e-13,
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        "x*y": 0.5000000202669453
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.3261243870001636,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.3261243870001636,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000000202669453,
        0.9999999955123707
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=4.874572422189505e-15 cons=0.20414940771910253 wall_s=16.946 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
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  "residual": 4.874572422189505e-15,
  "conservation_residual": 0.20414940771910253,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(c*x - d)"
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  "wall_s_total": 16.946110842001872,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "x*y": -0.4999999999999995
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        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 8.432904978000806,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "zero_eq_retry": 2
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      "free_const_values": [
        -0.49999999999999944,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.999999999999996,
      "reward": null,
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        "x*y": 0.5000000016230245
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      "structure_ok": false,
      "wall_s": 8.513205864001065,
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      "wall_raw_s": 8.513205864001065,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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      "free_const_values": [
        0.5000000016230245,
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=7.432949899490554e-15 cons=0.12872708870819677 wall_s=17.919 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.432949899490554e-15,
  "conservation_residual": 0.12872708870819677,
  "equations": [
    "x*(2*a - b*y)",
    "y*(c*x + 3*d)"
  ],
  "wall_s_total": 17.91897443400012,
  "wall_s_per_eq": [
    8.61092520099919,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "residual_heldout": 1.2013785502861094e-14,
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        "x*y": -0.4999999999886096
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      "structure_ok": false,
      "wall_s": 8.61092520099919,
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      "wall_raw_s": 8.61092520099919,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4999999999889062,
        0.4999999999886096
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + 3*d)",
      "r2_train": 0.9999999999999959,
      "reward": null,
      "residual_heldout": 2.8521142961200138e-15,
      "pred_coeffs": {
        "x*y": 0.4999999956167846
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.30804923300093,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.30804923300093,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4999999956167846,
        -0.33333334929102615
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.0992459943976155 cons=0.3413575328687574 wall_s=17.610 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0992459943976155,
  "conservation_residual": 0.3413575328687574,
  "equations": [
    "a*x - 2*b*y**2",
    "y*(c*x - 3*d)"
  ],
  "wall_s_total": 17.610038238000925,
  "wall_s_per_eq": [
    8.636321170000883,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "a*x - 2*b*y**2",
      "r2_train": 0.7660461777825899,
      "reward": null,
      "residual_heldout": 0.19849198879516677,
      "pred_coeffs": {
        "y^2": -0.1917339399431332,
        "x": 0.3311612165821123
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.636321170000883,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.636321170000883,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3311612165821123,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - 3*d)",
      "r2_train": 0.9999999999999506,
      "reward": null,
      "residual_heldout": 6.422522102617745e-14,
      "pred_coeffs": {
        "x*y": 0.5000000000000009
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.973717068000042,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.973717068000042,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000000000000009,
        0.33333333333333365
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=1.4757145423986006e-13 cons=0.351596177125071 wall_s=17.204 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.4757145423986006e-13,
  "conservation_residual": 0.351596177125071,
  "equations": [
    "x*(a - b*y)",
    "-y*(c*x + 2*d)"
  ],
  "wall_s_total": 17.203909452000516,
  "wall_s_per_eq": [
    7.802911920000042,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(a - b*y)",
      "r2_train": 0.9999999999999707,
      "reward": null,
      "residual_heldout": 2.3772580414631024e-14,
      "pred_coeffs": {
        "x*y": -0.5000000045628126
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.802911920000042,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.802911920000042,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9999999965112008,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + 2*d)",
      "r2_train": 0.9999999999998609,
      "reward": null,
      "residual_heldout": 2.713703280650891e-13,
      "pred_coeffs": {
        "x*y": 0.5000001683532851
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.400997532000474,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.400997532000474,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000001683532851,
        0.5000001427149534
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.11418943715729203 cons=0.19935339853613485 wall_s=17.619 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.11418943715729203,
  "conservation_residual": 0.19935339853613485,
  "equations": [
    "x*(3*a + b*y)",
    "x*(-c*x + d)"
  ],
  "wall_s_total": 17.61900247400081,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(3*a + b*y)",
      "r2_train": 0.9999999999999711,
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      "residual_heldout": 2.1834301300295137e-14,
      "pred_coeffs": {
        "x*y": -0.5000000743995614
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.82466557800035,
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      "wall_raw_s": 8.82466557800035,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        0.33333337613143843,
        -0.5000000743995614
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + d)",
      "r2_train": 0.8714986615665947,
      "reward": null,
      "residual_heldout": 0.22837887431456222,
      "pred_coeffs": {
        "x^2": 0.36968353527790987,
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.794336896000459,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.794336896000459,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.36968353527790987,
        -0.8394852115316352
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=4.4188431309350274e-15 cons=0.4857499532948677 wall_s=16.697 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.4188431309350274e-15,
  "conservation_residual": 0.4857499532948677,
  "equations": [
    "-x*(4*a + b*y)",
    "y*(-c*x + 4*d)"
  ],
  "wall_s_total": 16.69685708200086,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-x*(4*a + b*y)",
      "r2_train": 0.9999999999999908,
      "reward": null,
      "residual_heldout": 5.3254244381921506e-15,
      "pred_coeffs": {
        "x*y": -0.4999999983943374
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.711298862001058,
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      "wall_raw_s": 7.711298862001058,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.250000002352958,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + 4*d)",
      "r2_train": 0.9999999999999968,
      "reward": null,
      "residual_heldout": 3.5122618236779043e-15,
      "pred_coeffs": {
        "x*y": 0.5000000000000012
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      "true_coeffs": {
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.985558219999803,
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      "wall_raw_s": 8.985558219999803,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000000000000012,
        -0.25000000000000056
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=7.073901758827458e-14 cons=0.45131961873230736 wall_s=18.786 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.073901758827458e-14,
  "conservation_residual": 0.45131961873230736,
  "equations": [
    "x*(a + b*y)",
    "y*(-c*x + d)"
  ],
  "wall_s_total": 18.786448720000408,
  "wall_s_per_eq": [
    11.223560472000827,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9999999999998795,
      "reward": null,
      "residual_heldout": 1.2903250368096782e-13,
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        "x*y": -0.5000000801523855
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        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 11.223560472000827,
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      "wall_raw_s": 11.223560472000827,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9999999849797068,
        -0.5000000801523855
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + d)",
      "r2_train": 0.9999999999999903,
      "reward": null,
      "residual_heldout": 1.2445531495581344e-14,
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        "x*y": 0.500000000384502
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      "true_coeffs": {
        "y": -1.0,
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      "structure_ok": false,
      "wall_s": 7.562888247999581,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.562888247999581,
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      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.500000000384502,
        -1.0000000007724585
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=2.5153986853510673e-32 cons=0.24573099098182288 wall_s=41.652 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.5153986853510673e-32,
  "conservation_residual": 0.24573099098182288,
  "equations": [
    "x*(y - 2.0)*(-0.5)",
    "(x - 1*2.0)*y*0.5"
  ],
  "wall_s_total": 41.65180647899979,
  "wall_s_per_eq": [
    33.1977121710006,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y - 2.0)*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.8367250765796123e-32,
      "pred_coeffs": {
        "x*y": -0.5
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 33.1977121710006,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1*2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.194072294122522e-32,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.454094307999185,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=2.250638107150173e-32 cons=0.2549330655819312 wall_s=16.209 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.250638107150173e-32,
  "conservation_residual": 0.2549330655819312,
  "equations": [
    "(y - 1*2.0)*x*(-0.5)",
    "(x - 2.0)*y*0.5"
  ],
  "wall_s_total": 16.209120629999234,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 1*2.0)*x*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.11640802221216e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.651705561000199,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.3848681920881862e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.557415068999035,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=2.7899198043249186e-32 cons=0.2493831432152292 wall_s=17.595 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.7899198043249186e-32,
  "conservation_residual": 0.2493831432152292,
  "equations": [
    "x*(-0.5)*(y - 2.0)",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 17.595436587000222,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-0.5)*(y - 2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.376896260003841e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.803469979999136,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.2029433486459957e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.791966607001086,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=1.3970833075731028e-32 cons=0.28916643815265836 wall_s=17.784 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.3970833075731028e-32,
  "conservation_residual": 0.28916643815265836,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 17.783546530999956,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.3685798934842877e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.042758710998896,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.4255867216619182e-32,
      "pred_coeffs": {
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      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.74078782000106,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=2.1429661124483083e-32 cons=0.27666375722195846 wall_s=17.424 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.1429661124483083e-32,
  "conservation_residual": 0.27666375722195846,
  "equations": [
    "(y - 2.0)*(-0.5)*x",
    "(x - 2.0)*y*0.5"
  ],
  "wall_s_total": 17.42365631999928,
  "wall_s_per_eq": [
    9.340129190999505,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 2.0)*(-0.5)*x",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.0882397404226487e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.340129190999505,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.1976924844739682e-32,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.083527128999776,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=2.0486635934258803e-32 cons=0.15499031282782136 wall_s=17.434 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.0486635934258803e-32,
  "conservation_residual": 0.15499031282782136,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*0.5*(x - 2.0)"
  ],
  "wall_s_total": 17.433977204000257,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.448838741669954e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.030384039000637,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*0.5*(x - 2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.648488445181807e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.40359316499962,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=2.4917183622744753e-16 cons=0.24521922138622831 wall_s=17.216 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.4917183622744753e-16,
  "conservation_residual": 0.24521922138622831,
  "equations": [
    "(y - 1.8215667)*x*(-0.5) + x*0.08921666",
    "y*(-(-0.5)*x - 1.0)"
  ],
  "wall_s_total": 17.216331285000706,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "(y - 1.8215667)*x*(-0.5) + x*0.08921666",
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      "reward": null,
      "residual_heldout": 4.983436724548951e-16,
      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.200537148000876,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "free_const_values": null,
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    },
    {
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      "target": "dy/dt",
      "equation": "y*(-(-0.5)*x - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.3088716012066878e-32,
      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.01579413699983,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=7.13811777731508e-16 cons=0.13662663486416987 wall_s=17.853 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.13811777731508e-16,
  "conservation_residual": 0.13662663486416987,
  "equations": [
    "(2.0 - y)*x*0.5",
    "(x - 3.681364e-8*(x - 2.0) - 2.0)*0.5*y"
  ],
  "wall_s_total": 17.853117114998895,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 2.1511003998405154e-32,
      "pred_coeffs": {
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      },
      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.148887609999292,
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      "budget": {
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        "timeout_in_seconds": 100,
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      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 3.681364e-8*(x - 2.0) - 2.0)*0.5*y",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 1.427623555463016e-15,
      "pred_coeffs": {
        "x*y": 0.49999998159318
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.704229504999603,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=1.3742587010383076e-32 cons=0.2593350915156855 wall_s=17.066 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.3742587010383076e-32,
  "conservation_residual": 0.2593350915156855,
  "equations": [
    "(y - 2.0)*x*(-0.5)",
    "(x - 2.0)*y*0.5"
  ],
  "wall_s_total": 17.0662272440004,
  "wall_s_per_eq": [
    8.176571625999713,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 2.0)*x*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.331414358419402e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.176571625999713,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.417103043657213e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.889655618000688,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=1.7461972906102551e-32 cons=0.2813962298181219 wall_s=17.287 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7461972906102551e-32,
  "conservation_residual": 0.2813962298181219,
  "equations": [
    "x*0.5*(2.0 - y)",
    "y*(x - 2.0)*0.5"
  ],
  "wall_s_total": 17.28654594100044,
  "wall_s_per_eq": [
    9.67300791100024,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*0.5*(2.0 - y)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.064598099981394e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.67300791100024,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x - 2.0)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.4277964812391167e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.6135380300002,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=1.7461891957492846e-32 cons=0.24035803943323897 wall_s=17.419 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7461891957492846e-32,
  "conservation_residual": 0.24035803943323897,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 17.419314522001514,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.7972376697771702e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.631548297000336,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.6951407217213988e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.787766225001178,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=2.420321832941858e-32 cons=0.15890408321189817 wall_s=16.702 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.420321832941858e-32,
  "conservation_residual": 0.15890408321189817,
  "equations": [
    "x*(-0.5)*(y - 1*2.0)",
    "y*0.5*(x - 2.0)"
  ],
  "wall_s_total": 16.701822170000014,
  "wall_s_per_eq": [
    8.007082718000675,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-0.5)*(y - 1*2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.9402663267611277e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.007082718000675,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*0.5*(x - 2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.9003773391225884e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.69473945199934,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=1.6085029226799313e-32 cons=0.20212843995845842 wall_s=17.239 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.6085029226799313e-32,
  "conservation_residual": 0.20212843995845842,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 17.239216167999984,
  "wall_s_per_eq": [
    8.803793995999513,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.0441030504298485e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.803793995999513,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.1729027949300143e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.435422172000472,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=2.959807396703543e-32 cons=0.31350656984821285 wall_s=16.410 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.959807396703543e-32,
  "conservation_residual": 0.31350656984821285,
  "equations": [
    "x*(y - 2.0)*(-0.5)",
    "y*(x - 2.0)*0.5"
  ],
  "wall_s_total": 16.410108428000967,
  "wall_s_per_eq": [
    8.678001050000603,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y - 2.0)*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.50172014556813e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.678001050000603,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
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      "target": "dy/dt",
      "equation": "y*(x - 2.0)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.417894647838957e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.732107378000364,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=3.122382360938309e-32 cons=0.15012655014637255 wall_s=19.331 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.122382360938309e-32,
  "conservation_residual": 0.15012655014637255,
  "equations": [
    "(2.0 - y)*x*0.5",
    "(x - 1*2.0)*y*0.5"
  ],
  "wall_s_total": 19.331043317997683,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(2.0 - y)*x*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.907177275985494e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.784920942998724,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1*2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.3375874458911234e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.546122374998959,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=2.7224109977761493e-15 cons=0.3924895095224724 wall_s=18.684 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.7224109977761493e-15,
  "conservation_residual": 0.3924895095224724,
  "equations": [
    "x*(0.5950506 + y*(-0.5)) - (-0.40494943)*x",
    "y*(-(-0.5)*x - 1.0)"
  ],
  "wall_s_total": 18.683813983001528,
  "wall_s_per_eq": [
    9.865337225000985,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(0.5950506 + y*(-0.5)) - (-0.40494943)*x",
      "r2_train": 0.9999999999999949,
      "reward": null,
      "residual_heldout": 5.4448219955522985e-15,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.865337225000985,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-(-0.5)*x - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.4318071090047938e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.818476758000543,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=1.2012345153963336e-32 cons=0.3494592682652089 wall_s=17.867 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.2012345153963336e-32,
  "conservation_residual": 0.3494592682652089,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "(x - 2.0)*y*0.5"
  ],
  "wall_s_total": 17.867477212999802,
  "wall_s_per_eq": [
    9.222110904000147,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.1366519879340406e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.222110904000147,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.2658170428586265e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.645366308999655,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=1.1449338601829133e-32 cons=0.33086185322521283 wall_s=18.261 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.1449338601829133e-32,
  "conservation_residual": 0.33086185322521283,
  "equations": [
    "x*(2.0 - y)*0.5",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 18.260537699999986,
  "wall_s_per_eq": [
    9.107765990000189,
    9.152771709999797
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(2.0 - y)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.1669494642931069e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.107765990000189,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.1229182560727196e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.152771709999797,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=1.889878211033565e-32 cons=0.23250115963193843 wall_s=16.493 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.889878211033565e-32,
  "conservation_residual": 0.23250115963193843,
  "equations": [
    "(y - 2.0)*x*(-0.5)",
    "(2.0 - x)*y*(-0.5)"
  ],
  "wall_s_total": 16.49306230399816,
  "wall_s_per_eq": [
    8.280485961999148,
    8.21257634199901
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(y - 2.0)*x*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.8604309657706325e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.280485961999148,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(2.0 - x)*y*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.919325456296497e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.21257634199901,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=2.318589045865241e-32 cons=0.2859610814738695 wall_s=18.381 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.318589045865241e-32,
  "conservation_residual": 0.2859610814738695,
  "equations": [
    "(y - 2.0)*x*(-0.5)",
    "y*(x - 1*2.0)*0.5"
  ],
  "wall_s_total": 18.381189554998855,
  "wall_s_per_eq": [
    8.706935374999375,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 2.0)*x*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.8291101360800756e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.706935374999375,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x - 1*2.0)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.8080679556504066e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.67425417999948,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.05801255256661834 cons=0.16751705189405847 wall_s=16.806 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.05801255256661834,
  "conservation_residual": 0.16751705189405847,
  "equations": [
    "x*(2*a - b*y)",
    "-x*(c*x + 3*d)"
  ],
  "wall_s_total": 16.806099868001183,
  "wall_s_per_eq": [
    9.188116785000602,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(2*a - b*y)",
      "r2_train": 0.9999999999999963,
      "reward": null,
      "residual_heldout": 7.071400302026714e-15,
      "pred_coeffs": {
        "x*y": -0.5000000000000002
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.188116785000602,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.188116785000602,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000000000000001,
        0.5000000000000002
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + 3*d)",
      "r2_train": 0.833630027535049,
      "reward": null,
      "residual_heldout": 0.1160251051332296,
      "pred_coeffs": {
        "x^2": 0.44929175331352134,
        "x": -1.0750227959878458
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.617983083000581,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.617983083000581,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.44929175331352134,
        0.3583409319959486
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.09545568236475979 cons=0.120633414229765 wall_s=16.682 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.09545568236475979,
  "conservation_residual": 0.120633414229765,
  "equations": [
    "x*(-a - 3*b*y)",
    "x*(-c*x - d)"
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  "wall_s_total": 16.68237507899903,
  "wall_s_per_eq": [
    9.28039589599939,
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a - 3*b*y)",
      "r2_train": 0.9999999999785135,
      "reward": null,
      "residual_heldout": 2.0782233503757166e-11,
      "pred_coeffs": {
        "x*y": -0.5000022267703027
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 9.28039589599939,
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      "wall_raw_s": 9.28039589599939,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0000048451685817,
        0.16666740892343423
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x - d)",
      "r2_train": 0.8520740952522423,
      "reward": null,
      "residual_heldout": 0.19091136470873735,
      "pred_coeffs": {
        "x^2": 0.4345722090219192,
        "x": -1.0359228334289876
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.401979182999639,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.401979182999639,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4345722090219192,
        1.0359228334289876
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.08123965327185488 cons=0.19301221466955396 wall_s=16.753 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08123965327185488,
  "conservation_residual": 0.19301221466955396,
  "equations": [
    "x*(-a + b*y)",
    "x*(c*x - d)"
  ],
  "wall_s_total": 16.75272414900064,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9999999999991973,
      "reward": null,
      "residual_heldout": 6.493959058319044e-13,
      "pred_coeffs": {
        "x*y": -0.5000003985059741
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.366006394000578,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.366006394000578,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0000006749287833,
        -0.5000003985059741
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(c*x - d)",
      "r2_train": 0.850606921271986,
      "reward": null,
      "residual_heldout": 0.16247930654306036,
      "pred_coeffs": {
        "x^2": 0.42607446817891875,
        "x": -0.9983044374371353
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.386717755000063,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.386717755000063,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.42607446817891875,
        0.9983044374371353
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=3.046688744755247e-10 cons=0.2891598723980085 wall_s=18.023 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.046688744755247e-10,
  "conservation_residual": 0.2891598723980085,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 18.023282690999622,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.684422844000437,
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      "wall_raw_s": 9.684422844000437,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -1.0000223943088542,
        -0.5000122598431339
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + d)",
      "r2_train": 0.9999999999985139,
      "reward": null,
      "residual_heldout": 1.4635332577135903e-12,
      "pred_coeffs": {
        "x*y": 0.5000005693200534
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.338859846999185,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.338859846999185,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000005693200534,
        -1.0000013513984634
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=3.898765563806023e-12 cons=0.2766644671705869 wall_s=14.933 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.898765563806023e-12,
  "conservation_residual": 0.2766644671705869,
  "equations": [
    "x*(a - b*y)",
    "y*(2*c*x + d)"
  ],
  "wall_s_total": 14.932586107001043,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(a - b*y)",
      "r2_train": 0.9999999999999888,
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      "residual_heldout": 1.666705769421761e-14,
      "pred_coeffs": {
        "x*y": -0.500000004612489
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.431455396999809,
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      "wall_raw_s": 7.431455396999809,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9999999964794659,
        0.500000004612489
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(2*c*x + d)",
      "r2_train": 0.999999999992702,
      "reward": null,
      "residual_heldout": 7.780864069917828e-12,
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        "x*y": 0.5000011947601585
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      "structure_ok": false,
      "wall_s": 7.5011307100012345,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.5011307100012345,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.25000059738007924,
        -1.0000029895199285
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.08016927570136774 cons=0.13020776751684657 wall_s=16.958 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08016927570136774,
  "conservation_residual": 0.13020776751684657,
  "equations": [
    "-x*(a + b*y)",
    "2*c*x*(x + y) + d*y"
  ],
  "wall_s_total": 16.95755980099966,
  "wall_s_per_eq": [
    7.460731623999891,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-x*(a + b*y)",
      "r2_train": 0.9999999999169941,
      "reward": null,
      "residual_heldout": 5.2572943689356314e-11,
      "pred_coeffs": {
        "x*y": -0.5000035190990282
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.460731623999891,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.460731623999891,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0000087929845676,
        0.5000035190990282
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "2*c*x*(x + y) + d*y",
      "r2_train": 0.8558679459604658,
      "reward": null,
      "residual_heldout": 0.16033855135016253,
      "pred_coeffs": {
        "x*y": 0.13259470729600145,
        "x^2": 0.13259470729600145
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 9.49682817699977,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.49682817699977,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        0.06629735364800073,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=1.9523661749725556e-10 cons=0.24522184725569246 wall_s=19.697 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.9523661749725556e-10,
  "conservation_residual": 0.24522184725569246,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x - d)"
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  "wall_s_total": 19.69668093600194,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9999999999959779,
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        "x*y": -0.4999990769330827
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 9.421156762000464,
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      "wall_raw_s": 9.421156762000464,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      "free_const_values": [
        -0.9999979928981044,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "y*(c*x - d)",
      "r2_train": 0.9999999996215896,
      "reward": null,
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        "x*y": 0.5000040612134008
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      "structure_ok": false,
      "wall_s": 10.275524174001475,
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      "wall_raw_s": 10.275524174001475,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      },
      "free_const_values": [
        0.5000040612134008,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=1.7111564087231284e-10 cons=0.13662724949645827 wall_s=19.547 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7111564087231284e-10,
  "conservation_residual": 0.13662724949645827,
  "equations": [
    "x*(-3*a - b*y)",
    "y*(c*x + 3*d)"
  ],
  "wall_s_total": 19.546902801001124,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9999999995402468,
      "reward": null,
      "residual_heldout": 3.422015633179616e-10,
      "pred_coeffs": {
        "x*y": -0.4999981121794578
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.579817867999736,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.579817867999736,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.33333470826821676,
        0.4999981121794578
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + 3*d)",
      "r2_train": 0.9999999999999665,
      "reward": null,
      "residual_heldout": 2.971842666412848e-14,
      "pred_coeffs": {
        "x*y": 0.4999999944449467
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 11.967084933001388,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.967084933001388,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4999999944449467,
        -0.33333335656071583
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.08542102592417983 cons=0.16024735410332208 wall_s=17.057 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08542102592417983,
  "conservation_residual": 0.16024735410332208,
  "equations": [
    "x*(a - 4*b*y)",
    "x*(-c*x + 2*d)"
  ],
  "wall_s_total": 17.057438503999947,
  "wall_s_per_eq": [
    7.980372422000073,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(a - 4*b*y)",
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      "reward": null,
      "residual_heldout": 9.216369807648639e-14,
      "pred_coeffs": {
        "x*y": -0.5000000472390097
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.980372422000073,
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      "wall_raw_s": 7.980372422000073,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9999999914229056,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + 2*d)",
      "r2_train": 0.8639534313673692,
      "reward": null,
      "residual_heldout": 0.17084205184826748,
      "pred_coeffs": {
        "x^2": 0.4545364167082325,
        "x": -1.0793374680868817
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.077066081999874,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.077066081999874,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4545364167082325,
        -0.5396687340434408
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=9.526128020474495e-15 cons=0.2813962310711071 wall_s=18.310 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.526128020474495e-15,
  "conservation_residual": 0.2813962310711071,
  "equations": [
    "x*(2*a - b*y)",
    "-y*(c*x + d)"
  ],
  "wall_s_total": 18.310446060000686,
  "wall_s_per_eq": [
    10.925777066000592,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(2*a - b*y)",
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      "residual_heldout": 1.572990044563054e-14,
      "pred_coeffs": {
        "x*y": -0.49999999999999944
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 10.925777066000592,
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      "wall_raw_s": 10.925777066000592,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        0.4999999999999995,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.999999999999994,
      "reward": null,
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      "pred_coeffs": {
        "x*y": 0.5000000025830609
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.384668994000094,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.384668994000094,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000000025830609,
        0.9999999993741914
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=5.655008770835609e-12 cons=0.24035835261742367 wall_s=17.407 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.655008770835609e-12,
  "conservation_residual": 0.24035835261742367,
  "equations": [
    "-x*(a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 17.407386884000516,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
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      "residual_heldout": 4.888369686205594e-13,
      "pred_coeffs": {
        "x*y": -0.5000003483304235
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.879800372998943,
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      "wall_raw_s": 9.879800372998943,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0000007148433123,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + d)",
      "r2_train": 0.9999999999911682,
      "reward": null,
      "residual_heldout": 1.0821180573050658e-11,
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        "x*y": 0.5000011374188821
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.527586511001573,
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      "wall_raw_s": 7.527586511001573,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000011374188821,
        -1.000003387947025
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.12579467290677163 cons=0.08360432851238474 wall_s=17.648 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.12579467290677163,
  "conservation_residual": 0.08360432851238474,
  "equations": [
    "-(a + 2*b*y)*(x + y)",
    "-x*(c*x + d)"
  ],
  "wall_s_total": 17.64827585400053,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9521217176306229,
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      "residual_heldout": 0.04073882021935239,
      "pred_coeffs": {
        "x*y": -0.23491553195552314,
        "y^2": -0.23491553195552314
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        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.425853044000178,
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      "wall_raw_s": 7.425853044000178,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -0.5189104535047752,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + d)",
      "r2_train": 0.8450634005086677,
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        "x^2": 0.4294904579582272,
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      "true_coeffs": {
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 10.222422810000353,
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      "wall_raw_s": 10.222422810000353,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4294904579582272,
        1.0329986669915152
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=1.5877415507687012e-13 cons=0.20212847599769423 wall_s=18.101 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
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  "residual": 1.5877415507687012e-13,
  "conservation_residual": 0.20212847599769423,
  "equations": [
    "x*(-3*a + b*y)",
    "-y*(c*x + d)"
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  "wall_s_total": 18.10108657299861,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "x*y": -0.4999999999999998
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        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 9.463424972000212,
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      "wall_raw_s": 9.463424972000212,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "zero_eq_retry": 2
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      "free_const_values": [
        -0.3333333333333331,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.9999999999993299,
      "reward": null,
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        "x*y": 0.5000001122990896
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      "structure_ok": false,
      "wall_s": 8.637661600998399,
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      "wall_raw_s": 8.637661600998399,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.5000001122990896,
        0.9999999804477071
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=1.9530670965115825e-14 cons=0.3135066181447235 wall_s=19.310 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.9530670965115825e-14,
  "conservation_residual": 0.3135066181447235,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(c*x - d)"
  ],
  "wall_s_total": 19.309917238999333,
  "wall_s_per_eq": [
    10.934868885999094,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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        "x*y": -0.4999999030092514
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      "structure_ok": false,
      "wall_s": 10.934868885999094,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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      "zero_eq": false,
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    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.9999999999999953,
      "reward": null,
      "residual_heldout": 4.241503104166205e-15,
      "pred_coeffs": {
        "x*y": 0.5000000009771464
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.375048353000238,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.375048353000238,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000000009771464,
        0.9999999993899771
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=7.387562745548512e-15 cons=0.15012654960263427 wall_s=18.493 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.387562745548512e-15,
  "conservation_residual": 0.15012654960263427,
  "equations": [
    "x*(2*a - b*y)",
    "y*(c*x + 3*d)"
  ],
  "wall_s_total": 18.492910965000192,
  "wall_s_per_eq": [
    7.624594324999634,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(2*a - b*y)",
      "r2_train": 0.9999999999999941,
      "reward": null,
      "residual_heldout": 8.529384487671803e-15,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.624594324999634,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.624594324999634,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5,
        0.5
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + 3*d)",
      "r2_train": 0.999999999999996,
      "reward": null,
      "residual_heldout": 6.245741003425221e-15,
      "pred_coeffs": {
        "x*y": 0.49999999822827035
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.868316640000558,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.868316640000558,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49999999822827035,
        -0.3333333387129975
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.14945176578550004 cons=0.3257356752534722 wall_s=15.345 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.14945176578550004,
  "conservation_residual": 0.3257356752534722,
  "equations": [
    "a*x - 2*b*y**2",
    "y*(c*x - 3*d)"
  ],
  "wall_s_total": 15.345258295998065,
  "wall_s_per_eq": [
    7.695002648999434,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "a*x - 2*b*y**2",
      "r2_train": 0.7294583611912729,
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      "residual_heldout": 0.29890353157096833,
      "pred_coeffs": {
        "y^2": -0.1986133947188627,
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.695002648999434,
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      "wall_raw_s": 7.695002648999434,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        0.3553803620668479,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - 3*d)",
      "r2_train": 0.9999999999999676,
      "reward": null,
      "residual_heldout": 3.175387122408848e-14,
      "pred_coeffs": {
        "x*y": 0.4999999999999996
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.65025564699863,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.65025564699863,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4999999999999996,
        0.33333333333333315
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=1.141198230734364e-12 cons=0.3494594528266273 wall_s=18.118 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.141198230734364e-12,
  "conservation_residual": 0.3494594528266273,
  "equations": [
    "x*(a - b*y)",
    "-y*(c*x + 2*d)"
  ],
  "wall_s_total": 18.11788029699892,
  "wall_s_per_eq": [
    10.669296883999777,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(a - b*y)",
      "r2_train": 0.9999999999999665,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.5000000013117298
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 10.669296883999777,
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      "wall_raw_s": 10.669296883999777,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9999999991404109,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + 2*d)",
      "r2_train": 0.9999999999977047,
      "reward": null,
      "residual_heldout": 2.250382546966653e-12,
      "pred_coeffs": {
        "x*y": 0.5000002568818637
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.448583412999142,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.448583412999142,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000002568818637,
        0.49999992706406454
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.09262707633383731 cons=0.2102949050339481 wall_s=17.421 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.09262707633383731,
  "conservation_residual": 0.2102949050339481,
  "equations": [
    "x*(3*a + b*y)",
    "x*(-c*x + d)"
  ],
  "wall_s_total": 17.420808615999704,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(3*a + b*y)",
      "r2_train": 0.999999999999983,
      "reward": null,
      "residual_heldout": 1.3540850495271823e-14,
      "pred_coeffs": {
        "x*y": -0.5000000073856321
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.258903619998819,
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      "wall_raw_s": 7.258903619998819,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.33333333843448165,
        -0.5000000073856321
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + d)",
      "r2_train": 0.842927412294228,
      "reward": null,
      "residual_heldout": 0.18525415266766107,
      "pred_coeffs": {
        "x^2": 0.4563395409767955,
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 10.161904996000885,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.161904996000885,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4563395409767955,
        -1.0755116715428985
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=8.126320528186135e-15 cons=0.2325011596963294 wall_s=15.677 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.126320528186135e-15,
  "conservation_residual": 0.2325011596963294,
  "equations": [
    "-x*(4*a + b*y)",
    "y*(-c*x + 4*d)"
  ],
  "wall_s_total": 15.67747592699925,
  "wall_s_per_eq": [
    8.54291525500048,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-x*(4*a + b*y)",
      "r2_train": 0.9999999999999898,
      "reward": null,
      "residual_heldout": 1.1216899659526778e-14,
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        "x*y": -0.49999999986368593
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.54291525500048,
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      "wall_raw_s": 8.54291525500048,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.2500000002311812,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + 4*d)",
      "r2_train": 0.9999999999999962,
      "reward": null,
      "residual_heldout": 5.035741396845493e-15,
      "pred_coeffs": {
        "x*y": 0.49999999999999944
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.13456067199877,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.13456067199877,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49999999999999944,
        -0.24999999999999972
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=9.574868453715303e-13 cons=0.2859611001272939 wall_s=19.339 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.574868453715303e-13,
  "conservation_residual": 0.2859611001272939,
  "equations": [
    "x*(a + b*y)",
    "y*(-c*x + d)"
  ],
  "wall_s_total": 19.33902245200079,
  "wall_s_per_eq": [
    10.976562145000571,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(a + b*y)",
      "r2_train": 0.9999999999987523,
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      "residual_heldout": 1.4340386324564872e-12,
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        "x*y": -0.5000001803609779
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        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 10.976562145000571,
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      "wall_raw_s": 10.976562145000571,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9999999665075053,
        -0.5000001803609779
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + d)",
      "r2_train": 0.9999999999992251,
      "reward": null,
      "residual_heldout": 4.809350582865735e-13,
      "pred_coeffs": {
        "x*y": 0.5000002235877853
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.36246030700022,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.36246030700022,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000002235877853,
        -1.0000001789451693
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=1.474868368921389e-32 cons=0.2696688348437952 wall_s=20.342 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.474868368921389e-32,
  "conservation_residual": 0.2696688348437952,
  "equations": [
    "x*(-0.5)*(y - 2.0)",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 20.34229937100099,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-0.5)*(y - 2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.5477564020176862e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 10.946674259999781,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.4019803358250913e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.395625111001209,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=1.703051120758433e-32 cons=0.2697836940998729 wall_s=18.952 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.703051120758433e-32,
  "conservation_residual": 0.2697836940998729,
  "equations": [
    "(y - 2.0)*x*(-0.5)",
    "(2.0 - x)*y*(-0.5)"
  ],
  "wall_s_total": 18.95168485100112,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 2.0)*x*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.7330961458916597e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.869984872000714,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(2.0 - x)*y*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.6730060956252067e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.081699979000405,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=2.312683226211943e-32 cons=0.22400768570967966 wall_s=18.483 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.312683226211943e-32,
  "conservation_residual": 0.22400768570967966,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 18.48274654799934,
  "wall_s_per_eq": [
    9.39943591500014,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.0488301381701022e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.39943591500014,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.576536314253784e-32,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.0833106329992,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=2.2548554492110302e-32 cons=0.2432272847335921 wall_s=17.173 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.2548554492110302e-32,
  "conservation_residual": 0.2432272847335921,
  "equations": [
    "x*(1.0 - 0.5*y)",
    "y*0.5*(x - 1*2.0)"
  ],
  "wall_s_total": 17.172560289998728,
  "wall_s_per_eq": [
    8.642810683999414,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 - 0.5*y)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.229762323025703e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.642810683999414,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*0.5*(x - 1*2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.2799485753963575e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.529749605999314,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=2.040286404784727e-32 cons=0.2840520082294754 wall_s=18.786 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.040286404784727e-32,
  "conservation_residual": 0.2840520082294754,
  "equations": [
    "x*(y - 1*2.0)*(-0.5)",
    "y*(x - 2.0)*0.5"
  ],
  "wall_s_total": 18.786301396001363,
  "wall_s_per_eq": [
    8.912752016000013,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y - 1*2.0)*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.012185621196806e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.912752016000013,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x - 2.0)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.068387188372648e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.87354938000135,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=2.1724581697945224e-32 cons=0.2326673304273854 wall_s=19.200 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.1724581697945224e-32,
  "conservation_residual": 0.2326673304273854,
  "equations": [
    "x*(-0.5)*(y - 2.0)",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 19.199913862999892,
  "wall_s_per_eq": [
    9.417429606999576,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(-0.5)*(y - 2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.9385561607714012e-32,
      "pred_coeffs": {
        "x*y": -0.5
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      "true_coeffs": {
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        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 9.417429606999576,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.4063601788176433e-32,
      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.782484256000316,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=1.8655989415315327e-32 cons=0.21116397659113642 wall_s=19.232 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.8655989415315327e-32,
  "conservation_residual": 0.21116397659113642,
  "equations": [
    "(y - 2.0)*x*(-0.5)",
    "y*0.5*(x - 2.0)"
  ],
  "wall_s_total": 19.23240550400078,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "residual_heldout": 1.8561857949381518e-32,
      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.964242035999632,
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    {
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.268163468001148,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=1.6558382824059372e-32 cons=0.22981563042630976 wall_s=19.330 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.6558382824059372e-32,
  "conservation_residual": 0.22981563042630976,
  "equations": [
    "x*(y*(-0.5) - 1*(-1.0))",
    "y*(x - 1*2.0)*0.5"
  ],
  "wall_s_total": 19.33047269999952,
  "wall_s_per_eq": [
    10.080022195999845,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(y*(-0.5) - 1*(-1.0))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.7664119314726197e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 10.080022195999845,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x - 1*2.0)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.5452646333392546e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.250450503999673,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=1.7207987762921192e-32 cons=0.27133918105815225 wall_s=18.198 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7207987762921192e-32,
  "conservation_residual": 0.27133918105815225,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*(x*0.5 - 1*1.0)"
  ],
  "wall_s_total": 18.19776133599771,
  "wall_s_per_eq": [
    9.272885680999025,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.5216450589852574e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.272885680999025,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1*1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.9199524935989808e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.924875654998687,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=2.3080614666207163e-32 cons=0.22764635567847027 wall_s=20.062 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.3080614666207163e-32,
  "conservation_residual": 0.22764635567847027,
  "equations": [
    "x*0.5*(2.0 - y)",
    "y*(x - 2.0)*0.5"
  ],
  "wall_s_total": 20.06205936999868,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*0.5*(2.0 - y)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.1841709867486507e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 10.79597339099928,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x - 2.0)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.431951946492782e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.2660859789994,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=1.549415549581328e-32 cons=0.3359187647861589 wall_s=18.933 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.549415549581328e-32,
  "conservation_residual": 0.3359187647861589,
  "equations": [
    "x*(y*(-0.5) - 1*(-1.0))",
    "y*0.5*(x - 1*2.0)"
  ],
  "wall_s_total": 18.93312899800003,
  "wall_s_per_eq": [
    8.523049802000969,
    10.41007919599906
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y*(-0.5) - 1*(-1.0))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.6103007955195255e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.523049802000969,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*0.5*(x - 1*2.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.4885303036431304e-32,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
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        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.41007919599906,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=1.442840656723228e-32 cons=0.27933305331039526 wall_s=18.163 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.442840656723228e-32,
  "conservation_residual": 0.27933305331039526,
  "equations": [
    "(y - 1*2.0)*x*(-0.5)",
    "y*(x - 2.0)*0.5"
  ],
  "wall_s_total": 18.163116207999337,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 1*2.0)*x*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.5973891711551264e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.678125082000406,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x - 2.0)*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.2882921422913296e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.484991125998931,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=1.6192383776963915e-32 cons=0.3186333053157852 wall_s=17.690 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.6192383776963915e-32,
  "conservation_residual": 0.3186333053157852,
  "equations": [
    "x*(1.0 - 0.5*y)",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 17.689799652000147,
  "wall_s_per_eq": [
    8.908134866000182,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(1.0 - 0.5*y)",
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      "residual_heldout": 1.4925689985608051e-32,
      "pred_coeffs": {
        "x*y": -0.5
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      "true_coeffs": {
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        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.908134866000182,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.7459077568319782e-32,
      "pred_coeffs": {
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      "true_coeffs": {
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.781664785999965,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=2.380521394994936e-32 cons=0.2577514177338325 wall_s=18.300 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.380521394994936e-32,
  "conservation_residual": 0.2577514177338325,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 18.300308922000113,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
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      "residual_heldout": 2.5205714229668495e-32,
      "pred_coeffs": {
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      },
      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 9.003527986000336,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.2404713670230224e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.296780935999777,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=1.7738849287411812e-32 cons=0.256586351899207 wall_s=17.661 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7738849287411812e-32,
  "conservation_residual": 0.256586351899207,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "(x - 2.0)*0.5*y"
  ],
  "wall_s_total": 17.661084668998228,
  "wall_s_per_eq": [
    8.70990029299901,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.7694097436392818e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.70990029299901,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*0.5*y",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.7783601138430806e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.951184375999219,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=1.4491778432812616e-32 cons=0.28678456938727426 wall_s=18.380 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.4491778432812616e-32,
  "conservation_residual": 0.28678456938727426,
  "equations": [
    "x*(-0.5)*(y - 1*2.0)",
    "(x - 2.0)*y*0.5"
  ],
  "wall_s_total": 18.38021352299984,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-0.5)*(y - 1*2.0)",
      "r2_train": 1.0,
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      "residual_heldout": 1.4865890423958435e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.045924648000437,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0)*y*0.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.4117666441666798e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.334288874999402,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=2.1864793933221714e-32 cons=0.22183533787135593 wall_s=18.436 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.1864793933221714e-32,
  "conservation_residual": 0.22183533787135593,
  "equations": [
    "(2.0 - y)*0.5*x",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 18.435829850001028,
  "wall_s_per_eq": [
    9.71549342400067,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(2.0 - y)*0.5*x",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.324970541459138e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.71549342400067,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.047988245185205e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.720336426000358,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=1.5111294392026135e-32 cons=0.23886723529208492 wall_s=18.229 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.5111294392026135e-32,
  "conservation_residual": 0.23886723529208492,
  "equations": [
    "x*(1.0 - 0.5*y)",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 18.228789214001154,
  "wall_s_per_eq": [
    8.488416733000122,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 - 0.5*y)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.5929843746711143e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.488416733000122,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.4292745037341128e-32,
      "pred_coeffs": {
        "x*y": 0.5
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.740372481001032,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=2.0913991657247483e-32 cons=0.26212278264229527 wall_s=18.218 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.0913991657247483e-32,
  "conservation_residual": 0.26212278264229527,
  "equations": [
    "x*(1.0 - 0.5*y)",
    "y*(-(-0.5)*x - 1.0)"
  ],
  "wall_s_total": 18.217878637000467,
  "wall_s_per_eq": [
    9.017638465000346,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 - 0.5*y)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.832843888530632e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.017638465000346,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-(-0.5)*x - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.3499544429188646e-32,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.200240172000122,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=2.0574445112373484e-32 cons=0.2477077510480232 wall_s=17.892 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.0574445112373484e-32,
  "conservation_residual": 0.2477077510480232,
  "equations": [
    "x*(1.0 + y*(-0.5))",
    "y*(x*0.5 - 1.0)"
  ],
  "wall_s_total": 17.89225809399977,
  "wall_s_per_eq": [
    8.48862262900002,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(1.0 + y*(-0.5))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.3241387163147464e-32,
      "pred_coeffs": {
        "x*y": -0.5
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.48862262900002,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5 - 1.0)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.79075030615995e-32,
      "pred_coeffs": {
        "x*y": 0.5
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.403635464999752,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=False residual=0.34553563775585217 cons=0.06849659746214537 wall_s=19.220 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.34553563775585217,
  "conservation_residual": 0.06849659746214537,
  "equations": [
    "2*a*(-x + y)",
    "-x*(c*x + 3*d)"
  ],
  "wall_s_total": 19.219865346000006,
  "wall_s_per_eq": [
    8.097941145999357,
    11.121924200000649
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*a*(-x + y)",
      "r2_train": 0.46294342781206677,
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        "x": 0.49575965204769584,
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.097941145999357,
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      "wall_raw_s": 8.097941145999357,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -0.24787982602384792,
        1.0
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + 3*d)",
      "r2_train": 0.838249262062283,
      "reward": null,
      "residual_heldout": 0.14656742591463842,
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        "x^2": 0.43052423310412935,
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 11.121924200000649,
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      "wall_raw_s": 11.121924200000649,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.43052423310412935,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.08553944301395351 cons=0.1638624140405075 wall_s=17.106 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08553944301395351,
  "conservation_residual": 0.1638624140405075,
  "equations": [
    "x*(-a - 3*b*y)",
    "x*(-c*x - d)"
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  "wall_s_total": 17.106169811000655,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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        "x*y": -0.5000024543973891
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 8.074342883999634,
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      "wall_raw_s": 8.074342883999634,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -1.0000052545427731,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x - d)",
      "r2_train": 0.8607425187871196,
      "reward": null,
      "residual_heldout": 0.17107888600261315,
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        "x^2": 0.4424464789598738,
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      "true_coeffs": {
        "y": -1.0,
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      "structure_ok": false,
      "wall_s": 9.03182692700102,
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      "wall_raw_s": 9.03182692700102,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4424464789598738,
        1.0478553932013757
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.08595673836236711 cons=0.1468768110481016 wall_s=20.845 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08595673836236711,
  "conservation_residual": 0.1468768110481016,
  "equations": [
    "x*(-a + b*y)",
    "x*(c*x - d)"
  ],
  "wall_s_total": 20.84540458000083,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "wall_s": 9.28229113999987,
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      "budget": {
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(c*x - d)",
      "r2_train": 0.847425027564388,
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        "x^2": 0.44040291573101725,
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      "structure_ok": false,
      "wall_s": 11.563113440000961,
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      "wall_raw_s": 11.563113440000961,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.44040291573101725,
        1.038640897238157
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.08801303960102759 cons=0.29726437277706874 wall_s=15.115 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
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  "residual": 0.08801303960102759,
  "conservation_residual": 0.29726437277706874,
  "equations": [
    "y*(a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 15.114637225000479,
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "y*(a + b*y)",
      "r2_train": 0.814281747096954,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.437637717999678,
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      "wall_raw_s": 7.437637717999678,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "y*(c*x + d)",
      "r2_train": 0.999999999414472,
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      "structure_ok": false,
      "wall_s": 7.676999507000801,
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      "wall_raw_s": 7.676999507000801,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000085217274951,
        -1.0000254416554701
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=3.7701330515047064e-13 cons=0.28405222330316887 wall_s=19.769 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
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  "residual": 3.7701330515047064e-13,
  "conservation_residual": 0.28405222330316887,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(2*c*x + d)"
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  "wall_s_total": 19.768668495002203,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 11.510261708001053,
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      "wall_raw_s": 11.510261708001053,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -0.49999999999999833,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "y*(2*c*x + d)",
      "r2_train": 0.9999999999992824,
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      "structure_ok": false,
      "wall_s": 8.25840678700115,
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      "wall_raw_s": 8.25840678700115,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      },
      "free_const_values": [
        0.2500002045047072,
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      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.0820857457407859 cons=0.18488055382280427 wall_s=15.636 ok=True

```json
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  "recovered": false,
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  "residual": 0.0820857457407859,
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  "equations": [
    "-x*(a + b*y)",
    "2*c*x*(x + y) + d*y"
  ],
  "wall_s_total": 15.636084084999311,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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        "x*y": -0.5000062334584177
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      "structure_ok": false,
      "wall_s": 7.58093904099951,
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
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    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "2*c*x*(x + y) + d*y",
      "r2_train": 0.8536322191506509,
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      "structure_ok": false,
      "wall_s": 8.0551450439998,
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      "wall_raw_s": 8.0551450439998,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=3.0714416370322283e-10 cons=0.21116579406195868 wall_s=19.371 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
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  "residual": 3.0714416370322283e-10,
  "conservation_residual": 0.21116579406195868,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x - d)"
  ],
  "wall_s_total": 19.37115180299952,
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
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  "eq_results": [
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        "x*y": -0.5000005986721571
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      "structure_ok": false,
      "wall_s": 11.048948835999909,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0000010288919654,
        -0.5000005986721571
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.9999999994522186,
      "reward": null,
      "residual_heldout": 6.12679670525434e-10,
      "pred_coeffs": {
        "x*y": 0.500004642892103
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.322202966999612,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.322202966999612,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.500004642892103,
        1.0000007222835672
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=8.122070127370004e-14 cons=0.22981564453980227 wall_s=17.608 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.122070127370004e-14,
  "conservation_residual": 0.22981564453980227,
  "equations": [
    "x*(-3*a - b*y)",
    "y*(3*c*x - d)"
  ],
  "wall_s_total": 17.607986424000046,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "r2_train": 0.9999999999999688,
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      "residual_heldout": 3.913779957453072e-14,
      "pred_coeffs": {
        "x*y": -0.4999999996888853
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.09668210000018,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.09668210000018,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.33333333413360555,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(3*c*x - d)",
      "r2_train": 0.9999999999998889,
      "reward": null,
      "residual_heldout": 1.2330360297286935e-13,
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        "x*y": 0.5000000330854404
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      "structure_ok": false,
      "wall_s": 9.511304323999866,
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      "wall_raw_s": 9.511304323999866,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.1666666776951468,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.09279850801102477 cons=0.14045001300648902 wall_s=21.028 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
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  "conservation_residual": 0.14045001300648902,
  "equations": [
    "x*(a - 4*b*y)",
    "x*(-c*x + 2*d)"
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  "wall_s_total": 21.028212148999955,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "wall_raw_s": 12.193479026000205,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "r2_train": 0.8578783652431824,
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        "x^2": 0.4280310861842922,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.83473312299975,
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      "wall_raw_s": 8.83473312299975,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4280310861842922,
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=1.9919408383998933e-14 cons=0.22764638070674342 wall_s=15.130 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.9919408383998933e-14,
  "conservation_residual": 0.22764638070674342,
  "equations": [
    "x*(2*a - b*y)",
    "-y*(c*x + 3*d)"
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  "wall_s_total": 15.129524576999756,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.52188412599935,
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "-y*(c*x + 3*d)",
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      "structure_ok": false,
      "wall_s": 7.607640451000407,
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      "wall_raw_s": 7.607640451000407,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000000538850916,
        0.33333336922326634
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=6.461454178756916e-11 cons=0.33592097432547313 wall_s=20.410 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A4_physo",
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  "recovered": false,
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  "residual": 6.461454178756916e-11,
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  "equations": [
    "-x*(a + b*y)",
    "y*(c*x + d)"
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  "wall_s_total": 20.41042183799982,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "wall_s": 12.644275548000223,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "zero_eq_retry": 2
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      "free_const_values": [
        -1.00000073076777,
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      "zero_eq": false,
      "zero_eq_retries": 0
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    {
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      "equation": "y*(c*x + d)",
      "r2_train": 0.9999999998732589,
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        "x*y": 0.5000041255952182
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      "structure_ok": false,
      "wall_s": 7.766146289999597,
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      "wall_raw_s": 7.766146289999597,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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        "wall_cap_s": 120,
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      "free_const_values": [
        0.5000041255952182,
        -1.0000116307973814
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  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.09583124643894801 cons=0.17046897169322545 wall_s=14.893 ok=True

```json
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  "n_samples": 400,
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  "recovered": false,
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  "residual": 0.09583124643894801,
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    "-x*(c*x + d)"
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  "wall_s_total": 14.89271269100027,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
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  "eq_results": [
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        "x*y": -0.24254826385965667,
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      "free_const_values": [
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    {
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      "wall_s": 7.598780952999732,
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        "max_n_evaluations": 2500,
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  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=1.325972448402395e-13 cons=0.31863333612784495 wall_s=19.598 ok=True

```json
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  "recovered": false,
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  "residual": 1.325972448402395e-13,
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    "x*(-3*a + b*y)",
    "-y*(c*x + d)"
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  "wall_s_total": 19.59771833100058,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
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        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000000459627728,
        0.9999999925340424
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=6.330350570819993e-14 cons=0.2577514738018479 wall_s=15.367 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.330350570819993e-14,
  "conservation_residual": 0.2577514738018479,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(c*x - d)"
  ],
  "wall_s_total": 15.366649104000317,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-2*a + b*y)",
      "r2_train": 0.9999999999998682,
      "reward": null,
      "residual_heldout": 1.2172778522449516e-13,
      "pred_coeffs": {
        "x*y": -0.49999988754737223
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.772718875999999,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.772718875999999,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49999993571643836,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.999999999999995,
      "reward": null,
      "residual_heldout": 4.879226191904689e-15,
      "pred_coeffs": {
        "x*y": 0.5000000007504006
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.593930228000318,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.593930228000318,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000000007504006,
        0.9999999995400863
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=4.596942524562963e-14 cons=0.2565863473240652 wall_s=20.676 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.596942524562963e-14,
  "conservation_residual": 0.2565863473240652,
  "equations": [
    "x*(2*a - b*y)",
    "y*(c*x + 3*d)"
  ],
  "wall_s_total": 20.67605036399982,
  "wall_s_per_eq": [
    12.602019315998405,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(2*a - b*y)",
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      "residual_heldout": 6.820736697312987e-15,
      "pred_coeffs": {
        "x*y": -0.4999999999999998
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 12.602019315998405,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.602019315998405,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4999999999999998,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + 3*d)",
      "r2_train": 0.9999999999999207,
      "reward": null,
      "residual_heldout": 8.511811379394627e-14,
      "pred_coeffs": {
        "x*y": 0.49999999101521864
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.074031048001416,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.074031048001416,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49999999101521864,
        -0.3333333600628281
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.14090805937153342 cons=0.3592142710171588 wall_s=15.209 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.14090805937153342,
  "conservation_residual": 0.3592142710171588,
  "equations": [
    "a*x - 2*b*y**2",
    "y*(c*x - 3*d)"
  ],
  "wall_s_total": 15.2089577250008,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "a*x - 2*b*y**2",
      "r2_train": 0.7039550143144541,
      "reward": null,
      "residual_heldout": 0.28181611874303975,
      "pred_coeffs": {
        "y^2": -0.1903323519174014,
        "x": 0.3620599730504532
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.4853998930011585,
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      "wall_raw_s": 7.4853998930011585,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - 3*d)",
      "r2_train": 0.9999999999999656,
      "reward": null,
      "residual_heldout": 2.71000433958837e-14,
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        "x*y": 0.5000000000000003
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.723557831999642,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.723557831999642,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000000000000003,
        0.3333333333333335
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=9.45667328818734e-12 cons=0.22183561319717832 wall_s=20.923 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.45667328818734e-12,
  "conservation_residual": 0.22183561319717832,
  "equations": [
    "x*(a - b*y)",
    "-y*(c*x + 2*d)"
  ],
  "wall_s_total": 20.922736039001393,
  "wall_s_per_eq": [
    13.214544619000662,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(a - b*y)",
      "r2_train": 0.9999999999999716,
      "reward": null,
      "residual_heldout": 3.855995848517701e-14,
      "pred_coeffs": {
        "x*y": -0.5000000020334018
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 13.214544619000662,
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      "wall_raw_s": 13.214544619000662,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.999999998614052,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + 2*d)",
      "r2_train": 0.9999999999817097,
      "reward": null,
      "residual_heldout": 1.8874786617889502e-11,
      "pred_coeffs": {
        "x*y": 0.5000006272822806
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      "true_coeffs": {
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.70819142000073,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.70819142000073,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000006272822806,
        0.49999982148757344
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.07465961326789028 cons=0.15539775630907213 wall_s=17.280 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.07465961326789028,
  "conservation_residual": 0.15539775630907213,
  "equations": [
    "x*(3*a + b*y)",
    "x*(-c*x + d)"
  ],
  "wall_s_total": 17.27997995700207,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(3*a + b*y)",
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      "reward": null,
      "residual_heldout": 2.6041730427006646e-14,
      "pred_coeffs": {
        "x*y": -0.5000000766302288
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.838813418000427,
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      "wall_raw_s": 7.838813418000427,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        0.333333380138131,
        -0.5000000766302288
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + d)",
      "r2_train": 0.8332266676772642,
      "reward": null,
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        "x^2": 0.42355130349737735,
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      "true_coeffs": {
        "y": -1.0,
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      "structure_ok": false,
      "wall_s": 9.441166539001642,
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      "wall_raw_s": 9.441166539001642,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.42355130349737735,
        -0.993039851957417
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=1.199590283065324e-12 cons=0.2621230671658359 wall_s=20.800 ok=True

```json
{
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  "recoverable": true,
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  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.199590283065324e-12,
  "conservation_residual": 0.2621230671658359,
  "equations": [
    "-x*(4*a + b*y)",
    "y*(-c*x + 4*d)"
  ],
  "wall_s_total": 20.800368373998936,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-x*(4*a + b*y)",
      "r2_train": 0.9999999999999915,
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      "residual_heldout": 6.673462881785429e-15,
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        "x*y": -0.4999999964828109
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 7.8571648789984465,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -0.2500000050118664,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "y*(-c*x + 4*d)",
      "r2_train": 0.999999999997351,
      "reward": null,
      "residual_heldout": 2.3925071032488627e-12,
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        "x*y": 0.500000482155925
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 12.943203495000489,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.943203495000489,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      },
      "free_const_values": [
        -0.500000482155925,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=9.46900366626951e-13 cons=0.24770746259370477 wall_s=17.141 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.46900366626951e-13,
  "conservation_residual": 0.24770746259370477,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x - d)"
  ],
  "wall_s_total": 17.140916039998046,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9999999999981106,
      "reward": null,
      "residual_heldout": 1.868560254381598e-12,
      "pred_coeffs": {
        "x*y": -0.5000006599819434
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.017812018999393,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.017812018999393,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.000001081125686,
        -0.5000006599819434
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.9999999999999685,
      "reward": null,
      "residual_heldout": 2.5240478872304195e-14,
      "pred_coeffs": {
        "x*y": 0.5000000008838884
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.123104020998653,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.123104020998653,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000000008838884,
        0.9999999994500086
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.00551672994659938 cons=0.2901445749762576 wall_s=18.284 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00551672994659938,
  "conservation_residual": 0.2901445749762576,
  "equations": [
    "x*(1.0008632 + y*(-0.504338))",
    "y*(x*0.48925734 - 1*0.98262507)"
  ],
  "wall_s_total": 18.284486818001824,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "x*(1.0008632 + y*(-0.504338))",
      "r2_train": 0.9944147053465728,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.504338
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 10.034264055000676,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.48925734 - 1*0.98262507)",
      "r2_train": 0.9952013172709739,
      "reward": null,
      "residual_heldout": 0.007144100598790711,
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        "x*y": 0.48925734
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      "true_coeffs": {
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        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.250222763001148,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.007724499975057007 cons=0.15283114987941904 wall_s=16.520 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007724499975057007,
  "conservation_residual": 0.15283114987941904,
  "equations": [
    "x*(1.0150998 + y*(-0.501196))",
    "y*(x*0.49896368 - 1.0057948)"
  ],
  "wall_s_total": 16.520230992002325,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "x*(1.0150998 + y*(-0.501196))",
      "r2_train": 0.9959247513137091,
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      "structure_ok": false,
      "wall_s": 8.657813273001011,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49896368 - 1.0057948)",
      "r2_train": 0.9945827562554966,
      "reward": null,
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      },
      "structure_ok": false,
      "wall_s": 7.862417719001314,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.005443708349156006 cons=0.07939336692268759 wall_s=17.071 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005443708349156006,
  "conservation_residual": 0.07939336692268759,
  "equations": [
    "x*(0.9961808 + y*(-0.5013231))",
    "y*(x*0.49160227 - 1*0.98282343)"
  ],
  "wall_s_total": 17.070792104001157,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.9961808 + y*(-0.5013231))",
      "r2_train": 0.9934530200841539,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.5013231
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      },
      "structure_ok": false,
      "wall_s": 8.832149532001495,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49160227 - 1*0.98282343)",
      "r2_train": 0.9960141633102036,
      "reward": null,
      "residual_heldout": 0.004401780577526461,
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 8.238642571999662,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.0037217605400881835 cons=0.21961767130824103 wall_s=17.758 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0037217605400881835,
  "conservation_residual": 0.21961767130824103,
  "equations": [
    "(y - 2.0019221)*x*(-0.49269632)",
    "y*(x*0.50691783 - 1.0193927)"
  ],
  "wall_s_total": 17.75768624900229,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 2.0019221)*x*(-0.49269632)",
      "r2_train": 0.9935096020591664,
      "reward": null,
      "residual_heldout": 0.00289045560320707,
      "pred_coeffs": {
        "x*y": -0.49269632
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        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.588043507001203,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.50691783 - 1.0193927)",
      "r2_train": 0.995843314553623,
      "reward": null,
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      "structure_ok": false,
      "wall_s": 9.169642742001088,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.014967665651506921 cons=0.5145490381291576 wall_s=16.190 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.014967665651506921,
  "conservation_residual": 0.5145490381291576,
  "equations": [
    "x*(y - 1*1.9835308)*(-0.49320036)",
    "y*(x - 1*2.0025861)*0.49657547"
  ],
  "wall_s_total": 16.190360746000806,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9957975062064351,
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      "structure_ok": false,
      "wall_s": 8.144017631000679,
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x - 1*2.0025861)*0.49657547",
      "r2_train": 0.9864298471298852,
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      "structure_ok": false,
      "wall_s": 8.046343115000127,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.004566185273481648 cons=0.2445713287064613 wall_s=15.374 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004566185273481648,
  "conservation_residual": 0.2445713287064613,
  "equations": [
    "x*(0.99130374 + y*(-0.49996585))",
    "y*(x*0.50457215 - 1.0080831)"
  ],
  "wall_s_total": 15.373501730000498,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": false,
      "wall_s": 8.299069103000875,
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      "free_const_values": null,
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    {
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      },
      "structure_ok": false,
      "wall_s": 7.074432626999624,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.00970565345840378 cons=0.2865018398034677 wall_s=15.392 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00970565345840378,
  "conservation_residual": 0.2865018398034677,
  "equations": [
    "(1.9813949 - y)*x*0.5142674",
    "y*(x*0.4932635 - 0.98286605)"
  ],
  "wall_s_total": 15.39220615100021,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(1.9813949 - y)*x*0.5142674",
      "r2_train": 0.9933785201858852,
      "reward": null,
      "residual_heldout": 0.015100384415005398,
      "pred_coeffs": {
        "x*y": -0.5142674
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.781981312999051,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.4932635 - 0.98286605)",
      "r2_train": 0.9947161767274553,
      "reward": null,
      "residual_heldout": 0.0043109225018021615,
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        "x*y": 0.4932635
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 7.610224838001159,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.004242705756465211 cons=0.18088521339269614 wall_s=16.545 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
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  "recovered": false,
  "structure_ok": false,
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  "residual": 0.004242705756465211,
  "conservation_residual": 0.18088521339269614,
  "equations": [
    "x*(0.99158394 - 0.49646333*y)",
    "y*(-0.5044361)*(2.005306 - x)"
  ],
  "wall_s_total": 16.545478843001547,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.99158394 - 0.49646333*y)",
      "r2_train": 0.9941012091058903,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.49646333
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      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.837855187000969,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-0.5044361)*(2.005306 - x)",
      "r2_train": 0.9948840090737716,
      "reward": null,
      "residual_heldout": 0.0036958449289895604,
      "pred_coeffs": {
        "x*y": 0.5044361
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.707623656000578,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.006247432564247697 cons=0.5411544103755781 wall_s=16.330 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006247432564247697,
  "conservation_residual": 0.5411544103755781,
  "equations": [
    "x*(1.0073547 + y*(-0.500101))",
    "y*(x*0.49647474 - 0.9869882)"
  ],
  "wall_s_total": 16.33008329400036,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(1.0073547 + y*(-0.500101))",
      "r2_train": 0.9926407954488575,
      "reward": null,
      "residual_heldout": 0.0032645992630172082,
      "pred_coeffs": {
        "x*y": -0.500101
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      },
      "structure_ok": false,
      "wall_s": 8.488030848000562,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49647474 - 0.9869882)",
      "r2_train": 0.9923755203542556,
      "reward": null,
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      "structure_ok": false,
      "wall_s": 7.842052445999798,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.007609762181967015 cons=0.24494087124548514 wall_s=15.629 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007609762181967015,
  "conservation_residual": 0.24494087124548514,
  "equations": [
    "x*(0.98915786 + y*(-0.49094528))",
    "y*(x*0.48595655 - 1*0.97379476)"
  ],
  "wall_s_total": 15.628562371999578,
  "wall_s_per_eq": [
    7.834799688000203,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.98915786 + y*(-0.49094528))",
      "r2_train": 0.9957425586010477,
      "reward": null,
      "residual_heldout": 0.007271596835239382,
      "pred_coeffs": {
        "x*y": -0.49094528
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      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.834799688000203,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.48595655 - 1*0.97379476)",
      "r2_train": 0.9927501721146317,
      "reward": null,
      "residual_heldout": 0.007947927528694648,
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      "true_coeffs": {
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.793762683999375,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.006489001205630438 cons=0.48321140962648623 wall_s=16.480 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006489001205630438,
  "conservation_residual": 0.48321140962648623,
  "equations": [
    "x*(y*(-0.5042598) - 1*(-1.0116316))",
    "y*(x*0.49306607 - 0.98242253)"
  ],
  "wall_s_total": 16.479648779000854,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y*(-0.5042598) - 1*(-1.0116316))",
      "r2_train": 0.9923259088724561,
      "reward": null,
      "residual_heldout": 0.004041982552264168,
      "pred_coeffs": {
        "x*y": -0.5042598
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.668967040999632,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49306607 - 0.98242253)",
      "r2_train": 0.9929855504916346,
      "reward": null,
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.810681738001222,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.010658261915789398 cons=0.4542340370398163 wall_s=17.000 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.010658261915789398,
  "conservation_residual": 0.4542340370398163,
  "equations": [
    "x*(0.99943525 + y*(-0.5023117))",
    "y*0.50478274*(x - 1*1.9881389)"
  ],
  "wall_s_total": 17.000124919999507,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9959706112637181,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.5023117
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      "structure_ok": false,
      "wall_s": 8.162226716000077,
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      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
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      },
      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*0.50478274*(x - 1*1.9881389)",
      "r2_train": 0.9937710303029261,
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      "structure_ok": false,
      "wall_s": 8.83789820399943,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.004187651367161942 cons=0.24313219579364 wall_s=15.012 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004187651367161942,
  "conservation_residual": 0.24313219579364,
  "equations": [
    "x*(0.997818 + y*(-0.49982217))",
    "y*(-0.49935362)*(1.9917982 - x)"
  ],
  "wall_s_total": 15.011979130000327,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.996213366713805,
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      "residual_heldout": 0.0035523623880330175,
      "pred_coeffs": {
        "x*y": -0.49982217
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.657650492999892,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-0.49935362)*(1.9917982 - x)",
      "r2_train": 0.9963021757919429,
      "reward": null,
      "residual_heldout": 0.004822940346290867,
      "pred_coeffs": {
        "x*y": 0.49935362
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.354328637000435,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.007615437976035438 cons=0.4215888361623467 wall_s=16.563 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007615437976035438,
  "conservation_residual": 0.4215888361623467,
  "equations": [
    "x*0.4873302*(2.0072613 - y)",
    "y*(x*0.50108343 - 1.0105385)"
  ],
  "wall_s_total": 16.562734404000366,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "x*0.4873302*(2.0072613 - y)",
      "r2_train": 0.9948421426782252,
      "reward": null,
      "residual_heldout": 0.011146461141317957,
      "pred_coeffs": {
        "x*y": -0.4873302
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      "structure_ok": false,
      "wall_s": 8.311655401999815,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.50108343 - 1.0105385)",
      "r2_train": 0.9936284743464372,
      "reward": null,
      "residual_heldout": 0.004084414810752919,
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        "x*y": 0.50108343
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.251079002000552,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.00629498679072806 cons=0.26921805935799265 wall_s=17.121 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00629498679072806,
  "conservation_residual": 0.26921805935799265,
  "equations": [
    "x*(1.017127 + y*(-0.5067521))",
    "y*(-(-0.5003547)*x - 1.003533)"
  ],
  "wall_s_total": 17.121411899997838,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(1.017127 + y*(-0.5067521))",
      "r2_train": 0.9961880692453489,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.5067521
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 8.889098797999395,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-(-0.5003547)*x - 1.003533)",
      "r2_train": 0.9914131090859111,
      "reward": null,
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        "x*y": 0.5003547
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      "structure_ok": false,
      "wall_s": 8.232313101998443,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.004713440486395995 cons=0.38997781833015593 wall_s=16.294 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004713440486395995,
  "conservation_residual": 0.38997781833015593,
  "equations": [
    "x*(0.99575037 + y*(-0.49843493))",
    "y*(-(-0.50108343)*x - 0.99722886)"
  ],
  "wall_s_total": 16.29382943699966,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.99575037 + y*(-0.49843493))",
      "r2_train": 0.9951659855701105,
      "reward": null,
      "residual_heldout": 0.002319408930408462,
      "pred_coeffs": {
        "x*y": -0.49843493
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 8.112222758998541,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-(-0.50108343)*x - 0.99722886)",
      "r2_train": 0.9935101978320959,
      "reward": null,
      "residual_heldout": 0.007107472042383528,
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      "structure_ok": false,
      "wall_s": 8.181606678001117,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.0029057533331878836 cons=0.17116956103975253 wall_s=16.592 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0029057533331878836,
  "conservation_residual": 0.17116956103975253,
  "equations": [
    "x*(0.98011875 - 0.4952133*y)",
    "y*(x*0.49621242 - 0.98389244)"
  ],
  "wall_s_total": 16.592199581000386,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.98011875 - 0.4952133*y)",
      "r2_train": 0.9958976192017147,
      "reward": null,
      "residual_heldout": 0.0026763705769338435,
      "pred_coeffs": {
        "x*y": -0.4952133
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        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.284932796001158,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49621242 - 0.98389244)",
      "r2_train": 0.9970949310695316,
      "reward": null,
      "residual_heldout": 0.0031351360894419237,
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        "x*y": 0.49621242
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      "structure_ok": false,
      "wall_s": 8.307266784999229,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.005426301787198752 cons=0.2602235962455155 wall_s=16.711 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005426301787198752,
  "conservation_residual": 0.2602235962455155,
  "equations": [
    "x*(y*(-0.5001499) - 1*(-0.9999731))",
    "y*(x*0.49647725 - 1*0.98797363)"
  ],
  "wall_s_total": 16.710852766000244,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y*(-0.5001499) - 1*(-0.9999731))",
      "r2_train": 0.9957981886984242,
      "reward": null,
      "residual_heldout": 0.005800990322130867,
      "pred_coeffs": {
        "x*y": -0.5001499
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      "structure_ok": false,
      "wall_s": 7.744134855000084,
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      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
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        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49647725 - 1*0.98797363)",
      "r2_train": 0.9960909571950388,
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      "residual_heldout": 0.005051613252266638,
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      "structure_ok": false,
      "wall_s": 8.96671791100016,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.005878785431143903 cons=0.24965304489185602 wall_s=17.239 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005878785431143903,
  "conservation_residual": 0.24965304489185602,
  "equations": [
    "x*(1.0053473 - 0.50095606*y)",
    "y*(x*0.49485916 - 0.98928666)"
  ],
  "wall_s_total": 17.23909677700067,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9945525836357797,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.50095606
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      "structure_ok": false,
      "wall_s": 9.384613799000363,
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      "wall_cap_s": 120,
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        "target_mean_wall_s": 0
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      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49485916 - 0.98928666)",
      "r2_train": 0.9947246506317127,
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      "structure_ok": false,
      "wall_s": 7.854482978000306,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=50 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.004823914054209986 cons=0.14452475329595646 wall_s=17.809 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004823914054209986,
  "conservation_residual": 0.14452475329595646,
  "equations": [
    "(y - 1.9887846)*(-0.50039905)*x",
    "y*(x*0.49939075 - 0.9998179)"
  ],
  "wall_s_total": 17.809096323999256,
  "wall_s_per_eq": [
    9.585440003998883,
    8.223656320000373
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(y - 1.9887846)*(-0.50039905)*x",
      "r2_train": 0.9917932882856888,
      "reward": null,
      "residual_heldout": 0.002070734797400492,
      "pred_coeffs": {
        "x*y": -0.50039905
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.585440003998883,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49939075 - 0.9998179)",
      "r2_train": 0.9958738557006549,
      "reward": null,
      "residual_heldout": 0.007577093311019479,
      "pred_coeffs": {
        "x*y": 0.49939075
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.223656320000373,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=False residual=0.2794163781911289 cons=0.6645572959715714 wall_s=18.097 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.2794163781911289,
  "conservation_residual": 0.6645572959715714,
  "equations": [
    "2*a*(-x + y)",
    "-(x + y)*(c*x + d)"
  ],
  "wall_s_total": 18.096753748999618,
  "wall_s_per_eq": [
    9.314610802999596,
    8.782142946000022
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*a*(-x + y)",
      "r2_train": 0.4266942015779679,
      "reward": null,
      "residual_heldout": 0.4851731001914741,
      "pred_coeffs": {
        "x": 0.4756862314515109,
        "y": -0.4756862314515109
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.314610802999596,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.314610802999596,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.23784311572575545,
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-(x + y)*(c*x + d)",
      "r2_train": 0.9352981331437802,
      "reward": null,
      "residual_heldout": 0.07365965619078374,
      "pred_coeffs": {
        "x*y": 0.23446732422885502,
        "x^2": 0.23446732422885502
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.782142946000022,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.782142946000022,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.23446732422885502,
        0.5089522943608276
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.0668922917861472 cons=0.13359089526966011 wall_s=17.159 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0668922917861472,
  "conservation_residual": 0.13359089526966011,
  "equations": [
    "x*(-a - 3*b*y)",
    "x*(-c*x - d)"
  ],
  "wall_s_total": 17.159053055000186,
  "wall_s_per_eq": [
    9.410430535999694,
    7.748622519000492
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a - 3*b*y)",
      "r2_train": 0.9944351740416822,
      "reward": null,
      "residual_heldout": 0.0021111393626838354,
      "pred_coeffs": {
        "x*y": -0.49145072297389836
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.410430535999694,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.410430535999694,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9827592552203835,
        0.1638169076579661
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x - d)",
      "r2_train": 0.8831499549817863,
      "reward": null,
      "residual_heldout": 0.13167344420961055,
      "pred_coeffs": {
        "x^2": 0.4126189143256899,
        "x": -0.9526643323670838
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.748622519000492,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.748622519000492,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4126189143256899,
        0.9526643323670838
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.08948221626100743 cons=0.3382326615083942 wall_s=16.306 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08948221626100743,
  "conservation_residual": 0.3382326615083942,
  "equations": [
    "x*(-a + b*y)",
    "x*(c*x - d)"
  ],
  "wall_s_total": 16.30646206399979,
  "wall_s_per_eq": [
    8.12388603799991,
    8.182576025999879
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9951689798640531,
      "reward": null,
      "residual_heldout": 0.011572644806194276,
      "pred_coeffs": {
        "x*y": -0.5030500530397857
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.12388603799991,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.12388603799991,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0055174089007934,
        -0.5030500530397857
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(c*x - d)",
      "r2_train": 0.8581445441962623,
      "reward": null,
      "residual_heldout": 0.16739178771582058,
      "pred_coeffs": {
        "x^2": 0.370404319385707,
        "x": -0.8342794882524017
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.182576025999879,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.182576025999879,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.370404319385707,
        0.8342794882524017
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.1092070701727987 cons=0.41225028495884414 wall_s=17.608 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.1092070701727987,
  "conservation_residual": 0.41225028495884414,
  "equations": [
    "y*(a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 17.607638927998778,
  "wall_s_per_eq": [
    8.57639935899897,
    9.031239568999808
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "y*(a + b*y)",
      "r2_train": 0.8716488572725775,
      "reward": null,
      "residual_heldout": 0.21394797836689444,
      "pred_coeffs": {
        "y^2": -0.46118551947926534,
        "y": 1.1339249350528788
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.57639935899897,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.57639935899897,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.1339249350528788,
        -0.46118551947926534
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + d)",
      "r2_train": 0.9957252460382925,
      "reward": null,
      "residual_heldout": 0.004466161978702957,
      "pred_coeffs": {
        "x*y": 0.49614493453926967
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.031239568999808,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.031239568999808,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49614493453926967,
        -0.9884625465628053
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.005609219658565532 cons=0.27006905762928585 wall_s=15.939 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005609219658565532,
  "conservation_residual": 0.27006905762928585,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(-c*x - 2*d)"
  ],
  "wall_s_total": 15.938845815000604,
  "wall_s_per_eq": [
    7.648090501999832,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-2*a + b*y)",
      "r2_train": 0.9955927125200703,
      "reward": null,
      "residual_heldout": 0.007276902855542661,
      "pred_coeffs": {
        "x*y": -0.48723825368281126
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.648090501999832,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.648090501999832,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.486768172495593,
        -0.48723825368281126
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x - 2*d)",
      "r2_train": 0.9940442342166972,
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      "residual_heldout": 0.003941536461588403,
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        "x*y": 0.4996227023164947
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.290755313000773,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.290755313000773,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4996227023164947,
        0.4974627567289845
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.054506034702088146 cons=0.22553620301035074 wall_s=17.578 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.054506034702088146,
  "conservation_residual": 0.22553620301035074,
  "equations": [
    "-x*(a + 2*b*y)",
    "x*(c*x - 2*d)"
  ],
  "wall_s_total": 17.578001830001085,
  "wall_s_per_eq": [
    8.401990059999662,
    9.176011770001423
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-x*(a + 2*b*y)",
      "r2_train": 0.9931755359055802,
      "reward": null,
      "residual_heldout": 0.006598251887021233,
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        "x*y": -0.48263558068181833
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.401990059999662,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.401990059999662,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9734428448265251,
        0.24131779034090917
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(c*x - 2*d)",
      "r2_train": 0.8989575332076095,
      "reward": null,
      "residual_heldout": 0.10241381751715506,
      "pred_coeffs": {
        "x^2": 0.4447666083358955,
        "x": -1.1047549736484081
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.176011770001423,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.176011770001423,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4447666083358955,
        0.5523774868242041
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.00529125339478038 cons=0.2137573416897396 wall_s=16.704 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00529125339478038,
  "conservation_residual": 0.2137573416897396,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x - d)"
  ],
  "wall_s_total": 16.703824782000083,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9945659057933176,
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        "x*y": -0.49781432943879395
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.266011058000004,
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      "wall_raw_s": 8.266011058000004,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9971702363127324,
        -0.49781432943879395
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.9918395400792699,
      "reward": null,
      "residual_heldout": 0.005151280831584959,
      "pred_coeffs": {
        "x*y": 0.4883346603814568
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.43781372400008,
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      "wall_raw_s": 8.43781372400008,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4883346603814568,
        0.9812304094573129
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.0066864363776967485 cons=0.22352365029215615 wall_s=17.696 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0066864363776967485,
  "conservation_residual": 0.22352365029215615,
  "equations": [
    "x*(-3*a - b*y)",
    "y*(3*c*x - d)"
  ],
  "wall_s_total": 17.695605627000987,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.646712265999668,
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      "wall_raw_s": 8.646712265999668,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(3*c*x - d)",
      "r2_train": 0.9931589952870797,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.04889336100132,
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      "wall_raw_s": 9.04889336100132,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.17058589594640436,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.13252694957230468 cons=0.11651486574400749 wall_s=17.315 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.13252694957230468,
  "conservation_residual": 0.11651486574400749,
  "equations": [
    "x*(a - 4*b*y)",
    "x*(-c*x + 2*d)"
  ],
  "wall_s_total": 17.31524331199944,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(a - 4*b*y)",
      "r2_train": 0.9952609447728061,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.561001148998912,
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      "wall_raw_s": 8.561001148998912,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + 2*d)",
      "r2_train": 0.8237031780112243,
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        "x^2": 0.41852551692455553,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.754242163000526,
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      "wall_raw_s": 8.754242163000526,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.41852551692455553,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.00380212629262073 cons=0.435557650452642 wall_s=17.428 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
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  "residual": 0.00380212629262073,
  "conservation_residual": 0.435557650452642,
  "equations": [
    "x*(-a - b*y)",
    "-y*(c*x + 3*d)"
  ],
  "wall_s_total": 17.427840629001366,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.997681926520217,
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 9.090379602001121,
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      "wall_raw_s": 9.090379602001121,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9962927743916494,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + 3*d)",
      "r2_train": 0.9962719688331807,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.337461027000245,
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      "wall_raw_s": 8.337461027000245,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4955117456044105,
        0.33055147407950336
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.009282155607241603 cons=0.30260850623852953 wall_s=16.552 ok=True

```json
{
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  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
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  "residual": 0.009282155607241603,
  "conservation_residual": 0.30260850623852953,
  "equations": [
    "-x*(a + b*y)",
    "y*(c*x + d)"
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  "wall_s_total": 16.55170211800032,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "r2_train": 0.9970970839423454,
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        "x*y": -0.5043513508613231
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.397215779999897,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "zero_eq_retry": 2
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      "free_const_values": [
        -1.014590751250176,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "y*(c*x + d)",
      "r2_train": 0.9958996524457059,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.154486338000424,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.154486338000424,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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      },
      "free_const_values": [
        0.5022445938994686,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.07911484085215033 cons=0.14175629686610977 wall_s=17.198 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.07911484085215033,
  "conservation_residual": 0.14175629686610977,
  "equations": [
    "-(a + 2*b*y)*(x + y)",
    "-x*(c*x + d)"
  ],
  "wall_s_total": 17.19815079199907,
  "wall_s_per_eq": [
    8.625117845000204,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9503348751822172,
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        "x*y": -0.25396343915971953,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.625117845000204,
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      "wall_raw_s": 8.625117845000204,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [
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      "zero_eq": false,
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    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + d)",
      "r2_train": 0.8557359054121344,
      "reward": null,
      "residual_heldout": 0.1138260674989395,
      "pred_coeffs": {
        "x^2": 0.39927508963419445,
        "x": -0.9216473581012916
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.573032946998865,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.573032946998865,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.39927508963419445,
        0.9216473581012916
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.00509266680990894 cons=0.1609873430456117 wall_s=16.755 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00509266680990894,
  "conservation_residual": 0.1609873430456117,
  "equations": [
    "x*(-3*a + b*y)",
    "-y*(c*x + d)"
  ],
  "wall_s_total": 16.75472379799976,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-3*a + b*y)",
      "r2_train": 0.9967248653938378,
      "reward": null,
      "residual_heldout": 0.0056147239274642715,
      "pred_coeffs": {
        "x*y": -0.5045125659455343
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.933430999999473,
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      "wall_raw_s": 8.933430999999473,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.3352136977400536,
        -0.5045125659455343
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.9956807515685444,
      "reward": null,
      "residual_heldout": 0.004570609692353609,
      "pred_coeffs": {
        "x*y": 0.5004809815278105
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.821292798000286,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.821292798000286,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5004809815278105,
        0.9942149026184804
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.005098171892583588 cons=0.17448104114638763 wall_s=17.165 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005098171892583588,
  "conservation_residual": 0.17448104114638763,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(-2*c*x - d)"
  ],
  "wall_s_total": 17.164799938000215,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9953644567677861,
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      "residual_heldout": 0.0038279028733752335,
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        "x*y": -0.5018547239753558
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.569718156000818,
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      "wall_raw_s": 8.569718156000818,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5028270175382676,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-2*c*x - d)",
      "r2_train": 0.9955383464024341,
      "reward": null,
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      "pred_coeffs": {
        "x*y": 0.4931332276037957
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.595081781999397,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.595081781999397,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.24656661380189784,
        0.9835499692291436
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.005821112276295821 cons=0.14084910158657107 wall_s=16.340 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005821112276295821,
  "conservation_residual": 0.14084910158657107,
  "equations": [
    "-x*(a + b*y)",
    "y*(-c*x + d)"
  ],
  "wall_s_total": 16.33980271999826,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
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      "r2_train": 0.9953789697066235,
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        "x*y": -0.5078717867888585
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 7.534806986999683,
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      "wall_raw_s": 7.534806986999683,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0115604646670626,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + d)",
      "r2_train": 0.9944747533087414,
      "reward": null,
      "residual_heldout": 0.003283161419407857,
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        "x*y": 0.4879261895990313
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      "true_coeffs": {
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        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.804995732998577,
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      "wall_raw_s": 8.804995732998577,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4879261895990313,
        -0.9660815507340974
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.11948945280997504 cons=0.3689137603791611 wall_s=16.499 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.11948945280997504,
  "conservation_residual": 0.3689137603791611,
  "equations": [
    "a*x - 2*b*y**2",
    "y*(-c*x + d)"
  ],
  "wall_s_total": 16.498725420999108,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "a*x - 2*b*y**2",
      "r2_train": 0.6774544582417148,
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      "residual_heldout": 0.23202406543890727,
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        "y^2": -0.17913947942359884,
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      "true_coeffs": {
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        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.937547759000154,
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      "wall_raw_s": 8.937547759000154,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + d)",
      "r2_train": 0.9952334312878863,
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      "structure_ok": false,
      "wall_s": 7.561177661998954,
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      "wall_raw_s": 7.561177661998954,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5111084592397818,
        -1.0275520483554483
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.005730173053347402 cons=0.2495539538839176 wall_s=17.669 ok=True

```json
{
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  "recoverable": true,
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  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
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  "residual": 0.005730173053347402,
  "conservation_residual": 0.2495539538839176,
  "equations": [
    "x*(a - b*y)",
    "-y*(c*x + 2*d)"
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  "wall_s_total": 17.668609494998236,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "r2_train": 0.993877228976372,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.547675964999144,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "device": "cpu",
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        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "-y*(c*x + 2*d)",
      "r2_train": 0.995554910275229,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.120933529999093,
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      "wall_raw_s": 8.120933529999093,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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      },
      "free_const_values": [
        -0.5005439836966871,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.1186388366711553 cons=0.13541936815452463 wall_s=17.787 ok=True

```json
{
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  "recoverable": true,
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  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.1186388366711553,
  "conservation_residual": 0.13541936815452463,
  "equations": [
    "x*(3*a + b*y)",
    "x*(-c*x + d)"
  ],
  "wall_s_total": 17.787050405000628,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9925866568841983,
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        "x*y": -0.4936141029280838
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      "structure_ok": false,
      "wall_s": 9.038016967999283,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      "free_const_values": [
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      "zero_eq": false,
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    {
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      "r2_train": 0.8716182056439815,
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      "structure_ok": false,
      "wall_s": 8.749033437001344,
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        "max_n_evaluations": 2500,
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      },
      "free_const_values": [
        -0.4776224866327652,
        -1.1848444514673702
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.004403473564934264 cons=0.46732902244240737 wall_s=16.394 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004403473564934264,
  "conservation_residual": 0.46732902244240737,
  "equations": [
    "-x*(4*a + b*y)",
    "y*(-c*x + 4*d)"
  ],
  "wall_s_total": 16.39412987099786,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-x*(4*a + b*y)",
      "r2_train": 0.9938448209992341,
      "reward": null,
      "residual_heldout": 0.005854552699069704,
      "pred_coeffs": {
        "x*y": -0.49755135799145567
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.568832780998491,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.568832780998491,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.25018640416342286,
        0.49755135799145567
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + 4*d)",
      "r2_train": 0.995513282040842,
      "reward": null,
      "residual_heldout": 0.0029523944307988247,
      "pred_coeffs": {
        "x*y": 0.49963606355806855
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.825297089999367,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.825297089999367,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49963606355806855,
        -0.2514559735235109
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=50 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.006173556992843648 cons=0.28942104000812335 wall_s=16.684 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006173556992843648,
  "conservation_residual": 0.28942104000812335,
  "equations": [
    "x*(-a + b*y)",
    "y*(-c*x + d)"
  ],
  "wall_s_total": 16.684031401999164,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9950497099686553,
      "reward": null,
      "residual_heldout": 0.00622718581726408,
      "pred_coeffs": {
        "x*y": -0.5026596486634977
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.559689587998946,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.559689587998946,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0060818046994193,
        -0.5026596486634977
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + d)",
      "r2_train": 0.9982105315992421,
      "reward": null,
      "residual_heldout": 0.006119928168423215,
      "pred_coeffs": {
        "x*y": 0.5056024074249845
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.124341814000218,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.124341814000218,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5056024074249845,
        -1.0109183228417602
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.006568991789264985 cons=0.2354988446432906 wall_s=39.616 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006568991789264985,
  "conservation_residual": 0.2354988446432906,
  "equations": [
    "x*(1.0018661 + y*(-0.5010407))",
    "y*(x*0.5004313 - 1*1.0004232)"
  ],
  "wall_s_total": 39.61586468200039,
  "wall_s_per_eq": [
    31.69420914300099,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(1.0018661 + y*(-0.5010407))",
      "r2_train": 0.9902235650777399,
      "reward": null,
      "residual_heldout": 0.006053110750913315,
      "pred_coeffs": {
        "x*y": -0.5010407
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 31.69420914300099,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5004313 - 1*1.0004232)",
      "r2_train": 0.995104415257545,
      "reward": null,
      "residual_heldout": 0.007084872827616654,
      "pred_coeffs": {
        "x*y": 0.5004313
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.921655538999403,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.006382940298790196 cons=0.21439311044874804 wall_s=18.217 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006382940298790196,
  "conservation_residual": 0.21439311044874804,
  "equations": [
    "x*(y - 1*2.00517)*(-0.48992577)",
    "y*(x*0.4992854 - 0.9979073)"
  ],
  "wall_s_total": 18.216522198998064,
  "wall_s_per_eq": [
    10.086387379998996,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y - 1*2.00517)*(-0.48992577)",
      "r2_train": 0.9947351826216665,
      "reward": null,
      "residual_heldout": 0.007842358164681975,
      "pred_coeffs": {
        "x*y": -0.48992577
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 10.086387379998996,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.4992854 - 0.9979073)",
      "r2_train": 0.9961371465116415,
      "reward": null,
      "residual_heldout": 0.0049235224328984155,
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        "x*y": 0.4992854
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.130134818999068,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.007695675578849587 cons=0.2083441201140793 wall_s=16.394 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007695675578849587,
  "conservation_residual": 0.2083441201140793,
  "equations": [
    "x*(0.99274915 + y*(-0.50066906))",
    "(x - 1.9809619)*y*0.4965543"
  ],
  "wall_s_total": 16.393746813999314,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.99274915 + y*(-0.50066906))",
      "r2_train": 0.9934342786732475,
      "reward": null,
      "residual_heldout": 0.004583201895494961,
      "pred_coeffs": {
        "x*y": -0.50066906
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.646994445000018,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1.9809619)*y*0.4965543",
      "r2_train": 0.9939294644106192,
      "reward": null,
      "residual_heldout": 0.010808149262204213,
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.746752368999296,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.004637150006064877 cons=0.30849987005204105 wall_s=17.161 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.004637150006064877,
  "conservation_residual": 0.30849987005204105,
  "equations": [
    "(y - 1*1.9910138)*(-0.50333387)*x",
    "(2.0073462 - x)*y*(-0.50520027)"
  ],
  "wall_s_total": 17.16064983800061,
  "wall_s_per_eq": [
    8.565755048000938,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 1*1.9910138)*(-0.50333387)*x",
      "r2_train": 0.9970535228567479,
      "reward": null,
      "residual_heldout": 0.004414335073361404,
      "pred_coeffs": {
        "x*y": -0.50333387
      },
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      "structure_ok": false,
      "wall_s": 8.565755048000938,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(2.0073462 - x)*y*(-0.50520027)",
      "r2_train": 0.9956045604077994,
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      "structure_ok": false,
      "wall_s": 8.594894789999671,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.004958522265612344 cons=0.39632884613904107 wall_s=17.360 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004958522265612344,
  "conservation_residual": 0.39632884613904107,
  "equations": [
    "x*(0.99097586 + y*(-0.4944147))",
    "y*(x*0.49657744 - 1*1.0021428)"
  ],
  "wall_s_total": 17.359604190998652,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "r2_train": 0.9942731552120708,
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        "x*y": -0.4944147
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      "structure_ok": false,
      "wall_s": 9.124773872999867,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49657744 - 1*1.0021428)",
      "r2_train": 0.9922375405789625,
      "reward": null,
      "residual_heldout": 0.004911965109348312,
      "pred_coeffs": {
        "x*y": 0.49657744
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.234830317998785,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.0036735200329842546 cons=0.27061755059781717 wall_s=15.459 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0036735200329842546,
  "conservation_residual": 0.27061755059781717,
  "equations": [
    "x*(0.99411434 + y*(-0.49813423))",
    "y*(x*0.4979406 - 0.99533886)"
  ],
  "wall_s_total": 15.458872472998337,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "x*(0.99411434 + y*(-0.49813423))",
      "r2_train": 0.9961659764006305,
      "reward": null,
      "residual_heldout": 0.004234085840446968,
      "pred_coeffs": {
        "x*y": -0.49813423
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        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.845541685999706,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.4979406 - 0.99533886)",
      "r2_train": 0.9944337872654666,
      "reward": null,
      "residual_heldout": 0.0031129542255215414,
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        "x*y": 0.4979406
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.613330786998631,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.004233217805197536 cons=0.3459053265681213 wall_s=16.303 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004233217805197536,
  "conservation_residual": 0.3459053265681213,
  "equations": [
    "x*(0.99396324 + y*(-0.49759045))",
    "y*(-(-0.49632975)*x - 0.9882168)"
  ],
  "wall_s_total": 16.303056118000313,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "x*(0.99396324 + y*(-0.49759045))",
      "r2_train": 0.9952653380322037,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.49759045
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      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.52006727600019,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-(-0.49632975)*x - 0.9882168)",
      "r2_train": 0.9940842352569604,
      "reward": null,
      "residual_heldout": 0.0047779975467575255,
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        "x*y": 0.49632975
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      },
      "structure_ok": false,
      "wall_s": 7.7829888420001225,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.005237981794088435 cons=0.22830106006553588 wall_s=16.805 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005237981794088435,
  "conservation_residual": 0.22830106006553588,
  "equations": [
    "(y - 2.001353)*x*(-0.50538665)",
    "(x - 1.9962232)*y*0.5095674"
  ],
  "wall_s_total": 16.804627350000374,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 2.001353)*x*(-0.50538665)",
      "r2_train": 0.9921832495491809,
      "reward": null,
      "residual_heldout": 0.005121074225104149,
      "pred_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 8.71690651300014,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1.9962232)*y*0.5095674",
      "r2_train": 0.99179797383948,
      "reward": null,
      "residual_heldout": 0.005354889363072722,
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      "structure_ok": false,
      "wall_s": 8.087720837000234,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.004593147621714212 cons=0.24967819237682998 wall_s=16.053 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004593147621714212,
  "conservation_residual": 0.24967819237682998,
  "equations": [
    "x*(0.9840794 + y*(-0.49356064))",
    "y*(x*0.50983655 - 1.022815)"
  ],
  "wall_s_total": 16.053047409999635,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.9840794 + y*(-0.49356064))",
      "r2_train": 0.9915956712012836,
      "reward": null,
      "residual_heldout": 0.0036074996347157337,
      "pred_coeffs": {
        "x*y": -0.49356064
      },
      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.19510614399951,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.50983655 - 1.022815)",
      "r2_train": 0.9950909930846785,
      "reward": null,
      "residual_heldout": 0.00557879560871269,
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      "structure_ok": false,
      "wall_s": 7.857941266000125,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.005857844063959644 cons=0.20497667829180932 wall_s=16.715 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005857844063959644,
  "conservation_residual": 0.20497667829180932,
  "equations": [
    "x*(y*(-0.496437) - 1*(-0.987221))",
    "y*(x*0.49852094 - 0.998056)"
  ],
  "wall_s_total": 16.715294805000667,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y*(-0.496437) - 1*(-0.987221))",
      "r2_train": 0.9947194384562424,
      "reward": null,
      "residual_heldout": 0.005782042652426862,
      "pred_coeffs": {
        "x*y": -0.496437
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      "structure_ok": false,
      "wall_s": 8.093196367000928,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49852094 - 0.998056)",
      "r2_train": 0.9960035170597644,
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      "structure_ok": false,
      "wall_s": 8.622098437999739,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.005257324923006108 cons=0.32609466940612647 wall_s=16.518 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005257324923006108,
  "conservation_residual": 0.32609466940612647,
  "equations": [
    "x*(0.9970649 + y*(-0.49920347))",
    "y*(x*0.49888757 - 1.0008321)"
  ],
  "wall_s_total": 16.5183493479999,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9923351786798422,
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      "pred_coeffs": {
        "x*y": -0.49920347
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      "structure_ok": false,
      "wall_s": 8.853593752999586,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49888757 - 1.0008321)",
      "r2_train": 0.9945060351960257,
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      "structure_ok": false,
      "wall_s": 7.664755595000315,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.00533706397122658 cons=0.19884017792893985 wall_s=16.605 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00533706397122658,
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  "equations": [
    "x*(0.9899009 - 0.49726167*y)",
    "(x - 1.9819252)*0.50117064*y"
  ],
  "wall_s_total": 16.604881249000755,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9934106476504385,
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      "wall_s": 8.422284493999541,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1.9819252)*0.50117064*y",
      "r2_train": 0.9938984959930525,
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      "residual_heldout": 0.004686007415854106,
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      "structure_ok": false,
      "wall_s": 8.182596755001214,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.0035441772000940563 cons=0.22988701330195427 wall_s=16.528 ok=True

```json
{
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  "recovered": false,
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  "residual": 0.0035441772000940563,
  "conservation_residual": 0.22988701330195427,
  "equations": [
    "x*(0.99855447 - 0.49698648*y)",
    "y*(-(-0.5014179)*x - 1.0054559)"
  ],
  "wall_s_total": 16.52830363599969,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "wall_s": 8.478764498999226,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-(-0.5014179)*x - 1.0054559)",
      "r2_train": 0.9946077451075926,
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      "structure_ok": false,
      "wall_s": 8.049539137000465,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.004585889346414983 cons=0.17777793125529892 wall_s=16.099 ok=True

```json
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  "residual": 0.004585889346414983,
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  "equations": [
    "(y - 1.9917341)*x*(-0.49101663)",
    "y*(x*0.50339305 - 1.0043986)"
  ],
  "wall_s_total": 16.098813745998996,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "free_const_values": null,
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    {
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      "structure_ok": false,
      "wall_s": 8.003337186999488,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.003909488047663796 cons=0.23584630670814302 wall_s=16.098 ok=True

```json
{
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  "recovered": false,
  "structure_ok": false,
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  "residual": 0.003909488047663796,
  "conservation_residual": 0.23584630670814302,
  "equations": [
    "x*(2.0045354 - y)*0.4966347",
    "y*(x*0.49149555 - 0.98673415)"
  ],
  "wall_s_total": 16.09813039800065,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": false,
      "wall_s": 8.463849349000157,
      "wall_pad_s": 0.0,
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      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
      "zero_eq": false,
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    {
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      "structure_ok": false,
      "wall_s": 7.634281049000492,
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        "timeout_in_seconds": 100,
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}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.006674523724450184 cons=0.3342059063020591 wall_s=17.340 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.006674523724450184,
  "conservation_residual": 0.3342059063020591,
  "equations": [
    "x*(y*(-0.4954334) - 1*(-0.9897762))",
    "y*(-(-0.5064666)*x - 1.0066652)"
  ],
  "wall_s_total": 17.340465800998572,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "x*(y*(-0.4954334) - 1*(-0.9897762))",
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      "residual_heldout": 0.007564204226701996,
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      "structure_ok": false,
      "wall_s": 8.674821943999632,
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      "wall_cap_s": 120,
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      "free_const_values": null,
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    {
      "eq_i": 1,
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      "equation": "y*(-(-0.5064666)*x - 1.0066652)",
      "r2_train": 0.9940036539779915,
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      "structure_ok": false,
      "wall_s": 8.66564385699894,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.005288901651894563 cons=0.3364964965660895 wall_s=15.885 ok=True

```json
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  "residual": 0.005288901651894563,
  "conservation_residual": 0.3364964965660895,
  "equations": [
    "x*(0.99988186 + y*(-0.49877274))",
    "(x - 1*1.9980543)*y*0.5065786"
  ],
  "wall_s_total": 15.884872392000034,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "wall_s": 8.089380401999733,
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      "free_const_values": null,
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    {
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      "structure_ok": false,
      "wall_s": 7.795491990000301,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.007389539760880182 cons=0.2960690036323747 wall_s=16.007 ok=True

```json
{
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  "n_samples": 100,
  "arm": "A0_pysr",
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  "recovered": false,
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  "residual": 0.007389539760880182,
  "conservation_residual": 0.2960690036323747,
  "equations": [
    "x*(1.0053368 - 0.5001517*y)",
    "y*(x*0.49998295 - 0.9976847)"
  ],
  "wall_s_total": 16.006636592999712,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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    {
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.717366040998968,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.004788826778256941 cons=0.17855933073122665 wall_s=16.197 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004788826778256941,
  "conservation_residual": 0.17855933073122665,
  "equations": [
    "x*(1.0080429 - 0.50424683*y)",
    "(x - 1*2.00869)*0.50554055*y"
  ],
  "wall_s_total": 16.19687341700046,
  "wall_s_per_eq": [
    8.11960062199978,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(1.0080429 - 0.50424683*y)",
      "r2_train": 0.9953889607175855,
      "reward": null,
      "residual_heldout": 0.004695998344953844,
      "pred_coeffs": {
        "x*y": -0.50424683
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.11960062199978,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1*2.00869)*0.50554055*y",
      "r2_train": 0.9943671579874215,
      "reward": null,
      "residual_heldout": 0.004881655211560038,
      "pred_coeffs": {
        "x*y": 0.50554055
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.077272795000681,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.0045571984872766515 cons=0.1975959394871926 wall_s=16.757 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0045571984872766515,
  "conservation_residual": 0.1975959394871926,
  "equations": [
    "x*(1.0116314 + y*(-0.50736266))",
    "y*(x*0.5005622 - 1*1.001755)"
  ],
  "wall_s_total": 16.756724957000188,
  "wall_s_per_eq": [
    8.147194220999154,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(1.0116314 + y*(-0.50736266))",
      "r2_train": 0.9939231022130918,
      "reward": null,
      "residual_heldout": 0.0023741345707167065,
      "pred_coeffs": {
        "x*y": -0.50736266
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.147194220999154,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5005622 - 1*1.001755)",
      "r2_train": 0.9954323540023676,
      "reward": null,
      "residual_heldout": 0.006740262403836596,
      "pred_coeffs": {
        "x*y": 0.5005622
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.609530736001034,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.10521864508538725 cons=0.11633471728112377 wall_s=17.341 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.10521864508538725,
  "conservation_residual": 0.11633471728112377,
  "equations": [
    "x*(2*a - b*y)",
    "-x*(c*x + 3*d)"
  ],
  "wall_s_total": 17.340623251999205,
  "wall_s_per_eq": [
    7.784074159000738,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(2*a - b*y)",
      "r2_train": 0.9902235660370046,
      "reward": null,
      "residual_heldout": 0.006053205672818698,
      "pred_coeffs": {
        "x*y": -0.501041929180013
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.784074159000738,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.784074159000738,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.500934459268555,
        0.501041929180013
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + 3*d)",
      "r2_train": 0.851025295484214,
      "reward": null,
      "residual_heldout": 0.2043840844979558,
      "pred_coeffs": {
        "x^2": 0.4295315397007885,
        "x": -1.0310250911547951
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.556549092998466,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.556549092998466,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4295315397007885,
        0.3436750303849317
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.06847745985242577 cons=0.16181115979796726 wall_s=16.610 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.06847745985242577,
  "conservation_residual": 0.16181115979796726,
  "equations": [
    "x*(-a - 3*b*y)",
    "x*(-c*x - d)"
  ],
  "wall_s_total": 16.61024524900131,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a - 3*b*y)",
      "r2_train": 0.9947351826364623,
      "reward": null,
      "residual_heldout": 0.007842828964177283,
      "pred_coeffs": {
        "x*y": -0.4899274927697823
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.599531519001175,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.599531519001175,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9823903431680382,
        0.1633091642565941
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x - d)",
      "r2_train": 0.8487192408998621,
      "reward": null,
      "residual_heldout": 0.12911209074067426,
      "pred_coeffs": {
        "x^2": 0.44945595983524206,
        "x": -1.0529182586160875
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.010713730000134,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.010713730000134,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.44945595983524206,
        1.0529182586160875
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.10595928569517406 cons=0.10399762034636531 wall_s=17.440 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.10595928569517406,
  "conservation_residual": 0.10399762034636531,
  "equations": [
    "x*(-a + b*y)",
    "-x*(c*x + 2*d)"
  ],
  "wall_s_total": 17.43991701199957,
  "wall_s_per_eq": [
    7.4054782669991255,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9934342789125378,
      "reward": null,
      "residual_heldout": 0.004583202728349008,
      "pred_coeffs": {
        "x*y": -0.5006689555486111
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.4054782669991255,
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      "wall_raw_s": 7.4054782669991255,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9927488980371723,
        -0.5006689555486111
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + 2*d)",
      "r2_train": 0.8316902528370433,
      "reward": null,
      "residual_heldout": 0.20733536866199911,
      "pred_coeffs": {
        "x^2": 0.435814759398251,
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.034438745000443,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.034438745000443,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.435814759398251,
        0.496850837085481
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.004637018955758647 cons=0.3084975553191642 wall_s=17.651 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004637018955758647,
  "conservation_residual": 0.3084975553191642,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 17.65070723899953,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9970535256733677,
      "reward": null,
      "residual_heldout": 0.004414342432480064,
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        "x*y": -0.5033343752400323
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.462623811999947,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.462623811999947,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0021454418227238,
        -0.5033343752400323
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + d)",
      "r2_train": 0.9956045593359819,
      "reward": null,
      "residual_heldout": 0.004859695479037232,
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        "x*y": 0.5051971451867179
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.188083426999583,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.188083426999583,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5051971451867179,
        -1.0141067931324599
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.004958469044182851 cons=0.39632995831953083 wall_s=17.138 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004958469044182851,
  "conservation_residual": 0.39632995831953083,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(-c*x - 2*d)"
  ],
  "wall_s_total": 17.138214016998973,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-2*a + b*y)",
      "r2_train": 0.9942731521757471,
      "reward": null,
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        "x*y": -0.49441382695213776
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 7.351715073999003,
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      "wall_raw_s": 7.351715073999003,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49548698282383974,
        -0.49441382695213776
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x - 2*d)",
      "r2_train": 0.9922375389954842,
      "reward": null,
      "residual_heldout": 0.00491178567165728,
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        "x*y": 0.49657787026137973
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      "true_coeffs": {
        "y": -1.0,
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      },
      "structure_ok": false,
      "wall_s": 9.78649894299997,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.78649894299997,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49657787026137973,
        0.5010711549068672
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.09087500338584452 cons=0.21653057720651664 wall_s=17.482 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.09087500338584452,
  "conservation_residual": 0.21653057720651664,
  "equations": [
    "-x*(a + b*y)",
    "2*c*x*(x + y) + d*y"
  ],
  "wall_s_total": 17.482158263999736,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "-x*(a + b*y)",
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        "x*y": -0.49813499470073325
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.710274410999773,
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      "wall_raw_s": 7.710274410999773,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9941160553088314,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "2*c*x*(x + y) + d*y",
      "r2_train": 0.8316225122376865,
      "reward": null,
      "residual_heldout": 0.1775159380779497,
      "pred_coeffs": {
        "x*y": 0.13568157138330592,
        "x^2": 0.13568157138330592
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.771883852999963,
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      "wall_raw_s": 9.771883852999963,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.06784078569165296,
        -0.5362601574974365
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.004233245643226377 cons=0.3459058673221936 wall_s=15.618 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004233245643226377,
  "conservation_residual": 0.3459058673221936,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x - d)"
  ],
  "wall_s_total": 15.618457960001251,
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.8226348040007,
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      "wall_raw_s": 7.8226348040007,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      },
      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.9940842339543489,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.7958231560005515,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.7958231560005515,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4963314400134809,
        0.9882205472767788
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.005237988863117003 cons=0.22830052410571802 wall_s=18.289 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.005237988863117003,
  "conservation_residual": 0.22830052410571802,
  "equations": [
    "x*(-3*a - b*y)",
    "y*(3*c*x - d)"
  ],
  "wall_s_total": 18.289313348999713,
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9921832531902312,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 10.30437754599916,
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      "wall_raw_s": 10.30437754599916,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.33715284763623854,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(3*c*x - d)",
      "r2_train": 0.9917979749585317,
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      "structure_ok": false,
      "wall_s": 7.984935803000553,
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      "wall_raw_s": 7.984935803000553,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        0.16985570448476517,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.11487480094489567 cons=0.1213994935824044 wall_s=18.305 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.11487480094489567,
  "conservation_residual": 0.1213994935824044,
  "equations": [
    "-x*(a + 2*b*y)",
    "x*(-c*x + 2*d)"
  ],
  "wall_s_total": 18.30523783799981,
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": false,
      "wall_s": 10.287569848000203,
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      "wall_raw_s": 10.287569848000203,
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      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -0.9840805799447319,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
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      "target": "dy/dt",
      "equation": "x*(-c*x + 2*d)",
      "r2_train": 0.823073451644343,
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      "pred_coeffs": {
        "x^2": 0.43998585607152196,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.017667989999609,
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      "wall_raw_s": 8.017667989999609,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.43998585607152196,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.005857647439864835 cons=0.20497669417578798 wall_s=17.494 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.005857647439864835,
  "conservation_residual": 0.20497669417578798,
  "equations": [
    "x*(-a - b*y)",
    "-y*(c*x + d)"
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  "wall_s_total": 17.493649662997996,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-a - b*y)",
      "r2_train": 0.9947194381313768,
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        "x*y": -0.49643768315433545
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.745836307998616,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "zero_eq_retry": 2
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      "free_const_values": [
        -0.9872249673014414,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.9960035146903331,
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      "structure_ok": false,
      "wall_s": 7.74781335499938,
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      "wall_raw_s": 7.74781335499938,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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      },
      "free_const_values": [
        -0.4985216717212548,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.005257309662474053 cons=0.32609203287761274 wall_s=18.039 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005257309662474053,
  "conservation_residual": 0.32609203287761274,
  "equations": [
    "-x*(a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 18.03919257599955,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "r2_train": 0.9923351770894531,
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        "x*y": -0.49920911051444167
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.8881117239998275,
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      "wall_raw_s": 7.8881117239998275,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9970779581356298,
        0.49920911051444167
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + d)",
      "r2_train": 0.9945060370048274,
      "reward": null,
      "residual_heldout": 0.004444080194435232,
      "pred_coeffs": {
        "x*y": 0.4988894320413925
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.151080851999723,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.151080851999723,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4988894320413925,
        -1.0008377844429397
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.12095476470422531 cons=0.150155081673826 wall_s=15.611 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.12095476470422531,
  "conservation_residual": 0.150155081673826,
  "equations": [
    "-(a + 2*b*y)*(x + y)",
    "-x*(c*x + d)"
  ],
  "wall_s_total": 15.611046550000538,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-(a + 2*b*y)*(x + y)",
      "r2_train": 0.9478740445988545,
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      "residual_heldout": 0.045576570544261,
      "pred_coeffs": {
        "x*y": -0.2487990779177286,
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.747249975000159,
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      "wall_raw_s": 7.747249975000159,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -0.5440290710286689,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + d)",
      "r2_train": 0.8267773364542215,
      "reward": null,
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        "x^2": 0.4359176215138475,
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      "true_coeffs": {
        "y": -1.0,
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      "structure_ok": false,
      "wall_s": 7.863796575000379,
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      "wall_raw_s": 7.863796575000379,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4359176215138475,
        1.0117859162135716
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.0035441983192145126 cons=0.22988728383247697 wall_s=17.987 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0035441983192145126,
  "conservation_residual": 0.22988728383247697,
  "equations": [
    "x*(-3*a + b*y)",
    "-y*(c*x + d)"
  ],
  "wall_s_total": 17.986508169000444,
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 10.332317239999611,
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      "wall_raw_s": 10.332317239999611,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.9946077511833886,
      "reward": null,
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        "x*y": 0.5014185622733145
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.654190929000833,
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      "wall_raw_s": 7.654190929000833,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5014185622733145,
        1.0054574703759667
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.004586041392166615 cons=0.17777782745192985 wall_s=17.774 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.004586041392166615,
  "conservation_residual": 0.17777782745192985,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(-2*c*x - d)"
  ],
  "wall_s_total": 17.774357351001527,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-2*a + b*y)",
      "r2_train": 0.9947840698122556,
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      "structure_ok": false,
      "wall_s": 9.903810154000894,
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      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4889876132894619,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-2*c*x - d)",
      "r2_train": 0.9943946373746241,
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        "x*y": 0.5033930334655323
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      "structure_ok": false,
      "wall_s": 7.870547197000633,
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      "wall_raw_s": 7.870547197000633,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.25169651673276616,
        1.004393630838369
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.003909475061609837 cons=0.23584596351693776 wall_s=18.010 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.003909475061609837,
  "conservation_residual": 0.23584596351693776,
  "equations": [
    "x*(2*a - b*y)",
    "y*(-3*c*x + 2*d)"
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  "wall_s_total": 18.010465093000676,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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        "x*y": -0.49663480293998746
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.480619084999489,
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      "wall_raw_s": 7.480619084999489,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
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      "target": "dy/dt",
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      "r2_train": 0.9903320985885847,
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      "structure_ok": false,
      "wall_s": 10.529846008001186,
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      "wall_raw_s": 10.529846008001186,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.1638316635355665,
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.17361245580657814 cons=0.4720568794796529 wall_s=15.355 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
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  "residual": 0.17361245580657814,
  "conservation_residual": 0.4720568794796529,
  "equations": [
    "a*x - 2*b*y**2",
    "y*(c*x - 3*d)"
  ],
  "wall_s_total": 15.354783527998734,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "a*x - 2*b*y**2",
      "r2_train": 0.6869240393789928,
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      "residual_heldout": 0.3414400854986427,
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        "y^2": -0.17696067606921853,
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      "budget": {
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
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    {
      "eq_i": 1,
      "target": "dy/dt",
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      "r2_train": 0.9940036534578484,
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      "structure_ok": false,
      "wall_s": 7.652912366998862,
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      "wall_raw_s": 7.652912366998862,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.0052891295024832695 cons=0.33649752838314356 wall_s=18.533 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.0052891295024832695,
  "conservation_residual": 0.33649752838314356,
  "equations": [
    "x*(a - b*y)",
    "-y*(c*x + 2*d)"
  ],
  "wall_s_total": 18.532598783998765,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "wall_s": 10.78726324299896,
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      "budget": {
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        "max_n_evaluations": 2500,
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      "free_const_values": [
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      "zero_eq": false,
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    {
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        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.745335540999804,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.745335540999804,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5065787786855374,
        0.5060856019700095
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.07989195345050698 cons=0.1485053728776301 wall_s=19.082 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.07989195345050698,
  "conservation_residual": 0.1485053728776301,
  "equations": [
    "x*(3*a + b*y)",
    "x*(-c*x + d)"
  ],
  "wall_s_total": 19.08174378700096,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(3*a + b*y)",
      "r2_train": 0.9933639380799996,
      "reward": null,
      "residual_heldout": 0.00723499260285801,
      "pred_coeffs": {
        "x*y": -0.5001515456569016
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.447167635000369,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.447167635000369,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3351121662740467,
        -0.5001515456569016
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + d)",
      "r2_train": 0.8678619673331036,
      "reward": null,
      "residual_heldout": 0.15254891429815595,
      "pred_coeffs": {
        "x^2": 0.4388665743469216,
        "x": -1.0533701967653244
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.63457615200059,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.63457615200059,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4388665743469216,
        -1.0533701967653244
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.004788996305600961 cons=0.17856010804455189 wall_s=16.498 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004788996305600961,
  "conservation_residual": 0.17856010804455189,
  "equations": [
    "-x*(4*a + b*y)",
    "y*(-c*x + 4*d)"
  ],
  "wall_s_total": 16.497695452002517,
  "wall_s_per_eq": [
    8.240316115001406,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-x*(4*a + b*y)",
      "r2_train": 0.9953889600758815,
      "reward": null,
      "residual_heldout": 0.004696010695664031,
      "pred_coeffs": {
        "x*y": -0.5042469508349818
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.240316115001406,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.240316115001406,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.2520108135876192,
        0.5042469508349818
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + 4*d)",
      "r2_train": 0.9943671562982211,
      "reward": null,
      "residual_heldout": 0.004881981915537892,
      "pred_coeffs": {
        "x*y": 0.5055436719358289
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.257379337001112,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.257379337001112,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5055436719358289,
        -0.2538702188308608
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.004557405991856064 cons=0.19759222275605795 wall_s=18.582 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004557405991856064,
  "conservation_residual": 0.19759222275605795,
  "equations": [
    "x*(-a + b*y)",
    "y*(-c*x + d)"
  ],
  "wall_s_total": 18.581832063000547,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9939231050994192,
      "reward": null,
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        "x*y": -0.5073744851738444
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.3299816990002,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.3299816990002,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.011651625443756,
        -0.5073744851738444
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + d)",
      "r2_train": 0.995432354487329,
      "reward": null,
      "residual_heldout": 0.006740575804166373,
      "pred_coeffs": {
        "x*y": 0.5005655586536265
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 11.251850364000347,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.251850364000347,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5005655586536265,
        -1.001760356686077
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.007006467875435849 cons=0.20017781928853984 wall_s=19.740 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007006467875435849,
  "conservation_residual": 0.20017781928853984,
  "equations": [
    "(y - 1*1.9946238)*x*(-0.5042757)",
    "y*(x*0.5019199 - 1*1.0029489)"
  ],
  "wall_s_total": 19.74035144700065,
  "wall_s_per_eq": [
    10.734492114001114,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(y - 1*1.9946238)*x*(-0.5042757)",
      "r2_train": 0.9941486295430095,
      "reward": null,
      "residual_heldout": 0.006797148502087712,
      "pred_coeffs": {
        "x*y": -0.5042757
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 10.734492114001114,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.5019199 - 1*1.0029489)",
      "r2_train": 0.9948816459572237,
      "reward": null,
      "residual_heldout": 0.007215787248783986,
      "pred_coeffs": {
        "x*y": 0.5019199
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.005859332999535,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.0069333104423499586 cons=0.2812541687106144 wall_s=18.859 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0069333104423499586,
  "conservation_residual": 0.2812541687106144,
  "equations": [
    "x*(y - 2.0028732)*(-0.4949997)",
    "y*(x*0.49738672 - 0.9907335)"
  ],
  "wall_s_total": 18.859059062000597,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y - 2.0028732)*(-0.4949997)",
      "r2_train": 0.9943990358578019,
      "reward": null,
      "residual_heldout": 0.0070957673171428174,
      "pred_coeffs": {
        "x*y": -0.4949997
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.324627611998949,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49738672 - 0.9907335)",
      "r2_train": 0.9950230446521942,
      "reward": null,
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        "x*y": 0.49738672
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      "structure_ok": false,
      "wall_s": 9.534431450001648,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.005977422598473852 cons=0.30584112790919005 wall_s=16.772 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005977422598473852,
  "conservation_residual": 0.30584112790919005,
  "equations": [
    "x*(0.99100834 - 0.49681923*y)",
    "y*(x*0.49683505 - 0.99386257)"
  ],
  "wall_s_total": 16.77187312500064,
  "wall_s_per_eq": [
    8.610520386000644,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.99100834 - 0.49681923*y)",
      "r2_train": 0.9941496162980121,
      "reward": null,
      "residual_heldout": 0.006778878221124922,
      "pred_coeffs": {
        "x*y": -0.49681923
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.610520386000644,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.49683505 - 0.99386257)",
      "r2_train": 0.9945210003894549,
      "reward": null,
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        "x*y": 0.49683505
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.161352738999994,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.004765774164387752 cons=0.2172542424102291 wall_s=16.873 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004765774164387752,
  "conservation_residual": 0.2172542424102291,
  "equations": [
    "x*(y*(-0.49760085) - 1*(-0.9962759))",
    "y*0.5015176*(x - 2.0053222)"
  ],
  "wall_s_total": 16.87270373300089,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(y*(-0.49760085) - 1*(-0.9962759))",
      "r2_train": 0.9941649779388988,
      "reward": null,
      "residual_heldout": 0.0046428855117514045,
      "pred_coeffs": {
        "x*y": -0.49760085
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 8.842505832000825,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*0.5015176*(x - 2.0053222)",
      "r2_train": 0.9946600267148274,
      "reward": null,
      "residual_heldout": 0.0048886628170241,
      "pred_coeffs": {
        "x*y": 0.5015176
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.030197901000065,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.006357255667107943 cons=0.30436536845206225 wall_s=17.683 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006357255667107943,
  "conservation_residual": 0.30436536845206225,
  "equations": [
    "(y - 1.9983963)*x*(-0.49560934)",
    "(x - 1*1.9973068)*y*0.50119907"
  ],
  "wall_s_total": 17.682895333999113,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": false,
      "wall_s": 8.809795647999636,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1*1.9973068)*y*0.50119907",
      "r2_train": 0.9947086291410503,
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      "structure_ok": false,
      "wall_s": 8.873099685999478,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.0053604896884094705 cons=0.18364018128082066 wall_s=17.803 ok=True

```json
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  "residual": 0.0053604896884094705,
  "conservation_residual": 0.18364018128082066,
  "equations": [
    "x*(1.995683 - y)*0.49952254",
    "(1.9942329 - x)*(-0.49798495)*y"
  ],
  "wall_s_total": 17.803399627000545,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": false,
      "wall_s": 8.642876689000332,
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      "free_const_values": null,
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    {
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      "structure_ok": false,
      "wall_s": 9.160522938000213,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.005352094061674473 cons=0.31005918612954236 wall_s=17.800 ok=True

```json
{
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  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.005352094061674473,
  "conservation_residual": 0.31005918612954236,
  "equations": [
    "x*(1.006953 + y*(-0.502657))",
    "(x - 1.9950802)*y*0.4991562"
  ],
  "wall_s_total": 17.80029687500064,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": false,
      "wall_s": 9.471312994000982,
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      "free_const_values": null,
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    {
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      "r2_train": 0.9944440955605126,
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      "structure_ok": false,
      "wall_s": 8.328983880999658,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.005254630368031453 cons=0.2518734310393619 wall_s=17.974 ok=True

```json
{
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  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.005254630368031453,
  "conservation_residual": 0.2518734310393619,
  "equations": [
    "x*(0.9947795 + y*(-0.4965733))",
    "y*(x*0.5040901 - 1.0095406)"
  ],
  "wall_s_total": 17.97419050299868,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "r2_train": 0.9942124817130461,
      "reward": null,
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      "structure_ok": false,
      "wall_s": 8.803022330999738,
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      "wall_cap_s": 120,
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      "free_const_values": null,
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    {
      "eq_i": 1,
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      "equation": "y*(x*0.5040901 - 1.0095406)",
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      "structure_ok": false,
      "wall_s": 9.171168171998943,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.00647818646080329 cons=0.2957579260843962 wall_s=20.078 ok=True

```json
{
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  "residual": 0.00647818646080329,
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    "x*(1.0015602 - 0.50107616*y)",
    "y*(x*0.5021701 - 1.0054855)"
  ],
  "wall_s_total": 20.078227534999314,
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  "wall_pad_s_total": 0.0,
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  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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    {
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.004738485268821781 cons=0.2706745381916861 wall_s=18.084 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A0_pysr",
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  "recovered": false,
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  "residual": 0.004738485268821781,
  "conservation_residual": 0.2706745381916861,
  "equations": [
    "(y - 1*2.0015206)*(-0.49865812)*x",
    "(1.994931 - x)*(-0.49733436)*y"
  ],
  "wall_s_total": 18.08375223400253,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
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  "tau": 0.2,
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  "eq_results": [
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.005370729729652103 cons=0.30888263027670326 wall_s=18.238 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005370729729652103,
  "conservation_residual": 0.30888263027670326,
  "equations": [
    "x*(y - 2.000667)*(-0.5019013)",
    "(x - 2.0013645)*y*0.49946055"
  ],
  "wall_s_total": 18.237673766001535,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "r2_train": 0.99347021454734,
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      "pred_coeffs": {
        "x*y": -0.5019013
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      "true_coeffs": {
        "x": 1.0,
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      },
      "structure_ok": false,
      "wall_s": 9.018553189000158,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0013645)*y*0.49946055",
      "r2_train": 0.9943812710177921,
      "reward": null,
      "residual_heldout": 0.004846212542613994,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.219120577001377,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.006478272595074976 cons=0.29355040247841213 wall_s=18.064 ok=True

```json
{
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  "n_samples": 400,
  "arm": "A0_pysr",
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  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006478272595074976,
  "conservation_residual": 0.29355040247841213,
  "equations": [
    "x*(y - 1*1.996753)*(-0.49592134)",
    "y*(-(-0.5014065)*x - 0.998417)"
  ],
  "wall_s_total": 18.064018438999483,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(y - 1*1.996753)*(-0.49592134)",
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      "structure_ok": false,
      "wall_s": 9.45249914499982,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-(-0.5014065)*x - 0.998417)",
      "r2_train": 0.9953143747792795,
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        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.611519293999663,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.004843240077946523 cons=0.23277042296139758 wall_s=17.674 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004843240077946523,
  "conservation_residual": 0.23277042296139758,
  "equations": [
    "(y - 2.0042033)*x*(-0.495449)",
    "(x - 2.002824)*y*0.5000116"
  ],
  "wall_s_total": 17.67391841999961,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(y - 2.0042033)*x*(-0.495449)",
      "r2_train": 0.9952670053931909,
      "reward": null,
      "residual_heldout": 0.005211262972913299,
      "pred_coeffs": {
        "x*y": -0.495449
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.709039654999287,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.002824)*y*0.5000116",
      "r2_train": 0.9944757817134202,
      "reward": null,
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      "structure_ok": false,
      "wall_s": 8.964878765000321,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.006179348230410229 cons=0.23899620357386578 wall_s=18.302 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006179348230410229,
  "conservation_residual": 0.23899620357386578,
  "equations": [
    "x*(y - 1.9970437)*(-0.49984306)",
    "y*0.49911568*(x - 2.004883)"
  ],
  "wall_s_total": 18.302071993000936,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y - 1.9970437)*(-0.49984306)",
      "r2_train": 0.9946849452954781,
      "reward": null,
      "residual_heldout": 0.00684723613211351,
      "pred_coeffs": {
        "x*y": -0.49984306
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      "true_coeffs": {
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        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.517686307000986,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*0.49911568*(x - 2.004883)",
      "r2_train": 0.9945124712151374,
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      "structure_ok": false,
      "wall_s": 8.78438568599995,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.006008155343013556 cons=0.2562739864833158 wall_s=17.997 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006008155343013556,
  "conservation_residual": 0.2562739864833158,
  "equations": [
    "(y - 1*2.0032823)*x*(-0.49536768)",
    "(x - 2.001301)*y*0.49722135"
  ],
  "wall_s_total": 17.997003794998818,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "(y - 1*2.0032823)*x*(-0.49536768)",
      "r2_train": 0.9955306305908266,
      "reward": null,
      "residual_heldout": 0.004837094943208196,
      "pred_coeffs": {
        "x*y": -0.49536768
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      "structure_ok": false,
      "wall_s": 9.635792782999488,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.001301)*y*0.49722135",
      "r2_train": 0.9938709884558682,
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      "structure_ok": false,
      "wall_s": 8.36121101199933,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.006651887554650856 cons=0.26031993998858594 wall_s=18.543 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.006651887554650856,
  "conservation_residual": 0.26031993998858594,
  "equations": [
    "x*(2.0012794 - y)*0.49598902",
    "y*(x*0.50233316 - 1.004774)"
  ],
  "wall_s_total": 18.542790283001523,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9943055984865463,
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        "x*y": -0.49598902
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      "structure_ok": false,
      "wall_s": 9.505544797000766,
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x*0.50233316 - 1.004774)",
      "r2_train": 0.9941566221224833,
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      "structure_ok": false,
      "wall_s": 9.037245486000757,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.006270202341033125 cons=0.3330228052902794 wall_s=17.765 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006270202341033125,
  "conservation_residual": 0.3330228052902794,
  "equations": [
    "x*(1.0003744 + y*(-0.50150186))",
    "y*(x - 1*1.9987237)*0.4956464"
  ],
  "wall_s_total": 17.765449673999683,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9945855046893378,
      "reward": null,
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      "structure_ok": false,
      "wall_s": 8.655114372999378,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(x - 1*1.9987237)*0.4956464",
      "r2_train": 0.9952136147244836,
      "reward": null,
      "residual_heldout": 0.004951773789196446,
      "pred_coeffs": {
        "x*y": 0.4956464
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.110335301000305,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.00523135237505775 cons=0.329677224061443 wall_s=19.304 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00523135237505775,
  "conservation_residual": 0.329677224061443,
  "equations": [
    "x*(0.99570477 - 0.49812636*y)",
    "(x - 1*2.0069559)*0.50085306*y"
  ],
  "wall_s_total": 19.303941300999213,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(0.99570477 - 0.49812636*y)",
      "r2_train": 0.9937476172843693,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.49812636
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 9.87094984399846,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1*2.0069559)*0.50085306*y",
      "r2_train": 0.9938526680816689,
      "reward": null,
      "residual_heldout": 0.005385256095243737,
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        "x*y": 0.50085306
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.432991457000753,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.005143287303457483 cons=0.31012817839554274 wall_s=17.272 ok=True

```json
{
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  "recoverable": true,
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  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005143287303457483,
  "conservation_residual": 0.31012817839554274,
  "equations": [
    "x*0.4979814*(2.0028858 - y)",
    "(x - 1*1.9979682)*y*0.49836266"
  ],
  "wall_s_total": 17.272496452998894,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*0.4979814*(2.0028858 - y)",
      "r2_train": 0.9951597636477639,
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      "pred_coeffs": {
        "x*y": -0.4979814
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      "structure_ok": false,
      "wall_s": 8.67545820399937,
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      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 1*1.9979682)*y*0.49836266",
      "r2_train": 0.9951082849227806,
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      "true_coeffs": {
        "y": -1.0,
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      "structure_ok": false,
      "wall_s": 8.597038248999525,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `lotka_volterra` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.006725930665718536 cons=0.2731166074303611 wall_s=18.604 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006725930665718536,
  "conservation_residual": 0.2731166074303611,
  "equations": [
    "x*(y - 1.9913301)*(-0.5026324)",
    "(x - 2.0025022)*y*0.49613914"
  ],
  "wall_s_total": 18.603747773999203,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(y - 1.9913301)*(-0.5026324)",
      "r2_train": 0.9948452756005494,
      "reward": null,
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      "pred_coeffs": {
        "x*y": -0.5026324
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 9.500795693000327,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "(x - 2.0025022)*y*0.49613914",
      "r2_train": 0.9941802193409196,
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      "structure_ok": false,
      "wall_s": 9.102952080998875,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.07525222972468901 cons=0.1338437860786941 wall_s=15.934 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.07525222972468901,
  "conservation_residual": 0.1338437860786941,
  "equations": [
    "x*(2*a - b*y)",
    "-x*(c*x + 3*d)"
  ],
  "wall_s_total": 15.934082407999085,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(2*a - b*y)",
      "r2_train": 0.9941486303274351,
      "reward": null,
      "residual_heldout": 0.006797046245989383,
      "pred_coeffs": {
        "x*y": -0.5042747770436784
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 8.158325823000268,
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      "wall_raw_s": 8.158325823000268,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5029192124477326,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + 3*d)",
      "r2_train": 0.8395904842083239,
      "reward": null,
      "residual_heldout": 0.14370741320338862,
      "pred_coeffs": {
        "x^2": 0.43236074953612197,
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 7.775756584998817,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.775756584998817,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.43236074953612197,
        0.34308999388844386
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.07802722159027364 cons=0.16837550876258267 wall_s=19.246 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.07802722159027364,
  "conservation_residual": 0.16837550876258267,
  "equations": [
    "x*(-a - 3*b*y)",
    "x*(-c*x - d)"
  ],
  "wall_s_total": 19.24566808199961,
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9943990351677263,
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        "x*y": -0.495004624705476
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      "structure_ok": false,
      "wall_s": 11.634992645000239,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
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      "free_const_values": [
        -0.9914333374592423,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x - d)",
      "r2_train": 0.8513351311260557,
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      "structure_ok": false,
      "wall_s": 7.610675436999372,
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      "wall_raw_s": 7.610675436999372,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4482176412571774,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.08143760368367572 cons=0.1736778688169146 wall_s=20.271 ok=True

```json
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  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08143760368367572,
  "conservation_residual": 0.1736778688169146,
  "equations": [
    "x*(-a + b*y)",
    "x*(c*x - d)"
  ],
  "wall_s_total": 20.27070954699957,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9941496176443073,
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        "x*y": -0.4968236581940551
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      "true_coeffs": {
        "x": 1.0,
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      },
      "structure_ok": false,
      "wall_s": 8.889974405999965,
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      "wall_cap_s": 120,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
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      "equation": "x*(c*x - d)",
      "r2_train": 0.8431059965654554,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 11.380735140999604,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4263940038725306,
        0.9905602581737705
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.09900733670388287 cons=0.32488238866374813 wall_s=16.214 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.09900733670388287,
  "conservation_residual": 0.32488238866374813,
  "equations": [
    "y*(a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 16.213926989001266,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "y*(a + b*y)",
      "r2_train": 0.8200916039377781,
      "reward": null,
      "residual_heldout": 0.1931267897765386,
      "pred_coeffs": {
        "y^2": -0.47424451448695465,
        "y": 1.123737250045088
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.821830515000329,
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      "wall_raw_s": 7.821830515000329,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.123737250045088,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + d)",
      "r2_train": 0.9946600278688034,
      "reward": null,
      "residual_heldout": 0.00488788363122713,
      "pred_coeffs": {
        "x*y": 0.5015196310566052
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.392096474000937,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.392096474000937,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5015196310566052,
        -1.0057174437426055
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.006357310722767942 cons=0.3043705055563057 wall_s=19.389 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006357310722767942,
  "conservation_residual": 0.3043705055563057,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(2*c*x + d)"
  ],
  "wall_s_total": 19.388804551999783,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.258444957000393,
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      "wall_raw_s": 7.258444957000393,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49521132184474376,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(2*c*x + d)",
      "r2_train": 0.9947086302384552,
      "reward": null,
      "residual_heldout": 0.007324817582815454,
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        "x*y": 0.5012065378838927
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 12.13035959499939,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.13035959499939,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.25060326894194634,
        -1.00105457001938
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.08875629392525743 cons=0.14736101264753326 wall_s=17.380 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08875629392525743,
  "conservation_residual": 0.14736101264753326,
  "equations": [
    "-x*(a + b*y)",
    "2*c*x*(x + y) + d*y"
  ],
  "wall_s_total": 17.37956301399754,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-x*(a + b*y)",
      "r2_train": 0.995434972837828,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.740864459998193,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.740864459998193,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9968968458786072,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "2*c*x*(x + y) + d*y",
      "r2_train": 0.8496744546888371,
      "reward": null,
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      "pred_coeffs": {
        "x*y": 0.13493055474960644,
        "x^2": 0.13493055474960644
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.6386985539993475,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6386985539993475,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.06746527737480322,
        -0.5403696751200194
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.005352053004331479 cons=0.31005672150336877 wall_s=20.066 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005352053004331479,
  "conservation_residual": 0.31005672150336877,
  "equations": [
    "x*(-a + b*y)",
    "y*(c*x - d)"
  ],
  "wall_s_total": 20.06597285600037,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.9939084019651254,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.297996960000091,
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      "wall_raw_s": 8.297996960000091,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0069544611502026,
        -0.5026577179791194
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - d)",
      "r2_train": 0.9944440910022901,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 11.76797589600028,
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      "wall_raw_s": 11.76797589600028,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49915299910114996,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.005254631410520979 cons=0.25187338403006654 wall_s=15.572 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005254631410520979,
  "conservation_residual": 0.25187338403006654,
  "equations": [
    "x*(-3*a - b*y)",
    "y*(3*c*x - d)"
  ],
  "wall_s_total": 15.572231403000842,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-3*a - b*y)",
      "r2_train": 0.9942124838045086,
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      "residual_heldout": 0.005981494068322243,
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        "x*y": -0.4965737451761074
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 7.649463644000207,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.649463644000207,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.331593498540561,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(3*c*x - d)",
      "r2_train": 0.9939243645044422,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.922767759000635,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.922767759000635,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        0.16803015056977283,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.09860319324883662 cons=0.16558675405400816 wall_s=19.853 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.09860319324883662,
  "conservation_residual": 0.16558675405400816,
  "equations": [
    "x*(a - 4*b*y)",
    "x*(-c*x + 2*d)"
  ],
  "wall_s_total": 19.852800401000422,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(a - 4*b*y)",
      "r2_train": 0.9941304028598787,
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        "x*y": -0.5010762326294709
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.891567294000197,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + 2*d)",
      "r2_train": 0.8418017070578925,
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        "x^2": 0.4263520468344474,
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        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 11.961233107000226,
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      "wall_raw_s": 11.961233107000226,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
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      },
      "free_const_values": [
        -0.4263520468344474,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.004738428200101412 cons=0.2706745974109624 wall_s=16.030 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004738428200101412,
  "conservation_residual": 0.2706745974109624,
  "equations": [
    "x*(2*a - b*y)",
    "-y*(c*x + d)"
  ],
  "wall_s_total": 16.029896156996983,
  "wall_s_per_eq": [
    7.922875515998385,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(2*a - b*y)",
      "r2_train": 0.9935854752031951,
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      "residual_heldout": 0.004303385559471719,
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        "x*y": -0.49865815200771924
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      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
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      "structure_ok": false,
      "wall_s": 7.922875515998385,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.922875515998385,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49903736742304516,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.9946222206934984,
      "reward": null,
      "residual_heldout": 0.005173470840731106,
      "pred_coeffs": {
        "x*y": 0.49733449556130804
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.107020640998599,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.107020640998599,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49733449556130804,
        0.9921503206982795
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.005370827214266733 cons=0.30887987565592645 wall_s=20.257 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005370827214266733,
  "conservation_residual": 0.30887987565592645,
  "equations": [
    "-x*(a + b*y)",
    "y*(c*x + d)"
  ],
  "wall_s_total": 20.25676127299994,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 12.15884239099978,
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      "wall_raw_s": 12.15884239099978,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0041542204335963,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x + d)",
      "r2_train": 0.9943812712660781,
      "reward": null,
      "residual_heldout": 0.004846188541658811,
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        "x*y": 0.49946234668980216
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      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
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      "structure_ok": false,
      "wall_s": 8.097918882000158,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.097918882000158,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49946234668980216,
        -0.9996048209853489
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.12080972874237858 cons=0.15961733920056703 wall_s=16.157 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.12080972874237858,
  "conservation_residual": 0.15961733920056703,
  "equations": [
    "-(a + 2*b*y)*(x + y)",
    "-x*(c*x + d)"
  ],
  "wall_s_total": 16.157277936001265,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "structure_ok": false,
      "wall_s": 7.65935839300073,
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      "wall_raw_s": 7.65935839300073,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
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        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-x*(c*x + d)",
      "r2_train": 0.8533596824456781,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.497919543000535,
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      "wall_raw_s": 8.497919543000535,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.44976920604957,
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      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.004843254037429351 cons=0.23277042200365122 wall_s=20.159 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.004843254037429351,
  "conservation_residual": 0.23277042200365122,
  "equations": [
    "x*(a + 3*b*y)",
    "-y*(c*x + d)"
  ],
  "wall_s_total": 20.158840391999547,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "x*(a + 3*b*y)",
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.390423793000082,
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      "wall_raw_s": 8.390423793000082,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + d)",
      "r2_train": 0.9944757802719388,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 11.768416598999465,
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      "wall_raw_s": 11.768416598999465,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000118402349264,
        1.001436503157478
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.006179286867823141 cons=0.2389962674326634 wall_s=15.661 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.006179286867823141,
  "conservation_residual": 0.2389962674326634,
  "equations": [
    "x*(-2*a + b*y)",
    "y*(-2*c*x - d)"
  ],
  "wall_s_total": 15.66108524899937,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*(-2*a + b*y)",
      "r2_train": 0.9946849466622838,
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      "true_coeffs": {
        "x": 1.0,
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      "structure_ok": false,
      "wall_s": 8.024479825000526,
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      "wall_raw_s": 8.024479825000526,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49910681423781267,
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      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-2*c*x - d)",
      "r2_train": 0.9945124730401418,
      "reward": null,
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      "structure_ok": false,
      "wall_s": 7.636605423998844,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.636605423998844,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.24955919663586348,
        1.0006711007902822
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.006008249875066099 cons=0.25627510261381564 wall_s=20.571 ok=True

```json
{
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  "recoverable": true,
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  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.006008249875066099,
  "conservation_residual": 0.25627510261381564,
  "equations": [
    "-x*(2*a + b*y)",
    "y*(-c*x + d)"
  ],
  "wall_s_total": 20.570975761998852,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9955306307737268,
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        "x*y": -0.49536596260388477
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.819266089998564,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
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      "zero_eq_retries": 0
    },
    {
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      "target": "dy/dt",
      "equation": "y*(-c*x + d)",
      "r2_train": 0.9938709886477682,
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      "structure_ok": false,
      "wall_s": 12.751709672000288,
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      "wall_raw_s": 12.751709672000288,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [
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      "zero_eq": false,
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    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.16287112761427155 cons=0.39840361806762953 wall_s=16.077 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.16287112761427155,
  "conservation_residual": 0.39840361806762953,
  "equations": [
    "a*x - 2*b*y**2",
    "y*(c*x - 3*d)"
  ],
  "wall_s_total": 16.0773395060005,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.748990916670762,
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        "y^2": -0.18635898096432776,
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      "structure_ok": false,
      "wall_s": 8.146655999000359,
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      "wall_raw_s": 8.146655999000359,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.38327208510032046,
        0.09317949048216388
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(c*x - 3*d)",
      "r2_train": 0.994156622488324,
      "reward": null,
      "residual_heldout": 0.006274871613121713,
      "pred_coeffs": {
        "x*y": 0.5023338886412065
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.93068350700014,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.93068350700014,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5023338886412065,
        0.3349272717878773
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.00627006678383076 cons=0.33302683820882245 wall_s=20.034 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00627006678383076,
  "conservation_residual": 0.33302683820882245,
  "equations": [
    "x*(a - b*y)",
    "-y*(c*x + 2*d)"
  ],
  "wall_s_total": 20.03431949900005,
  "wall_s_per_eq": [
    7.588684689000729,
    12.44563480999932
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(a - b*y)",
      "r2_train": 0.9945855054475804,
      "reward": null,
      "residual_heldout": 0.007588589183371806,
      "pred_coeffs": {
        "x*y": -0.501500951711815
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.588684689000729,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.588684689000729,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0003723843600623,
        0.501500951711815
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "-y*(c*x + 2*d)",
      "r2_train": 0.9952136164172423,
      "reward": null,
      "residual_heldout": 0.004951544384289714,
      "pred_coeffs": {
        "x*y": 0.49565100012548036
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 12.44563480999932,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.44563480999932,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49565100012548036,
        0.49533520618422233
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.08740884237931594 cons=0.18676582921283186 wall_s=15.022 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08740884237931594,
  "conservation_residual": 0.18676582921283186,
  "equations": [
    "x*(3*a + b*y)",
    "x*(-c*x + d)"
  ],
  "wall_s_total": 15.022129849996418,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(3*a + b*y)",
      "r2_train": 0.9937476179919901,
      "reward": null,
      "residual_heldout": 0.005077451299333356,
      "pred_coeffs": {
        "x*y": -0.49812635575163905
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.63813736499651,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.63813736499651,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.33190157954685545,
        -0.49812635575163905
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "x*(-c*x + d)",
      "r2_train": 0.8351850552272165,
      "reward": null,
      "residual_heldout": 0.16974023345929853,
      "pred_coeffs": {
        "x^2": 0.42214460677205545,
        "x": -0.9866372668552799
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.383992484999908,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.383992484999908,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.42214460677205545,
        -0.9866372668552799
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.005143243214205917 cons=0.31012439397872493 wall_s=14.719 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005143243214205917,
  "conservation_residual": 0.31012439397872493,
  "equations": [
    "x*(a + b*y)",
    "y*(-c*x + 4*d)"
  ],
  "wall_s_total": 14.719363608001004,
  "wall_s_per_eq": [
    7.32950212400101,
    7.389861483999994
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(a + b*y)",
      "r2_train": 0.9951597620781074,
      "reward": null,
      "residual_heldout": 0.005680583237989642,
      "pred_coeffs": {
        "x*y": -0.49798727823003286
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 7.32950212400101,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.32950212400101,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9974084246660011,
        -0.49798727823003286
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + 4*d)",
      "r2_train": 0.9951082854814295,
      "reward": null,
      "residual_heldout": 0.0046059031904221925,
      "pred_coeffs": {
        "x*y": 0.49836242979222256
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.389861483999994,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.389861483999994,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49836242979222256,
        -0.2489282312570577
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `lotka_volterra` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.006726264219324142 cons=0.27311016353863965 wall_s=20.710 ok=True

```json
{
  "law": "lotka_volterra",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006726264219324142,
  "conservation_residual": 0.27311016353863965,
  "equations": [
    "x*(-a + b*y)",
    "y*(-c*x + d)"
  ],
  "wall_s_total": 20.710011823997775,
  "wall_s_per_eq": [
    12.452794277000066,
    8.257217546997708
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "x*(-a + b*y)",
      "r2_train": 0.994845276614674,
      "reward": null,
      "residual_heldout": 0.0068325840187555935,
      "pred_coeffs": {
        "x*y": -0.502643670659105
      },
      "true_coeffs": {
        "x": 1.0,
        "x*y": -0.5
      },
      "structure_ok": false,
      "wall_s": 12.452794277000066,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.452794277000066,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0009336570262686,
        -0.502643670659105
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dy/dt",
      "equation": "y*(-c*x + d)",
      "r2_train": 0.994180216872144,
      "reward": null,
      "residual_heldout": 0.006619944419892691,
      "pred_coeffs": {
        "x*y": 0.49613839490236195
      },
      "true_coeffs": {
        "y": -1.0,
        "x*y": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.257217546997708,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.257217546997708,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49613839490236195,
        -0.9935184281541409
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=1.6563315510761092e-14 cons=0.0 wall_s=31.796 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.6563315510761092e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-5.7937174) + u*(-2.127281) + u + u + u"
  ],
  "wall_s_total": 31.79645040899777,
  "wall_s_per_eq": [
    31.79645040899777
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-5.7937174) + u*(-2.127281) + u + u + u",
      "r2_train": 0.9999999999999708,
      "reward": null,
      "residual_heldout": 1.6563315510761092e-14,
      "pred_coeffs": {
        "u": -4.9209984
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 31.79645040899777,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=5.396945712355204e-14 cons=0.0 wall_s=8.469 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.396945712355204e-14,
  "conservation_residual": 0.0,
  "equations": [
    "-5.6001234*u - 1.320875*u - u - u + u + u + u + u"
  ],
  "wall_s_total": 8.468888874998811,
  "wall_s_per_eq": [
    8.468888874998811
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-5.6001234*u - 1.320875*u - u - u + u + u + u + u",
      "r2_train": 0.9999999999999483,
      "reward": null,
      "residual_heldout": 5.396945712355204e-14,
      "pred_coeffs": {
        "u": -4.9209984
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.468888874998811,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=3.1467575760049343e-14 cons=0.0 wall_s=8.633 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.1467575760049343e-14,
  "conservation_residual": 0.0,
  "equations": [
    "-u_x + u_x - (u + u + u + u*1.9209987 + 6.784826e-6) + 6.7710334e-6"
  ],
  "wall_s_total": 8.633395488002861,
  "wall_s_per_eq": [
    8.633395488002861
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_x + u_x - (u + u + u + u*1.9209987 + 6.784826e-6) + 6.7710334e-6",
      "r2_train": 0.9999999999999665,
      "reward": null,
      "residual_heldout": 3.1467575760049343e-14,
      "pred_coeffs": {
        "1": -1.3792600000000028e-08,
        "u": -4.9209987
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.633395488002861,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=3.5796554736821315e-14 cons=0.0 wall_s=8.633 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.5796554736821315e-14,
  "conservation_residual": 0.0,
  "equations": [
    "-u + (-u + u*(-0.044406) - 0.03361058*u)*3.6372342 - 1*0.1030085 - 1*(-0.103008516)"
  ],
  "wall_s_total": 8.63259810800082,
  "wall_s_per_eq": [
    8.63259810800082
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u + (-u + u*(-0.044406) - 0.03361058*u)*3.6372342 - 1*0.1030085 - 1*(-0.103008516)",
      "r2_train": 0.9999999999999712,
      "reward": null,
      "residual_heldout": 3.5796554736821315e-14,
      "pred_coeffs": {
        "1": 1.5999999991578306e-08,
        "u": -4.920998772943036
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.63259810800082,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=1.6513216335715604e-14 cons=0.0 wall_s=8.003 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.6513216335715604e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u - (-u - (u*(-8.920999) + u + u - 1.8000866e-5) - 1.8023193e-5)"
  ],
  "wall_s_total": 8.002722996003286,
  "wall_s_per_eq": [
    8.002722996003286
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u - (-u - (u*(-8.920999) + u + u - 1.8000866e-5) - 1.8023193e-5)",
      "r2_train": 0.9999999999999124,
      "reward": null,
      "residual_heldout": 1.6513216335715604e-14,
      "pred_coeffs": {
        "1": 2.2327000000001997e-08,
        "u": -4.920999
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.002722996003286,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=5.906463578474332e-14 cons=0.0 wall_s=8.212 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.906463578474332e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-5.3584113) - u - (-1.437413)*u"
  ],
  "wall_s_total": 8.211739151000074,
  "wall_s_per_eq": [
    8.211739151000074
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-5.3584113) - u - (-1.437413)*u",
      "r2_train": 0.9999999999999405,
      "reward": null,
      "residual_heldout": 5.906463578474332e-14,
      "pred_coeffs": {
        "u": -4.9209983
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.211739151000074,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=6.336462725096845e-14 cons=0.0 wall_s=7.829 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.336462725096845e-14,
  "conservation_residual": 0.0,
  "equations": [
    "-3.8052638*u - 1.1157347*u - u + u"
  ],
  "wall_s_total": 7.828782284999761,
  "wall_s_per_eq": [
    7.828782284999761
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-3.8052638*u - 1.1157347*u - u + u",
      "r2_train": 0.9999999999999843,
      "reward": null,
      "residual_heldout": 6.336462725096845e-14,
      "pred_coeffs": {
        "u": -4.9209985
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 7.828782284999761,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=9.415135462959364e-15 cons=0.0 wall_s=8.439 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.415135462959364e-15,
  "conservation_residual": 0.0,
  "equations": [
    "(-u + u + u - 0.04116278 - 1*(-0.04116278))*(-4.9209986)"
  ],
  "wall_s_total": 8.438638767001976,
  "wall_s_per_eq": [
    8.438638767001976
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(-u + u + u - 0.04116278 - 1*(-0.04116278))*(-4.9209986)",
      "r2_train": 0.9999999999999684,
      "reward": null,
      "residual_heldout": 9.415135462959364e-15,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.438638767001976,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=3.416521629560769e-14 cons=0.0 wall_s=8.458 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.416521629560769e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-3.8334475) + u*(-1.087551)"
  ],
  "wall_s_total": 8.458264646000316,
  "wall_s_per_eq": [
    8.458264646000316
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-3.8334475) + u*(-1.087551)",
      "r2_train": 0.9999999999999728,
      "reward": null,
      "residual_heldout": 3.416521629560769e-14,
      "pred_coeffs": {
        "u": -4.9209985
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.458264646000316,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=1.7183167900190352e-14 cons=0.0 wall_s=8.666 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7183167900190352e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-0.9999999)*(u*4.6259834e-7 - 1*(-4.920999))"
  ],
  "wall_s_total": 8.666400882000744,
  "wall_s_per_eq": [
    8.666400882000744
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-0.9999999)*(u*4.6259834e-7 - 1*(-4.920999))",
      "r2_train": 0.9999999999999721,
      "reward": null,
      "residual_heldout": 1.7183167900190352e-14,
      "pred_coeffs": {
        "u^2": -4.62598293740166e-07,
        "u": -4.920998507900101
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.666400882000744,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=2.2867915741347675e-14 cons=0.0 wall_s=8.414 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.2867915741347675e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-5.423627) + u*0.5026283"
  ],
  "wall_s_total": 8.414165135000076,
  "wall_s_per_eq": [
    8.414165135000076
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-5.423627) + u*0.5026283",
      "r2_train": 0.9999999999999603,
      "reward": null,
      "residual_heldout": 2.2867915741347675e-14,
      "pred_coeffs": {
        "u": -4.9209987
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.414165135000076,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=1.3010100464084943e-14 cons=0.0 wall_s=8.764 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.3010100464084943e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-3.9353495) - u - (-0.0143506415)*u"
  ],
  "wall_s_total": 8.7643594580004,
  "wall_s_per_eq": [
    8.7643594580004
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-3.9353495) - u - (-0.0143506415)*u",
      "r2_train": 0.9999999999999432,
      "reward": null,
      "residual_heldout": 1.3010100464084943e-14,
      "pred_coeffs": {
        "u": -4.9209988585
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.7643594580004,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=2.9024311052206195e-14 cons=0.0 wall_s=8.552 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.9024311052206195e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(u*1.8004262e-6 - 4.9209995)"
  ],
  "wall_s_total": 8.552499535002426,
  "wall_s_per_eq": [
    8.552499535002426
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(u*1.8004262e-6 - 4.9209995)",
      "r2_train": 0.9999999999999624,
      "reward": null,
      "residual_heldout": 2.9024311052206195e-14,
      "pred_coeffs": {
        "u^2": 1.8004262e-06,
        "u": -4.9209995
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.552499535002426,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=3.908320448919506e-14 cons=0.0 wall_s=8.672 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.908320448919506e-14,
  "conservation_residual": 0.0,
  "equations": [
    "-8.05275*u + u*0.73234636 + u*2.3994048"
  ],
  "wall_s_total": 8.671757239000726,
  "wall_s_per_eq": [
    8.671757239000726
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-8.05275*u + u*0.73234636 + u*2.3994048",
      "r2_train": 0.9999999999999508,
      "reward": null,
      "residual_heldout": 3.908320448919506e-14,
      "pred_coeffs": {
        "u": -4.920998839999999
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.671757239000726,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=5.724433769688104e-14 cons=0.0 wall_s=8.139 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.724433769688104e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.8417645) + u_xx*0.0080509875"
  ],
  "wall_s_total": 8.139272677999543,
  "wall_s_per_eq": [
    8.139272677999543
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.8417645) + u_xx*0.0080509875",
      "r2_train": 0.9999999999999792,
      "reward": null,
      "residual_heldout": 5.724433769688104e-14,
      "pred_coeffs": {
        "u_xx": 0.0080509875,
        "u": -4.8417645
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.139272677999543,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=1.5591933130223882e-14 cons=0.0 wall_s=8.895 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.5591933130223882e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.894563188001484,
  "wall_s_per_eq": [
    8.894563188001484
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999616,
      "reward": null,
      "residual_heldout": 1.5591933130223882e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.894563188001484,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=2.5006722474193935e-14 cons=0.0 wall_s=8.856 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.5006722474193935e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.856135945003189,
  "wall_s_per_eq": [
    8.856135945003189
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999607,
      "reward": null,
      "residual_heldout": 2.5006722474193935e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.856135945003189,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=6.34977863038215e-14 cons=0.0 wall_s=8.561 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.34977863038215e-14,
  "conservation_residual": 0.0,
  "equations": [
    "(-u_x + u_x - (-(-u_x + u_x - (-u - 1.5394425e-8)) - 1.5394425e-8))*(-4.920998)"
  ],
  "wall_s_total": 8.561054768997565,
  "wall_s_per_eq": [
    8.561054768997565
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(-u_x + u_x - (-(-u_x + u_x - (-u - 1.5394425e-8)) - 1.5394425e-8))*(-4.920998)",
      "r2_train": 0.9999999999999422,
      "reward": null,
      "residual_heldout": 6.34977863038215e-14,
      "pred_coeffs": {
        "1": -1.5151186927229998e-07,
        "u": -4.920998
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.561054768997565,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=1.1098830942855536e-13 cons=0.0 wall_s=9.114 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.1098830942855536e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209995) + u*u*1.6139591e-6"
  ],
  "wall_s_total": 9.114399991001847,
  "wall_s_per_eq": [
    9.114399991001847
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209995) + u*u*1.6139591e-6",
      "r2_train": 0.9999999999999751,
      "reward": null,
      "residual_heldout": 1.1098830942855536e-13,
      "pred_coeffs": {
        "u^2": 1.6139591e-06,
        "u": -4.9209995
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.114399991001847,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=3.604622823686471e-14 cons=0.0 wall_s=8.367 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.604622823686471e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-5.9209986) + u - 3.7383856e-5 + 3.7383856e-5"
  ],
  "wall_s_total": 8.36731489199883,
  "wall_s_per_eq": [
    8.36731489199883
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-5.9209986) + u - 3.7383856e-5 + 3.7383856e-5",
      "r2_train": 0.9999999999999658,
      "reward": null,
      "residual_heldout": 3.604622823686471e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.36731489199883,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=3.500926527572337e-13 cons=0.0 wall_s=9.362 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.500926527572337e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.361903491000703,
  "wall_s_per_eq": [
    9.361903491000703
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.999999999999474,
      "reward": null,
      "residual_heldout": 3.500926527572337e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227318832513
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.361903491000703,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.361903491000703,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227318832513
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=7.548027392692769e-13 cons=0.0 wall_s=7.945 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.548027392692769e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.945274347999657,
  "wall_s_per_eq": [
    7.945274347999657
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.99999999999931,
      "reward": null,
      "residual_heldout": 7.548027392692769e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227541281237
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.945274347999657,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.945274347999657,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227541281237
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=2.9151638916351927e-13 cons=0.0 wall_s=8.133 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.9151638916351927e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.132514589000493,
  "wall_s_per_eq": [
    8.132514589000493
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994869,
      "reward": null,
      "residual_heldout": 2.9151638916351927e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227650727327
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.132514589000493,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.132514589000493,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227650727327
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=6.509860090269372e-13 cons=0.0 wall_s=8.210 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.509860090269372e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.210120509000262,
  "wall_s_per_eq": [
    8.210120509000262
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999990076,
      "reward": null,
      "residual_heldout": 6.509860090269372e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227110603047
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.210120509000262,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.210120509000262,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227110603047
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=2.0432774471369996e-13 cons=0.0 wall_s=7.768 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.0432774471369996e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.767671705001703,
  "wall_s_per_eq": [
    7.767671705001703
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994286,
      "reward": null,
      "residual_heldout": 2.0432774471369996e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227959941567
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.767671705001703,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.767671705001703,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227959941567
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=1.9871312225627677e-13 cons=0.0 wall_s=7.755 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.9871312225627677e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.754575704999297,
  "wall_s_per_eq": [
    7.754575704999297
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994725,
      "reward": null,
      "residual_heldout": 1.9871312225627677e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228967795786
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.754575704999297,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.754575704999297,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228967795786
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=3.070946359179132e-13 cons=0.0 wall_s=8.737 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.070946359179132e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.736968205001176,
  "wall_s_per_eq": [
    8.736968205001176
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999996438,
      "reward": null,
      "residual_heldout": 3.070946359179132e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227862235076
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.736968205001176,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.736968205001176,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227862235076
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=3.64315776061211e-13 cons=0.0 wall_s=8.141 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.64315776061211e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.140830919001019,
  "wall_s_per_eq": [
    8.140830919001019
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994457,
      "reward": null,
      "residual_heldout": 3.64315776061211e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228258894227
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.140830919001019,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.140830919001019,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228258894227
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=6.6975494264432e-13 cons=0.0 wall_s=9.331 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.6975494264432e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.33148856600019,
  "wall_s_per_eq": [
    9.33148856600019
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999995994,
      "reward": null,
      "residual_heldout": 6.6975494264432e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228073166307
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.33148856600019,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.33148856600019,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228073166307
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=3.982613195758543e-13 cons=0.0 wall_s=9.563 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.982613195758543e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.563132776998827,
  "wall_s_per_eq": [
    9.563132776998827
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999996594,
      "reward": null,
      "residual_heldout": 3.982613195758543e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228946834954
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.563132776998827,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.563132776998827,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228946834954
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=1.9256256950943893e-12 cons=0.0 wall_s=8.432 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.9256256950943893e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.432499307000398,
  "wall_s_per_eq": [
    8.432499307000398
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994603,
      "reward": null,
      "residual_heldout": 1.9256256950943893e-12,
      "pred_coeffs": {
        "u_xx": 0.5000228246336904
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.432499307000398,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.432499307000398,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228246336904
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=8.322113203934198e-13 cons=0.0 wall_s=7.808 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 8.322113203934198e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.808442818000913,
  "wall_s_per_eq": [
    7.808442818000913
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999993417,
      "reward": null,
      "residual_heldout": 8.322113203934198e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228262516262
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.808442818000913,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.808442818000913,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228262516262
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=2.437247227378269e-13 cons=0.0 wall_s=8.409 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.437247227378269e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.409438919999957,
  "wall_s_per_eq": [
    8.409438919999957
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999995133,
      "reward": null,
      "residual_heldout": 2.437247227378269e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228484653437
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.409438919999957,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.409438919999957,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228484653437
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=6.523618675976193e-13 cons=0.0 wall_s=8.917 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.523618675976193e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.917369312999654,
  "wall_s_per_eq": [
    8.917369312999654
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999995519,
      "reward": null,
      "residual_heldout": 6.523618675976193e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228606453139
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.917369312999654,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.917369312999654,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228606453139
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=5.951766636436649e-13 cons=0.0 wall_s=8.203 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.951766636436649e-13,
  "conservation_residual": 0.0,
  "equations": [
    "-D*uxx"
  ],
  "wall_s_total": 8.203208171998995,
  "wall_s_per_eq": [
    8.203208171998995
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-D*uxx",
      "r2_train": 0.9999999999995042,
      "reward": null,
      "residual_heldout": 5.951766636436649e-13,
      "pred_coeffs": {
        "u_xx": 0.500022769674767
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.203208171998995,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.203208171998995,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.500022769674767
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=4.503745057687621e-13 cons=0.0 wall_s=8.461 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.503745057687621e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.46102959700147,
  "wall_s_per_eq": [
    8.46102959700147
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999990754,
      "reward": null,
      "residual_heldout": 4.503745057687621e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227608098681
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.46102959700147,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.46102959700147,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227608098681
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=3.9307021292358355e-13 cons=0.0 wall_s=8.026 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.9307021292358355e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.026360520001617,
  "wall_s_per_eq": [
    8.026360520001617
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999995731,
      "reward": null,
      "residual_heldout": 3.9307021292358355e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228107945405
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.026360520001617,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.026360520001617,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228107945405
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=9.325212483246726e-13 cons=0.0 wall_s=8.169 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 9.325212483246726e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.16920799700165,
  "wall_s_per_eq": [
    8.16920799700165
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.999999999999055,
      "reward": null,
      "residual_heldout": 9.325212483246726e-13,
      "pred_coeffs": {
        "u_xx": 0.50002280806108
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.16920799700165,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.16920799700165,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.50002280806108
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=1.4587920034479938e-12 cons=0.0 wall_s=7.745 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.4587920034479938e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.744714657001168,
  "wall_s_per_eq": [
    7.744714657001168
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999998107,
      "reward": null,
      "residual_heldout": 1.4587920034479938e-12,
      "pred_coeffs": {
        "u_xx": 0.5000228024911993
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.744714657001168,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.744714657001168,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228024911993
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=2.4017964745162727e-13 cons=0.0 wall_s=8.652 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.4017964745162727e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.652302049002174,
  "wall_s_per_eq": [
    8.652302049002174
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.999999999999565,
      "reward": null,
      "residual_heldout": 2.4017964745162727e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228931802861
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.652302049002174,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.652302049002174,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228931802861
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=1.7742668783916418e-14 cons=0.0 wall_s=9.749 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7742668783916418e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 9.749020403000031,
  "wall_s_per_eq": [
    9.749020403000031
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999654,
      "reward": null,
      "residual_heldout": 1.7742668783916418e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.749020403000031,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=2.3401059659180445e-14 cons=0.0 wall_s=8.893 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.3401059659180445e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.892919975998666,
  "wall_s_per_eq": [
    8.892919975998666
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.999999999999978,
      "reward": null,
      "residual_heldout": 2.3401059659180445e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.892919975998666,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=2.8104682585297644e-14 cons=0.0 wall_s=9.501 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.8104682585297644e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-u + u + (-u + u_x)*u_x*1.4840053e-7 - 4.920999)"
  ],
  "wall_s_total": 9.50108282400106,
  "wall_s_per_eq": [
    9.50108282400106
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-u + u + (-u + u_x)*u_x*1.4840053e-7 - 4.920999)",
      "r2_train": 0.9999999999999786,
      "reward": null,
      "residual_heldout": 2.8104682585297644e-14,
      "pred_coeffs": {
        "1": -1.69441598536719e-08,
        "u": -4.8888868206428,
        "u^2": -2.2139933550096827e-07,
        "u^3": 3.126686460776971e-08,
        "u_x": -1.8001700538662157e-08,
        "u_xx": 0.0032628855073407485
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.50108282400106,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=3.1699427840503914e-14 cons=0.0 wall_s=8.238 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.1699427840503914e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-6.3758645) - (-1.454866)*u"
  ],
  "wall_s_total": 8.237943574000383,
  "wall_s_per_eq": [
    8.237943574000383
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-6.3758645) - (-1.454866)*u",
      "r2_train": 0.9999999999999667,
      "reward": null,
      "residual_heldout": 3.1699427840503914e-14,
      "pred_coeffs": {
        "u": -4.9209985
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.237943574000383,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=2.8967540339482494e-14 cons=0.0 wall_s=8.294 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.8967540339482494e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-5.2131586) + u*0.29215997"
  ],
  "wall_s_total": 8.29407611300121,
  "wall_s_per_eq": [
    8.29407611300121
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-5.2131586) + u*0.29215997",
      "r2_train": 0.9999999999999541,
      "reward": null,
      "residual_heldout": 2.8967540339482494e-14,
      "pred_coeffs": {
        "u": -4.92099863
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.29407611300121,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=3.2907569360908204e-14 cons=0.0 wall_s=9.297 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.2907569360908204e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.074958) + u*(-0.8460407)"
  ],
  "wall_s_total": 9.296667637998326,
  "wall_s_per_eq": [
    9.296667637998326
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.074958) + u*(-0.8460407)",
      "r2_train": 0.9999999999999654,
      "reward": null,
      "residual_heldout": 3.2907569360908204e-14,
      "pred_coeffs": {
        "u": -4.920998699999999
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.296667637998326,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=4.5654965706313436e-14 cons=0.0 wall_s=9.586 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.5654965706313436e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920998)"
  ],
  "wall_s_total": 9.585718928999995,
  "wall_s_per_eq": [
    9.585718928999995
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920998)",
      "r2_train": 0.9999999999999405,
      "reward": null,
      "residual_heldout": 4.5654965706313436e-14,
      "pred_coeffs": {
        "u": -4.920998
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.585718928999995,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=5.39498304146572e-14 cons=0.0 wall_s=9.024 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.39498304146572e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 9.023564248000184,
  "wall_s_per_eq": [
    9.023564248000184
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999557,
      "reward": null,
      "residual_heldout": 5.39498304146572e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.023564248000184,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=3.168921130191529e-14 cons=0.0 wall_s=8.893 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.168921130191529e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.893422066001222,
  "wall_s_per_eq": [
    8.893422066001222
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999689,
      "reward": null,
      "residual_heldout": 3.168921130191529e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.893422066001222,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=2.5878461579366133e-14 cons=0.0 wall_s=9.160 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.5878461579366133e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 9.159527359999629,
  "wall_s_per_eq": [
    9.159527359999629
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999657,
      "reward": null,
      "residual_heldout": 2.5878461579366133e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.159527359999629,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=2.099066068325104e-14 cons=0.0 wall_s=8.482 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.099066068325104e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-5.9209986) - (-1)*u"
  ],
  "wall_s_total": 8.481941832997109,
  "wall_s_per_eq": [
    8.481941832997109
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-5.9209986) - (-1)*u",
      "r2_train": 0.9999999999999625,
      "reward": null,
      "residual_heldout": 2.099066068325104e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.481941832997109,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=3.016526510050153e-14 cons=0.0 wall_s=8.173 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.016526510050153e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.172801364002225,
  "wall_s_per_eq": [
    8.172801364002225
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999658,
      "reward": null,
      "residual_heldout": 3.016526510050153e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.172801364002225,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=5.020251185829621e-14 cons=0.0 wall_s=8.162 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.020251185829621e-14,
  "conservation_residual": 0.0,
  "equations": [
    "(-(-0.018359846)*u + u)*(u*u_x*2.6824185e-7 - 4.8322787)"
  ],
  "wall_s_total": 8.162073485997098,
  "wall_s_per_eq": [
    8.162073485997098
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(-(-0.018359846)*u + u)*(u*u_x*2.6824185e-7 - 4.8322787)",
      "r2_train": 0.9999999999999789,
      "reward": null,
      "residual_heldout": 5.020251185829621e-14,
      "pred_coeffs": {
        "u": -4.92099859276108
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.162073485997098,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=1.599477098328981e-14 cons=0.0 wall_s=8.571 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.599477098328981e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.570829652999237,
  "wall_s_per_eq": [
    8.570829652999237
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999728,
      "reward": null,
      "residual_heldout": 1.599477098328981e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.570829652999237,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=2.0977142168790983e-14 cons=0.0 wall_s=8.278 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.0977142168790983e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.278371784999763,
  "wall_s_per_eq": [
    8.278371784999763
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999665,
      "reward": null,
      "residual_heldout": 2.0977142168790983e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.278371784999763,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=1.8566006893885438e-14 cons=0.0 wall_s=8.818 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.8566006893885438e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.818096798000624,
  "wall_s_per_eq": [
    8.818096798000624
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999747,
      "reward": null,
      "residual_heldout": 1.8566006893885438e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.818096798000624,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=3.6050769586701113e-14 cons=0.0 wall_s=8.552 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.6050769586701113e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.551566154001193,
  "wall_s_per_eq": [
    8.551566154001193
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999478,
      "reward": null,
      "residual_heldout": 3.6050769586701113e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.551566154001193,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=2.8631740581505064e-14 cons=0.0 wall_s=8.545 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.8631740581505064e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.5446386170006,
  "wall_s_per_eq": [
    8.5446386170006
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999657,
      "reward": null,
      "residual_heldout": 2.8631740581505064e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.5446386170006,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=1.346408612745168e-14 cons=0.0 wall_s=8.509 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.346408612745168e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9209986)"
  ],
  "wall_s_total": 8.508580009998695,
  "wall_s_per_eq": [
    8.508580009998695
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9209986)",
      "r2_train": 0.9999999999999671,
      "reward": null,
      "residual_heldout": 1.346408612745168e-14,
      "pred_coeffs": {
        "u": -4.9209986
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.508580009998695,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=2.861204248109292e-14 cons=0.0 wall_s=8.791 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.861204248109292e-14,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.691248) + u*(-0.2297503) - 1.0855361e-7"
  ],
  "wall_s_total": 8.790700998997636,
  "wall_s_per_eq": [
    8.790700998997636
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.691248) + u*(-0.2297503) - 1.0855361e-7",
      "r2_train": 0.999999999999974,
      "reward": null,
      "residual_heldout": 2.861204248109292e-14,
      "pred_coeffs": {
        "1": -1.0855361e-07,
        "u": -4.9209983
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.790700998997636,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=7.284009492522709e-13 cons=0.0 wall_s=9.031 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.284009492522709e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.030654071000754,
  "wall_s_per_eq": [
    9.030654071000754
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.999999999999572,
      "reward": null,
      "residual_heldout": 7.284009492522709e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227347435071
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.030654071000754,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.030654071000754,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227347435071
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=7.42131532981908e-13 cons=0.0 wall_s=9.046 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.42131532981908e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.045721970000159,
  "wall_s_per_eq": [
    9.045721970000159
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999996811,
      "reward": null,
      "residual_heldout": 7.42131532981908e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227054118194
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.045721970000159,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.045721970000159,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227054118194
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=4.667442759387803e-13 cons=0.0 wall_s=7.340 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.667442759387803e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.340063581999857,
  "wall_s_per_eq": [
    7.340063581999857
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999996407,
      "reward": null,
      "residual_heldout": 4.667442759387803e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227992230722
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.340063581999857,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.340063581999857,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227992230722
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=6.328209462757217e-13 cons=0.0 wall_s=8.488 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.328209462757217e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.488279604000127,
  "wall_s_per_eq": [
    8.488279604000127
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999996144,
      "reward": null,
      "residual_heldout": 6.328209462757217e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228001292968
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.488279604000127,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.488279604000127,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228001292968
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=5.187477256510387e-13 cons=0.0 wall_s=8.570 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.187477256510387e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.570290816001943,
  "wall_s_per_eq": [
    8.570290816001943
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999992989,
      "reward": null,
      "residual_heldout": 5.187477256510387e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228471491476
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.570290816001943,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.570290816001943,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228471491476
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=6.415611328773879e-13 cons=0.0 wall_s=8.525 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.415611328773879e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.525202525001077,
  "wall_s_per_eq": [
    8.525202525001077
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999997107,
      "reward": null,
      "residual_heldout": 6.415611328773879e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228178685248
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.525202525001077,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.525202525001077,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228178685248
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=4.701865779976822e-13 cons=0.0 wall_s=7.570 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.701865779976822e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.569687964001787,
  "wall_s_per_eq": [
    7.569687964001787
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994195,
      "reward": null,
      "residual_heldout": 4.701865779976822e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228373983292
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.569687964001787,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.569687964001787,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228373983292
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=6.757972814346334e-13 cons=0.0 wall_s=8.379 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.757972814346334e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.379325355999754,
  "wall_s_per_eq": [
    8.379325355999754
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.999999999999152,
      "reward": null,
      "residual_heldout": 6.757972814346334e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227646688314
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.379325355999754,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.379325355999754,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227646688314
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=2.5744452152558445e-13 cons=0.0 wall_s=8.565 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.5744452152558445e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.565300579000905,
  "wall_s_per_eq": [
    8.565300579000905
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999996414,
      "reward": null,
      "residual_heldout": 2.5744452152558445e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227345807474
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.565300579000905,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.565300579000905,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227345807474
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=2.9888034699783e-13 cons=0.0 wall_s=7.868 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.9888034699783e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.868499781998253,
  "wall_s_per_eq": [
    7.868499781998253
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999996536,
      "reward": null,
      "residual_heldout": 2.9888034699783e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227916586973
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.868499781998253,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.868499781998253,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227916586973
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=2.51268653849458e-13 cons=0.0 wall_s=9.043 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.51268653849458e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.042746794999402,
  "wall_s_per_eq": [
    9.042746794999402
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999992871,
      "reward": null,
      "residual_heldout": 2.51268653849458e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227886890546
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.042746794999402,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.042746794999402,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227886890546
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=2.7392376402412487e-13 cons=0.0 wall_s=7.506 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.7392376402412487e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.50627322100263,
  "wall_s_per_eq": [
    7.50627322100263
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994826,
      "reward": null,
      "residual_heldout": 2.7392376402412487e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228278764458
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.50627322100263,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.50627322100263,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228278764458
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=3.883179138148162e-13 cons=0.0 wall_s=8.431 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.883179138148162e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.431051785999443,
  "wall_s_per_eq": [
    8.431051785999443
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994109,
      "reward": null,
      "residual_heldout": 3.883179138148162e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227490655534
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.431051785999443,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.431051785999443,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227490655534
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=7.915965393514142e-14 cons=0.0 wall_s=7.308 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.915965393514142e-14,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.308156398001302,
  "wall_s_per_eq": [
    7.308156398001302
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999993179,
      "reward": null,
      "residual_heldout": 7.915965393514142e-14,
      "pred_coeffs": {
        "u_xx": 0.5000227861378697
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.308156398001302,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.308156398001302,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227861378697
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=5.340329819069829e-13 cons=0.0 wall_s=10.171 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.340329819069829e-13,
  "conservation_residual": 0.0,
  "equations": [
    "-D*uxx"
  ],
  "wall_s_total": 10.171479074000672,
  "wall_s_per_eq": [
    10.171479074000672
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-D*uxx",
      "r2_train": 0.9999999999994356,
      "reward": null,
      "residual_heldout": 5.340329819069829e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228383173564
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.171479074000672,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.171479074000672,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000228383173564
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=4.5209172351783424e-13 cons=0.0 wall_s=8.820 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.5209172351783424e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.81972041699919,
  "wall_s_per_eq": [
    8.81972041699919
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994249,
      "reward": null,
      "residual_heldout": 4.5209172351783424e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228432274212
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.81972041699919,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.81972041699919,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228432274212
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=6.205005234317637e-13 cons=0.0 wall_s=7.801 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.205005234317637e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.801100874999975,
  "wall_s_per_eq": [
    7.801100874999975
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999995256,
      "reward": null,
      "residual_heldout": 6.205005234317637e-13,
      "pred_coeffs": {
        "u_xx": 0.5000227730559561
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.801100874999975,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.801100874999975,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000227730559561
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=8.987843125514002e-13 cons=0.0 wall_s=9.447 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 8.987843125514002e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.447226364998642,
  "wall_s_per_eq": [
    9.447226364998642
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999993276,
      "reward": null,
      "residual_heldout": 8.987843125514002e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228092223465
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.447226364998642,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.447226364998642,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228092223465
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=5.934637126264302e-13 cons=0.0 wall_s=7.900 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.934637126264302e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.899549813002523,
  "wall_s_per_eq": [
    7.899549813002523
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999995107,
      "reward": null,
      "residual_heldout": 5.934637126264302e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228182754882
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.899549813002523,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.899549813002523,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228182754882
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=3.2137771865791273e-13 cons=0.0 wall_s=8.904 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.2137771865791273e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.903735881998728,
  "wall_s_per_eq": [
    8.903735881998728
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999994287,
      "reward": null,
      "residual_heldout": 3.2137771865791273e-13,
      "pred_coeffs": {
        "u_xx": 0.5000228080227791
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.903735881998728,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.903735881998728,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000228080227791
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=7.2201211324736e-13 cons=0.0 wall_s=9.537 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.2201211324736e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.536925430998963,
  "wall_s_per_eq": [
    9.536925430998963
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999990733,
      "reward": null,
      "residual_heldout": 7.2201211324736e-13,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.536925430998963,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=1.0002337780570348e-12 cons=0.0 wall_s=9.469 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.0002337780570348e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9207935)"
  ],
  "wall_s_total": 9.46942565199788,
  "wall_s_per_eq": [
    9.46942565199788
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9207935)",
      "r2_train": 0.9999999999992928,
      "reward": null,
      "residual_heldout": 1.0002337780570348e-12,
      "pred_coeffs": {
        "u": -4.9207935
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.46942565199788,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=1.4099828997592633e-12 cons=0.0 wall_s=8.893 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.4099828997592633e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 8.892594539000129,
  "wall_s_per_eq": [
    8.892594539000129
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999992223,
      "reward": null,
      "residual_heldout": 1.4099828997592633e-12,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.892594539000129,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=1.1122847401865771e-12 cons=0.0 wall_s=9.419 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.1122847401865771e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.419450040000811,
  "wall_s_per_eq": [
    9.419450040000811
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999992119,
      "reward": null,
      "residual_heldout": 1.1122847401865771e-12,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.419450040000811,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=7.063564971529821e-13 cons=0.0 wall_s=9.908 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.063564971529821e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9207935)"
  ],
  "wall_s_total": 9.908130926000013,
  "wall_s_per_eq": [
    9.908130926000013
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9207935)",
      "r2_train": 0.9999999999988378,
      "reward": null,
      "residual_heldout": 7.063564971529821e-13,
      "pred_coeffs": {
        "u": -4.9207935
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.908130926000013,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=1.022616264725048e-12 cons=0.0 wall_s=9.056 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.022616264725048e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9207945)"
  ],
  "wall_s_total": 9.05632604800121,
  "wall_s_per_eq": [
    9.05632604800121
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9207945)",
      "r2_train": 0.9999999999989683,
      "reward": null,
      "residual_heldout": 1.022616264725048e-12,
      "pred_coeffs": {
        "u": -4.9207945
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.05632604800121,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=1.107059437275947e-12 cons=0.0 wall_s=8.805 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.107059437275947e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9207945)"
  ],
  "wall_s_total": 8.804983085999993,
  "wall_s_per_eq": [
    8.804983085999993
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9207945)",
      "r2_train": 0.9999999999989675,
      "reward": null,
      "residual_heldout": 1.107059437275947e-12,
      "pred_coeffs": {
        "u": -4.9207945
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.804983085999993,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=9.495596849943143e-13 cons=0.0 wall_s=9.048 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.495596849943143e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9207935)"
  ],
  "wall_s_total": 9.048298179000994,
  "wall_s_per_eq": [
    9.048298179000994
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9207935)",
      "r2_train": 0.9999999999987523,
      "reward": null,
      "residual_heldout": 9.495596849943143e-13,
      "pred_coeffs": {
        "u": -4.9207935
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.048298179000994,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=1.119314331069334e-12 cons=0.0 wall_s=9.250 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.119314331069334e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.250172238000232,
  "wall_s_per_eq": [
    9.250172238000232
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999991245,
      "reward": null,
      "residual_heldout": 1.119314331069334e-12,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.250172238000232,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=5.927361906403207e-13 cons=0.0 wall_s=9.438 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.927361906403207e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.43785725500129,
  "wall_s_per_eq": [
    9.43785725500129
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999989342,
      "reward": null,
      "residual_heldout": 5.927361906403207e-13,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.43785725500129,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=1.1556088662732592e-12 cons=0.0 wall_s=9.526 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.1556088662732592e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.526197153001704,
  "wall_s_per_eq": [
    9.526197153001704
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999991193,
      "reward": null,
      "residual_heldout": 1.1556088662732592e-12,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.526197153001704,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=1.066175164083158e-12 cons=0.0 wall_s=9.730 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.066175164083158e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9207945)"
  ],
  "wall_s_total": 9.730476269000064,
  "wall_s_per_eq": [
    9.730476269000064
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9207945)",
      "r2_train": 0.9999999999990419,
      "reward": null,
      "residual_heldout": 1.066175164083158e-12,
      "pred_coeffs": {
        "u": -4.9207945
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.730476269000064,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=7.775862709538878e-13 cons=0.0 wall_s=9.428 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.775862709538878e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.428118739000638,
  "wall_s_per_eq": [
    9.428118739000638
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999990659,
      "reward": null,
      "residual_heldout": 7.775862709538878e-13,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.428118739000638,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=1.1605947744965638e-12 cons=0.0 wall_s=8.955 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.1605947744965638e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9207945)"
  ],
  "wall_s_total": 8.95512459100064,
  "wall_s_per_eq": [
    8.95512459100064
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9207945)",
      "r2_train": 0.9999999999989575,
      "reward": null,
      "residual_heldout": 1.1605947744965638e-12,
      "pred_coeffs": {
        "u": -4.9207945
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.95512459100064,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=1.0266293078946671e-12 cons=0.0 wall_s=9.027 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.0266293078946671e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.027130599002703,
  "wall_s_per_eq": [
    9.027130599002703
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999990229,
      "reward": null,
      "residual_heldout": 1.0266293078946671e-12,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.027130599002703,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=7.597948836289656e-13 cons=0.0 wall_s=9.501 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.597948836289656e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.501401880999765,
  "wall_s_per_eq": [
    9.501401880999765
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999987707,
      "reward": null,
      "residual_heldout": 7.597948836289656e-13,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.501401880999765,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=7.243136750134819e-13 cons=0.0 wall_s=9.960 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.243136750134819e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 9.959942321002018,
  "wall_s_per_eq": [
    9.959942321002018
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999991607,
      "reward": null,
      "residual_heldout": 7.243136750134819e-13,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.959942321002018,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=1.0957377913666823e-12 cons=0.0 wall_s=8.845 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.0957377913666823e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 8.845295285002067,
  "wall_s_per_eq": [
    8.845295285002067
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.999999999999168,
      "reward": null,
      "residual_heldout": 1.0957377913666823e-12,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.845295285002067,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=9.737347163903841e-13 cons=0.0 wall_s=8.677 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 9.737347163903841e-13,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920794)"
  ],
  "wall_s_total": 8.676716607002163,
  "wall_s_per_eq": [
    8.676716607002163
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920794)",
      "r2_train": 0.9999999999987975,
      "reward": null,
      "residual_heldout": 9.737347163903841e-13,
      "pred_coeffs": {
        "u": -4.920794
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.676716607002163,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=1.1363293014853095e-12 cons=0.0 wall_s=9.225 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.1363293014853095e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9207945)"
  ],
  "wall_s_total": 9.225375575999351,
  "wall_s_per_eq": [
    9.225375575999351
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9207945)",
      "r2_train": 0.9999999999991768,
      "reward": null,
      "residual_heldout": 1.1363293014853095e-12,
      "pred_coeffs": {
        "u": -4.9207945
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.225375575999351,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=1.0772555687329372e-12 cons=0.0 wall_s=7.640 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.0772555687329372e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.640193875999103,
  "wall_s_per_eq": [
    7.640193875999103
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999988356,
      "reward": null,
      "residual_heldout": 1.0772555687329372e-12,
      "pred_coeffs": {
        "u_xx": 0.5000019892552942
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.640193875999103,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.640193875999103,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000019892552942
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=1.4441316247518028e-12 cons=0.0 wall_s=9.471 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.4441316247518028e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.470677882000018,
  "wall_s_per_eq": [
    9.470677882000018
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999989839,
      "reward": null,
      "residual_heldout": 1.4441316247518028e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020011746923
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.470677882000018,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.470677882000018,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020011746923
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=2.1291713092301052e-12 cons=0.0 wall_s=7.501 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.1291713092301052e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.501258248998056,
  "wall_s_per_eq": [
    7.501258248998056
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999989974,
      "reward": null,
      "residual_heldout": 2.1291713092301052e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020250823148
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.501258248998056,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.501258248998056,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020250823148
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=1.4578244531512018e-12 cons=0.0 wall_s=8.966 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.4578244531512018e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.965932335999241,
  "wall_s_per_eq": [
    8.965932335999241
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999989059,
      "reward": null,
      "residual_heldout": 1.4578244531512018e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020328607316
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.965932335999241,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.965932335999241,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020328607316
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=1.2014613612256562e-12 cons=0.0 wall_s=7.636 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.2014613612256562e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.6356540199994924,
  "wall_s_per_eq": [
    7.6356540199994924
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.999999999998205,
      "reward": null,
      "residual_heldout": 1.2014613612256562e-12,
      "pred_coeffs": {
        "u_xx": 0.5000019722016542
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.6356540199994924,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6356540199994924,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000019722016542
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=1.571986449569727e-12 cons=0.0 wall_s=7.642 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.571986449569727e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.641808350999781,
  "wall_s_per_eq": [
    7.641808350999781
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999985453,
      "reward": null,
      "residual_heldout": 1.571986449569727e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020614182242
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.641808350999781,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.641808350999781,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020614182242
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=1.3086791460492593e-12 cons=0.0 wall_s=10.131 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.3086791460492593e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 10.131107932000305,
  "wall_s_per_eq": [
    10.131107932000305
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999985545,
      "reward": null,
      "residual_heldout": 1.3086791460492593e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020018818703
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.131107932000305,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.131107932000305,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020018818703
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=1.5696778671821636e-12 cons=0.0 wall_s=7.694 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.5696778671821636e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.693980071002443,
  "wall_s_per_eq": [
    7.693980071002443
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999983553,
      "reward": null,
      "residual_heldout": 1.5696778671821636e-12,
      "pred_coeffs": {
        "u_xx": 0.500001985703386
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.693980071002443,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.693980071002443,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.500001985703386
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=1.8937364503951843e-12 cons=0.0 wall_s=9.882 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.8937364503951843e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.882114735999494,
  "wall_s_per_eq": [
    9.882114735999494
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999987598,
      "reward": null,
      "residual_heldout": 1.8937364503951843e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020214434726
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.882114735999494,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.882114735999494,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020214434726
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=7.309185361200251e-13 cons=0.0 wall_s=7.254 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.309185361200251e-13,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.254118999000639,
  "wall_s_per_eq": [
    7.254118999000639
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.999999999998496,
      "reward": null,
      "residual_heldout": 7.309185361200251e-13,
      "pred_coeffs": {
        "u_xx": 0.5000019991370664
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.254118999000639,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.254118999000639,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000019991370664
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=1.2863080629354117e-12 cons=0.0 wall_s=9.474 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.2863080629354117e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.474239742001373,
  "wall_s_per_eq": [
    9.474239742001373
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999985512,
      "reward": null,
      "residual_heldout": 1.2863080629354117e-12,
      "pred_coeffs": {
        "u_xx": 0.5000019948490924
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.474239742001373,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.474239742001373,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000019948490924
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=1.6278477193002499e-12 cons=0.0 wall_s=7.500 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.6278477193002499e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.499981614000717,
  "wall_s_per_eq": [
    7.499981614000717
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.999999999998822,
      "reward": null,
      "residual_heldout": 1.6278477193002499e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020298178589
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.499981614000717,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.499981614000717,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020298178589
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=1.1277303007503468e-12 cons=0.0 wall_s=7.576 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.1277303007503468e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.5756019380023645,
  "wall_s_per_eq": [
    7.5756019380023645
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999986359,
      "reward": null,
      "residual_heldout": 1.1277303007503468e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020230694385
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.5756019380023645,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.5756019380023645,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020230694385
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=1.6722641250781291e-12 cons=0.0 wall_s=9.267 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.6722641250781291e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.266558570001507,
  "wall_s_per_eq": [
    9.266558570001507
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999985614,
      "reward": null,
      "residual_heldout": 1.6722641250781291e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020282200611
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.266558570001507,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.266558570001507,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020282200611
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=1.6131273695617916e-12 cons=0.0 wall_s=7.625 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.6131273695617916e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-D*uxx"
  ],
  "wall_s_total": 7.624526711999351,
  "wall_s_per_eq": [
    7.624526711999351
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-D*uxx",
      "r2_train": 0.9999999999984778,
      "reward": null,
      "residual_heldout": 1.6131273695617916e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020127637352
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.624526711999351,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.624526711999351,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5000020127637352
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=1.0437976113465347e-12 cons=0.0 wall_s=9.920 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.0437976113465347e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.919646362999629,
  "wall_s_per_eq": [
    9.919646362999629
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999981436,
      "reward": null,
      "residual_heldout": 1.0437976113465347e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020091395813
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.919646362999629,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.919646362999629,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020091395813
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=1.1122439964973946e-12 cons=0.0 wall_s=7.921 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.1122439964973946e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.920740912999463,
  "wall_s_per_eq": [
    7.920740912999463
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999988926,
      "reward": null,
      "residual_heldout": 1.1122439964973946e-12,
      "pred_coeffs": {
        "u_xx": 0.500002029411761
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.920740912999463,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.920740912999463,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.500002029411761
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=1.5744668876018204e-12 cons=0.0 wall_s=7.996 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.5744668876018204e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.99631304000286,
  "wall_s_per_eq": [
    7.99631304000286
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999987438,
      "reward": null,
      "residual_heldout": 1.5744668876018204e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020535588465
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.99631304000286,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.99631304000286,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020535588465
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=1.4375495301296622e-12 cons=0.0 wall_s=9.674 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.4375495301296622e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.673543789998803,
  "wall_s_per_eq": [
    9.673543789998803
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999982024,
      "reward": null,
      "residual_heldout": 1.4375495301296622e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020167278487
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.673543789998803,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.673543789998803,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020167278487
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=1.683368088170625e-12 cons=0.0 wall_s=7.722 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.683368088170625e-12,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.721586949999619,
  "wall_s_per_eq": [
    7.721586949999619
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9999999999988355,
      "reward": null,
      "residual_heldout": 1.683368088170625e-12,
      "pred_coeffs": {
        "u_xx": 0.5000020450845338
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.721586949999619,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.721586949999619,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000020450845338
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.012564884426724791 cons=0.0 wall_s=8.774 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.012564884426724791,
  "conservation_residual": 0.0,
  "equations": [
    "-u + u_xx*0.40037245"
  ],
  "wall_s_total": 8.774082611002086,
  "wall_s_per_eq": [
    8.774082611002086
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u + u_xx*0.40037245",
      "r2_train": 0.9949552701048598,
      "reward": null,
      "residual_heldout": 0.012564884426724791,
      "pred_coeffs": {
        "u_xx": 0.40037245,
        "u": -1.0
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.774082611002086,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.004157937313899578 cons=0.0 wall_s=8.294 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004157937313899578,
  "conservation_residual": 0.0,
  "equations": [
    "-2.5086324*u + u_xx*0.24974756"
  ],
  "wall_s_total": 8.293736452000303,
  "wall_s_per_eq": [
    8.293736452000303
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2.5086324*u + u_xx*0.24974756",
      "r2_train": 0.996503671186662,
      "reward": null,
      "residual_heldout": 0.004157937313899578,
      "pred_coeffs": {
        "u_xx": 0.24974756,
        "u": -2.5086324
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.293736452000303,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.0027532518999094585 cons=0.0 wall_s=9.591 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0027532518999094585,
  "conservation_residual": 0.0,
  "equations": [
    "u*(u_x*0.05552931 - 1.9610252) + u_xx*0.299812"
  ],
  "wall_s_total": 9.591126061997784,
  "wall_s_per_eq": [
    9.591126061997784
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(u_x*0.05552931 - 1.9610252) + u_xx*0.299812",
      "r2_train": 0.9977476832828783,
      "reward": null,
      "residual_heldout": 0.0027532518999094585,
      "pred_coeffs": {
        "u*u_x": 0.05552931,
        "u_xx": 0.299812
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.591126061997784,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.004509327073453717 cons=0.0 wall_s=8.093 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004509327073453717,
  "conservation_residual": 0.0,
  "equations": [
    "-u + u_xx*0.40038547"
  ],
  "wall_s_total": 8.092778879999969,
  "wall_s_per_eq": [
    8.092778879999969
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u + u_xx*0.40038547",
      "r2_train": 0.9975591980099622,
      "reward": null,
      "residual_heldout": 0.004509327073453717,
      "pred_coeffs": {
        "u_xx": 0.40038547,
        "u": -1.0
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.092778879999969,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.005526843083391713 cons=0.0 wall_s=10.020 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005526843083391713,
  "conservation_residual": 0.0,
  "equations": [
    "-u + u_xx*0.39785528"
  ],
  "wall_s_total": 10.019914345997677,
  "wall_s_per_eq": [
    10.019914345997677
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u + u_xx*0.39785528",
      "r2_train": 0.9930267468404856,
      "reward": null,
      "residual_heldout": 0.005526843083391713,
      "pred_coeffs": {
        "u_xx": 0.39785528,
        "u": -1.0
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.019914345997677,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.00839123256625938 cons=0.0 wall_s=8.146 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00839123256625938,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9143963)"
  ],
  "wall_s_total": 8.146292677996826,
  "wall_s_per_eq": [
    8.146292677996826
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9143963)",
      "r2_train": 0.995715528306869,
      "reward": null,
      "residual_heldout": 0.00839123256625938,
      "pred_coeffs": {
        "u": -4.9143963
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.146292677996826,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.0068395210250817556 cons=0.0 wall_s=8.688 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0068395210250817556,
  "conservation_residual": 0.0,
  "equations": [
    "-u + u_xx*0.39710197"
  ],
  "wall_s_total": 8.687510178999219,
  "wall_s_per_eq": [
    8.687510178999219
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u + u_xx*0.39710197",
      "r2_train": 0.9928149904468105,
      "reward": null,
      "residual_heldout": 0.0068395210250817556,
      "pred_coeffs": {
        "u_xx": 0.39710197,
        "u": -1.0
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.687510178999219,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.011658008391256221 cons=0.0 wall_s=8.776 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.011658008391256221,
  "conservation_residual": 0.0,
  "equations": [
    "-u - u_xx*((-u + u_x)*u_x*(-0.008457374) - 1*0.3871703)"
  ],
  "wall_s_total": 8.775544042000547,
  "wall_s_per_eq": [
    8.775544042000547
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u - u_xx*((-u + u_x)*u_x*(-0.008457374) - 1*0.3871703)",
      "r2_train": 0.9956775070799301,
      "reward": null,
      "residual_heldout": 0.011658008391256221,
      "pred_coeffs": {
        "1": 0.029334143808714717,
        "u": -1.5191348865762524,
        "u^2": 0.767966442459298,
        "u^3": -0.7737695390861098,
        "u_x": 0.004116620413384958,
        "u_xx": 0.3693175440626034
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.775544042000547,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0019646836935193813 cons=0.0 wall_s=8.669 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0019646836935193813,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.5037698"
  ],
  "wall_s_total": 8.66924629300047,
  "wall_s_per_eq": [
    8.66924629300047
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.5037698",
      "r2_train": 0.994795008026455,
      "reward": null,
      "residual_heldout": 0.0019646836935193813,
      "pred_coeffs": {
        "u_xx": 0.5037698
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.66924629300047,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.005800742434668563 cons=0.0 wall_s=9.057 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005800742434668563,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-3.2170951) + u_xx*0.17397656"
  ],
  "wall_s_total": 9.057211625997297,
  "wall_s_per_eq": [
    9.057211625997297
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-3.2170951) + u_xx*0.17397656",
      "r2_train": 0.9962361739229445,
      "reward": null,
      "residual_heldout": 0.005800742434668563,
      "pred_coeffs": {
        "u_xx": 0.17397656,
        "u": -3.2170951
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.057211625997297,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.006632421826322745 cons=0.0 wall_s=8.353 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006632421826322745,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.4997079"
  ],
  "wall_s_total": 8.352728236997791,
  "wall_s_per_eq": [
    8.352728236997791
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.4997079",
      "r2_train": 0.9953070493584274,
      "reward": null,
      "residual_heldout": 0.006632421826322745,
      "pred_coeffs": {
        "u_xx": 0.4997079
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.352728236997791,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.005204219812050509 cons=0.0 wall_s=9.800 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005204219812050509,
  "conservation_residual": 0.0,
  "equations": [
    "-u*(u_xx - 1*(-4.9187427)) + u_xx*u_xx*(-0.10006715)"
  ],
  "wall_s_total": 9.799693300999934,
  "wall_s_per_eq": [
    9.799693300999934
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u*(u_xx - 1*(-4.9187427)) + u_xx*u_xx*(-0.10006715)",
      "r2_train": 0.9968349451479042,
      "reward": null,
      "residual_heldout": 0.005204219812050509,
      "pred_coeffs": {
        "u*u_xx": -1.0,
        "u_xx^2": -0.10006715
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.799693300999934,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.005325575445119351 cons=0.0 wall_s=8.675 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005325575445119351,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.917331)"
  ],
  "wall_s_total": 8.674911137997697,
  "wall_s_per_eq": [
    8.674911137997697
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.917331)",
      "r2_train": 0.9967112526802511,
      "reward": null,
      "residual_heldout": 0.005325575445119351,
      "pred_coeffs": {
        "u": -4.917331
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.674911137997697,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.004090866503638269 cons=0.0 wall_s=8.233 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004090866503638269,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.50405467"
  ],
  "wall_s_total": 8.23325924400342,
  "wall_s_per_eq": [
    8.23325924400342
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.50405467",
      "r2_train": 0.9952701263466306,
      "reward": null,
      "residual_heldout": 0.004090866503638269,
      "pred_coeffs": {
        "u_xx": 0.50405467
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.23325924400342,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.0052852995122335275 cons=0.0 wall_s=8.676 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0052852995122335275,
  "conservation_residual": 0.0,
  "equations": [
    "-u + u_xx*0.40074918"
  ],
  "wall_s_total": 8.675650566998229,
  "wall_s_per_eq": [
    8.675650566998229
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u + u_xx*0.40074918",
      "r2_train": 0.995649930752435,
      "reward": null,
      "residual_heldout": 0.0052852995122335275,
      "pred_coeffs": {
        "u_xx": 0.40074918,
        "u": -1.0
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.675650566998229,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.03298274932553104 cons=0.0 wall_s=8.457 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.03298274932553104,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.4982501"
  ],
  "wall_s_total": 8.457278215999395,
  "wall_s_per_eq": [
    8.457278215999395
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.4982501",
      "r2_train": 0.9977313944334975,
      "reward": null,
      "residual_heldout": 0.03298274932553104,
      "pred_coeffs": {
        "u_xx": 0.4982501
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.457278215999395,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.011973728955669298 cons=0.0 wall_s=8.189 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.011973728955669298,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.50392896"
  ],
  "wall_s_total": 8.188952212000004,
  "wall_s_per_eq": [
    8.188952212000004
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.50392896",
      "r2_train": 0.9966999151291466,
      "reward": null,
      "residual_heldout": 0.011973728955669298,
      "pred_coeffs": {
        "u_xx": 0.50392896
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.188952212000004,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.0026535169517922625 cons=0.0 wall_s=9.588 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0026535169517922625,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-2.347253) + u_xx*0.2586821"
  ],
  "wall_s_total": 9.588073833998351,
  "wall_s_per_eq": [
    9.588073833998351
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-2.347253) + u_xx*0.2586821",
      "r2_train": 0.9941062863089924,
      "reward": null,
      "residual_heldout": 0.0026535169517922625,
      "pred_coeffs": {
        "u_xx": 0.2586821,
        "u": -2.347253
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.588073833998351,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.002979313512031298 cons=0.0 wall_s=8.834 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.002979313512031298,
  "conservation_residual": 0.0,
  "equations": [
    "-u - 0.0018858229*u_x*u_x*u_x*(u_x - u_xx - 2.6241493) + u_xx*0.3922137"
  ],
  "wall_s_total": 8.833560672999738,
  "wall_s_per_eq": [
    8.833560672999738
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u - 0.0018858229*u_x*u_x*u_x*(u_x - u_xx - 2.6241493) + u_xx*0.3922137",
      "r2_train": 0.996757227252017,
      "reward": null,
      "residual_heldout": 0.002979313512031298,
      "pred_coeffs": {
        "u": -1.0
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.833560672999738,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=50 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.0027148051028528693 cons=0.0 wall_s=8.939 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0027148051028528693,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.8886127)"
  ],
  "wall_s_total": 8.939350996002759,
  "wall_s_per_eq": [
    8.939350996002759
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.8886127)",
      "r2_train": 0.9956312453734042,
      "reward": null,
      "residual_heldout": 0.0027148051028528693,
      "pred_coeffs": {
        "u": -4.8886127
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.939350996002759,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.01571400759230123 cons=0.0 wall_s=8.188 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01571400759230123,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.187616102000902,
  "wall_s_per_eq": [
    8.187616102000902
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9937918372758235,
      "reward": null,
      "residual_heldout": 0.01571400759230123,
      "pred_coeffs": {
        "u_xx": 0.5018387676009322
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.187616102000902,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.187616102000902,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5018387676009322
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.004172453184579701 cons=0.0 wall_s=10.963 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004172453184579701,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 10.962589824997849,
  "wall_s_per_eq": [
    10.962589824997849
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9948782011925005,
      "reward": null,
      "residual_heldout": 0.004172453184579701,
      "pred_coeffs": {
        "u_xx": 0.5048655568930267
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.962589824997849,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.962589824997849,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5048655568930267
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.002429966032976526 cons=0.0 wall_s=8.556 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.002429966032976526,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.555700940996758,
  "wall_s_per_eq": [
    8.555700940996758
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9962360692264641,
      "reward": null,
      "residual_heldout": 0.002429966032976526,
      "pred_coeffs": {
        "u_xx": 0.5004932659436486
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.555700940996758,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.555700940996758,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5004932659436486
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.004352782064019199 cons=0.0 wall_s=8.348 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004352782064019199,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.347794039000291,
  "wall_s_per_eq": [
    8.347794039000291
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9967724150202258,
      "reward": null,
      "residual_heldout": 0.004352782064019199,
      "pred_coeffs": {
        "u_xx": 0.5021093104097807
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.347794039000291,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.347794039000291,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5021093104097807
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.006462258386988665 cons=0.0 wall_s=10.277 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006462258386988665,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 10.277178356001968,
  "wall_s_per_eq": [
    10.277178356001968
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9909176266122706,
      "reward": null,
      "residual_heldout": 0.006462258386988665,
      "pred_coeffs": {
        "u_xx": 0.49934608874652675
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.277178356001968,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.277178356001968,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49934608874652675
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.011648138044164954 cons=0.0 wall_s=9.078 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.011648138044164954,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.077864277998742,
  "wall_s_per_eq": [
    9.077864277998742
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9947875462590544,
      "reward": null,
      "residual_heldout": 0.011648138044164954,
      "pred_coeffs": {
        "u_xx": 0.5059345125674388
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.077864277998742,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.077864277998742,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5059345125674388
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.008176103603285715 cons=0.0 wall_s=7.727 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008176103603285715,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.727291687999241,
  "wall_s_per_eq": [
    7.727291687999241
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9918206618902661,
      "reward": null,
      "residual_heldout": 0.008176103603285715,
      "pred_coeffs": {
        "u_xx": 0.4974266067376464
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.727291687999241,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.727291687999241,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4974266067376464
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.006977575471706528 cons=0.0 wall_s=10.386 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006977575471706528,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 10.38567901100032,
  "wall_s_per_eq": [
    10.38567901100032
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9921305767173667,
      "reward": null,
      "residual_heldout": 0.006977575471706528,
      "pred_coeffs": {
        "u_xx": 0.5003319520091984
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.38567901100032,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.38567901100032,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5003319520091984
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0019647060946263793 cons=0.0 wall_s=8.185 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0019647060946263793,
  "conservation_residual": 0.0,
  "equations": [
    "-D*uxx"
  ],
  "wall_s_total": 8.185201069998584,
  "wall_s_per_eq": [
    8.185201069998584
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-D*uxx",
      "r2_train": 0.9947950076689015,
      "reward": null,
      "residual_heldout": 0.0019647060946263793,
      "pred_coeffs": {
        "u_xx": 0.5037701704831615
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.185201069998584,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.185201069998584,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5037701704831615
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.00958451755078758 cons=0.0 wall_s=8.266 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00958451755078758,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.265706717000285,
  "wall_s_per_eq": [
    8.265706717000285
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9917541529590795,
      "reward": null,
      "residual_heldout": 0.00958451755078758,
      "pred_coeffs": {
        "u_xx": 0.5062972430701992
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.265706717000285,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.265706717000285,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5062972430701992
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.006632243417392261 cons=0.0 wall_s=11.650 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006632243417392261,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 11.649788743998215,
  "wall_s_per_eq": [
    11.649788743998215
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9953070502460811,
      "reward": null,
      "residual_heldout": 0.006632243417392261,
      "pred_coeffs": {
        "u_xx": 0.4997062220128419
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 11.649788743998215,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.649788743998215,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4997062220128419
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.005208167834805218 cons=0.0 wall_s=7.721 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005208167834805218,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.720962717998191,
  "wall_s_per_eq": [
    7.720962717998191
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.995103988391669,
      "reward": null,
      "residual_heldout": 0.005208167834805218,
      "pred_coeffs": {
        "u_xx": 0.49666188024219504
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.720962717998191,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.720962717998191,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49666188024219504
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.004616098125768204 cons=0.0 wall_s=7.753 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004616098125768204,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.753395460997126,
  "wall_s_per_eq": [
    7.753395460997126
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.996651524695606,
      "reward": null,
      "residual_heldout": 0.004616098125768204,
      "pred_coeffs": {
        "u_xx": 0.5017702769697554
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.753395460997126,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.753395460997126,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5017702769697554
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.004090835124982426 cons=0.0 wall_s=10.393 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004090835124982426,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 10.393073167000694,
  "wall_s_per_eq": [
    10.393073167000694
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9952701261645478,
      "reward": null,
      "residual_heldout": 0.004090835124982426,
      "pred_coeffs": {
        "u_xx": 0.5040552039279547
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.393073167000694,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.393073167000694,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5040552039279547
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.005938906037032185 cons=0.0 wall_s=7.916 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005938906037032185,
  "conservation_residual": 0.0,
  "equations": [
    "-D*uxx"
  ],
  "wall_s_total": 7.916233218998968,
  "wall_s_per_eq": [
    7.916233218998968
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-D*uxx",
      "r2_train": 0.9946365377620003,
      "reward": null,
      "residual_heldout": 0.005938906037032185,
      "pred_coeffs": {
        "u_xx": 0.5039628357553908
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.916233218998968,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.916233218998968,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5039628357553908
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.03298270813262427 cons=0.0 wall_s=7.376 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.03298270813262427,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.375641741000436,
  "wall_s_per_eq": [
    7.375641741000436
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.997731393975028,
      "reward": null,
      "residual_heldout": 0.03298270813262427,
      "pred_coeffs": {
        "u_xx": 0.49825030323891306
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.375641741000436,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.375641741000436,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49825030323891306
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.011973963248467102 cons=0.0 wall_s=10.620 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.011973963248467102,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 10.619920451001235,
  "wall_s_per_eq": [
    10.619920451001235
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9966999163703253,
      "reward": null,
      "residual_heldout": 0.011973963248467102,
      "pred_coeffs": {
        "u_xx": 0.5039299829055836
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.619920451001235,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.619920451001235,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5039299829055836
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.003710081581209305 cons=0.0 wall_s=8.070 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003710081581209305,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.069911595001031,
  "wall_s_per_eq": [
    8.069911595001031
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9921460592140889,
      "reward": null,
      "residual_heldout": 0.003710081581209305,
      "pred_coeffs": {
        "u_xx": 0.4997560416582921
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.069911595001031,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.069911595001031,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4997560416582921
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0017171860966788764 cons=0.0 wall_s=7.599 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0017171860966788764,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.599011136000627,
  "wall_s_per_eq": [
    7.599011136000627
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9946617519328849,
      "reward": null,
      "residual_heldout": 0.0017171860966788764,
      "pred_coeffs": {
        "u_xx": 0.4967820074349962
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.599011136000627,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.599011136000627,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4967820074349962
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=50 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0036023264551759793 cons=0.0 wall_s=8.389 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0036023264551759793,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.389189636000083,
  "wall_s_per_eq": [
    8.389189636000083
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.994802238881247,
      "reward": null,
      "residual_heldout": 0.0036023264551759793,
      "pred_coeffs": {
        "u_xx": 0.4956488034553704
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.389189636000083,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.389189636000083,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4956488034553704
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.004357870372894249 cons=0.0 wall_s=9.317 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004357870372894249,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.5005632"
  ],
  "wall_s_total": 9.317313142000785,
  "wall_s_per_eq": [
    9.317313142000785
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.5005632",
      "r2_train": 0.9971447176458618,
      "reward": null,
      "residual_heldout": 0.004357870372894249,
      "pred_coeffs": {
        "u_xx": 0.5005632
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.317313142000785,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.006647518824930665 cons=0.0 wall_s=8.620 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006647518824930665,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49579304"
  ],
  "wall_s_total": 8.620004519001668,
  "wall_s_per_eq": [
    8.620004519001668
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49579304",
      "r2_train": 0.9961970695859774,
      "reward": null,
      "residual_heldout": 0.006647518824930665,
      "pred_coeffs": {
        "u_xx": 0.49579304
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.620004519001668,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.015628481003859787 cons=0.0 wall_s=8.392 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.015628481003859787,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.920329)"
  ],
  "wall_s_total": 8.391726581998228,
  "wall_s_per_eq": [
    8.391726581998228
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.920329)",
      "r2_train": 0.9952890666395896,
      "reward": null,
      "residual_heldout": 0.015628481003859787,
      "pred_coeffs": {
        "u": -4.920329
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.391726581998228,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.008413078408760249 cons=0.0 wall_s=9.119 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008413078408760249,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49936172"
  ],
  "wall_s_total": 9.11860736500239,
  "wall_s_per_eq": [
    9.11860736500239
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49936172",
      "r2_train": 0.9960981111426919,
      "reward": null,
      "residual_heldout": 0.008413078408760249,
      "pred_coeffs": {
        "u_xx": 0.49936172
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.11860736500239,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.004409701901976432 cons=0.0 wall_s=9.263 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004409701901976432,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.925991)"
  ],
  "wall_s_total": 9.263215402999776,
  "wall_s_per_eq": [
    9.263215402999776
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.925991)",
      "r2_train": 0.9940015142123692,
      "reward": null,
      "residual_heldout": 0.004409701901976432,
      "pred_coeffs": {
        "u": -4.925991
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.263215402999776,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.005017731075921952 cons=0.0 wall_s=9.387 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005017731075921952,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.921974)"
  ],
  "wall_s_total": 9.387396018999425,
  "wall_s_per_eq": [
    9.387396018999425
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.921974)",
      "r2_train": 0.9955480892622434,
      "reward": null,
      "residual_heldout": 0.005017731075921952,
      "pred_coeffs": {
        "u": -4.921974
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.387396018999425,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.010488554973723698 cons=0.0 wall_s=9.248 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.010488554973723698,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.50429785"
  ],
  "wall_s_total": 9.24834725799883,
  "wall_s_per_eq": [
    9.24834725799883
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.50429785",
      "r2_train": 0.9968678264762744,
      "reward": null,
      "residual_heldout": 0.010488554973723698,
      "pred_coeffs": {
        "u_xx": 0.50429785
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.24834725799883,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.003758470579061615 cons=0.0 wall_s=8.711 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003758470579061615,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.924027)"
  ],
  "wall_s_total": 8.710627284999646,
  "wall_s_per_eq": [
    8.710627284999646
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.924027)",
      "r2_train": 0.9956506012807381,
      "reward": null,
      "residual_heldout": 0.003758470579061615,
      "pred_coeffs": {
        "u": -4.924027
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.710627284999646,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.003970567914135244 cons=0.0 wall_s=8.543 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003970567914135244,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.50230914"
  ],
  "wall_s_total": 8.543239836999419,
  "wall_s_per_eq": [
    8.543239836999419
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.50230914",
      "r2_train": 0.99526471707296,
      "reward": null,
      "residual_heldout": 0.003970567914135244,
      "pred_coeffs": {
        "u_xx": 0.50230914
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.543239836999419,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.009590568471927902 cons=0.0 wall_s=8.879 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.009590568471927902,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9307866)"
  ],
  "wall_s_total": 8.878888043000188,
  "wall_s_per_eq": [
    8.878888043000188
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9307866)",
      "r2_train": 0.9959242859168234,
      "reward": null,
      "residual_heldout": 0.009590568471927902,
      "pred_coeffs": {
        "u": -4.9307866
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.878888043000188,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.005253634154920078 cons=0.0 wall_s=8.969 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005253634154920078,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.899386)"
  ],
  "wall_s_total": 8.968953388000955,
  "wall_s_per_eq": [
    8.968953388000955
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.899386)",
      "r2_train": 0.9951789406095006,
      "reward": null,
      "residual_heldout": 0.005253634154920078,
      "pred_coeffs": {
        "u": -4.899386
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.968953388000955,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0077381491045372544 cons=0.0 wall_s=8.798 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0077381491045372544,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.50209093"
  ],
  "wall_s_total": 8.797578099998645,
  "wall_s_per_eq": [
    8.797578099998645
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.50209093",
      "r2_train": 0.9959199819837483,
      "reward": null,
      "residual_heldout": 0.0077381491045372544,
      "pred_coeffs": {
        "u_xx": 0.50209093
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.797578099998645,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0043873938718345185 cons=0.0 wall_s=8.675 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0043873938718345185,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.50145626"
  ],
  "wall_s_total": 8.67500029799703,
  "wall_s_per_eq": [
    8.67500029799703
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.50145626",
      "r2_train": 0.9964126744579141,
      "reward": null,
      "residual_heldout": 0.0043873938718345185,
      "pred_coeffs": {
        "u_xx": 0.50145626
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.67500029799703,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.005890194147182526 cons=0.0 wall_s=8.351 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005890194147182526,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.50379425"
  ],
  "wall_s_total": 8.350937873001385,
  "wall_s_per_eq": [
    8.350937873001385
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.50379425",
      "r2_train": 0.9946424759344957,
      "reward": null,
      "residual_heldout": 0.005890194147182526,
      "pred_coeffs": {
        "u_xx": 0.50379425
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.350937873001385,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.007521317517416081 cons=0.0 wall_s=9.736 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007521317517416081,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.5011788"
  ],
  "wall_s_total": 9.73602197999935,
  "wall_s_per_eq": [
    9.73602197999935
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.5011788",
      "r2_train": 0.9955496315439948,
      "reward": null,
      "residual_heldout": 0.007521317517416081,
      "pred_coeffs": {
        "u_xx": 0.5011788
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.73602197999935,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.0042718187746208875 cons=0.0 wall_s=9.013 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0042718187746208875,
  "conservation_residual": 0.0,
  "equations": [
    "-u + u_xx*0.39780667"
  ],
  "wall_s_total": 9.012527697999758,
  "wall_s_per_eq": [
    9.012527697999758
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u + u_xx*0.39780667",
      "r2_train": 0.9962718659922102,
      "reward": null,
      "residual_heldout": 0.0042718187746208875,
      "pred_coeffs": {
        "u_xx": 0.39780667,
        "u": -1.0
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.012527697999758,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.008991890353976928 cons=0.0 wall_s=8.890 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008991890353976928,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49875093"
  ],
  "wall_s_total": 8.890352028000052,
  "wall_s_per_eq": [
    8.890352028000052
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49875093",
      "r2_train": 0.9952304441828533,
      "reward": null,
      "residual_heldout": 0.008991890353976928,
      "pred_coeffs": {
        "u_xx": 0.49875093
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.890352028000052,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.007504454074893074 cons=0.0 wall_s=8.303 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007504454074893074,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9015965)"
  ],
  "wall_s_total": 8.303488960002142,
  "wall_s_per_eq": [
    8.303488960002142
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9015965)",
      "r2_train": 0.9958691531028815,
      "reward": null,
      "residual_heldout": 0.007504454074893074,
      "pred_coeffs": {
        "u": -4.9015965
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.303488960002142,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0021636144225140115 cons=0.0 wall_s=8.617 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0021636144225140115,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49723375"
  ],
  "wall_s_total": 8.61663283800226,
  "wall_s_per_eq": [
    8.61663283800226
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49723375",
      "r2_train": 0.9950724783177628,
      "reward": null,
      "residual_heldout": 0.0021636144225140115,
      "pred_coeffs": {
        "u_xx": 0.49723375
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.61663283800226,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.00716081343451277 cons=0.0 wall_s=8.196 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00716081343451277,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.922561)"
  ],
  "wall_s_total": 8.19596550499773,
  "wall_s_per_eq": [
    8.19596550499773
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.922561)",
      "r2_train": 0.9967928155714156,
      "reward": null,
      "residual_heldout": 0.00716081343451277,
      "pred_coeffs": {
        "u": -4.922561
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.19596550499773,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.004358023355953558 cons=0.0 wall_s=11.358 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004358023355953558,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 11.357812567999645,
  "wall_s_per_eq": [
    11.357812567999645
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9971447187710005,
      "reward": null,
      "residual_heldout": 0.004358023355953558,
      "pred_coeffs": {
        "u_xx": 0.500564544324422
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 11.357812567999645,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.357812567999645,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.500564544324422
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.006646973099213042 cons=0.0 wall_s=7.828 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006646973099213042,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.827983348000998,
  "wall_s_per_eq": [
    7.827983348000998
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9961970699283833,
      "reward": null,
      "residual_heldout": 0.006646973099213042,
      "pred_coeffs": {
        "u_xx": 0.49579524442777856
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.827983348000998,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.827983348000998,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49579524442777856
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.01599975426857221 cons=0.0 wall_s=7.690 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01599975426857221,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.690205324000999,
  "wall_s_per_eq": [
    7.690205324000999
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9920276189719549,
      "reward": null,
      "residual_heldout": 0.01599975426857221,
      "pred_coeffs": {
        "u_xx": 0.49949175416818076
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.690205324000999,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.690205324000999,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49949175416818076
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.00841307362596381 cons=0.0 wall_s=11.644 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00841307362596381,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 11.644020039999305,
  "wall_s_per_eq": [
    11.644020039999305
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9960981125031326,
      "reward": null,
      "residual_heldout": 0.00841307362596381,
      "pred_coeffs": {
        "u_xx": 0.4993620158201572
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 11.644020039999305,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.644020039999305,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4993620158201572
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0060249536533800024 cons=0.0 wall_s=7.947 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0060249536533800024,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.9466012039993075,
  "wall_s_per_eq": [
    7.9466012039993075
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9923439493319038,
      "reward": null,
      "residual_heldout": 0.0060249536533800024,
      "pred_coeffs": {
        "u_xx": 0.4990295174438278
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.9466012039993075,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.9466012039993075,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4990295174438278
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0033461302303366587 cons=0.0 wall_s=7.489 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0033461302303366587,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.489260882000963,
  "wall_s_per_eq": [
    7.489260882000963
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9947295174550544,
      "reward": null,
      "residual_heldout": 0.0033461302303366587,
      "pred_coeffs": {
        "u_xx": 0.49834152808663196
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.489260882000963,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.489260882000963,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49834152808663196
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.01048900975732753 cons=0.0 wall_s=7.628 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01048900975732753,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.62806022100267,
  "wall_s_per_eq": [
    7.62806022100267
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.996867825148917,
      "reward": null,
      "residual_heldout": 0.01048900975732753,
      "pred_coeffs": {
        "u_xx": 0.5043000947301858
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.62806022100267,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.62806022100267,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5043000947301858
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0032202134641715462 cons=0.0 wall_s=11.171 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0032202134641715462,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 11.170634052999958,
  "wall_s_per_eq": [
    11.170634052999958
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9953272047920382,
      "reward": null,
      "residual_heldout": 0.0032202134641715462,
      "pred_coeffs": {
        "u_xx": 0.5018451178245082
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 11.170634052999958,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.170634052999958,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5018451178245082
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.003970542689620483 cons=0.0 wall_s=8.897 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003970542689620483,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.89691345599931,
  "wall_s_per_eq": [
    8.89691345599931
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9952647171174528,
      "reward": null,
      "residual_heldout": 0.003970542689620483,
      "pred_coeffs": {
        "u_xx": 0.5023072530688643
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.89691345599931,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.89691345599931,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5023072530688643
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.010586772091536847 cons=0.0 wall_s=7.870 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.010586772091536847,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.869813597000757,
  "wall_s_per_eq": [
    7.869813597000757
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9943243445940029,
      "reward": null,
      "residual_heldout": 0.010586772091536847,
      "pred_coeffs": {
        "u_xx": 0.5004310439984783
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.869813597000757,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.869813597000757,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5004310439984783
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.005570559261280465 cons=0.0 wall_s=7.481 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005570559261280465,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.4809042060005595,
  "wall_s_per_eq": [
    7.4809042060005595
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9948760593831409,
      "reward": null,
      "residual_heldout": 0.005570559261280465,
      "pred_coeffs": {
        "u_xx": 0.4955186472512577
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.4809042060005595,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.4809042060005595,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4955186472512577
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0077382273564283125 cons=0.0 wall_s=11.343 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0077382273564283125,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 11.343293949001236,
  "wall_s_per_eq": [
    11.343293949001236
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9959199811613385,
      "reward": null,
      "residual_heldout": 0.0077382273564283125,
      "pred_coeffs": {
        "u_xx": 0.5020965044457785
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 11.343293949001236,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.343293949001236,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5020965044457785
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.004387394012274844 cons=0.0 wall_s=8.167 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004387394012274844,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.167283656999643,
  "wall_s_per_eq": [
    8.167283656999643
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9964126761742551,
      "reward": null,
      "residual_heldout": 0.004387394012274844,
      "pred_coeffs": {
        "u_xx": 0.501456281847106
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.167283656999643,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.167283656999643,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.501456281847106
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.005890193842530993 cons=0.0 wall_s=7.569 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005890193842530993,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.568959428001108,
  "wall_s_per_eq": [
    7.568959428001108
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9946424766340273,
      "reward": null,
      "residual_heldout": 0.005890193842530993,
      "pred_coeffs": {
        "u_xx": 0.5037944863732382
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.568959428001108,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.568959428001108,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5037944863732382
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.007521252510427164 cons=0.0 wall_s=8.332 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007521252510427164,
  "conservation_residual": 0.0,
  "equations": [
    "-D*uxx"
  ],
  "wall_s_total": 8.332393295997463,
  "wall_s_per_eq": [
    8.332393295997463
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-D*uxx",
      "r2_train": 0.9955496299289406,
      "reward": null,
      "residual_heldout": 0.007521252510427164,
      "pred_coeffs": {
        "u_xx": 0.5011782736733261
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.332393295997463,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.332393295997463,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.5011782736733261
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.005511131286533403 cons=0.0 wall_s=11.074 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005511131286533403,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 11.073908566999307,
  "wall_s_per_eq": [
    11.073908566999307
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9954231411858777,
      "reward": null,
      "residual_heldout": 0.005511131286533403,
      "pred_coeffs": {
        "u_xx": 0.49995871500525474
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 11.073908566999307,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.073908566999307,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49995871500525474
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.008991892963742322 cons=0.0 wall_s=7.851 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008991892963742322,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.8509651189997385,
  "wall_s_per_eq": [
    7.8509651189997385
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.995230443564831,
      "reward": null,
      "residual_heldout": 0.008991892963742322,
      "pred_coeffs": {
        "u_xx": 0.4987506324325858
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.8509651189997385,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.8509651189997385,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4987506324325858
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.009457937506868564 cons=0.0 wall_s=7.731 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.009457937506868564,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.731003983000846,
  "wall_s_per_eq": [
    7.731003983000846
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9953719352045703,
      "reward": null,
      "residual_heldout": 0.009457937506868564,
      "pred_coeffs": {
        "u_xx": 0.4995459462776611
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.731003983000846,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.731003983000846,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4995459462776611
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0021635888498257624 cons=0.0 wall_s=7.581 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0021635888498257624,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.5812192910016165,
  "wall_s_per_eq": [
    7.5812192910016165
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9950724787663455,
      "reward": null,
      "residual_heldout": 0.0021635888498257624,
      "pred_coeffs": {
        "u_xx": 0.49723410229767834
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.5812192910016165,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.5812192910016165,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49723410229767834
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=100 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.004150949899972673 cons=0.0 wall_s=13.536 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004150949899972673,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 13.535639460998937,
  "wall_s_per_eq": [
    13.535639460998937
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9960392534839511,
      "reward": null,
      "residual_heldout": 0.004150949899972673,
      "pred_coeffs": {
        "u_xx": 0.5031655586026244
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 13.535639460998937,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.535639460998937,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5031655586026244
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.005034131559982098 cons=0.0 wall_s=10.349 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005034131559982098,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49834388"
  ],
  "wall_s_total": 10.348787945000367,
  "wall_s_per_eq": [
    10.348787945000367
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49834388",
      "r2_train": 0.9948174879845855,
      "reward": null,
      "residual_heldout": 0.005034131559982098,
      "pred_coeffs": {
        "u_xx": 0.49834388
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.348787945000367,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0055809145292740284 cons=0.0 wall_s=9.466 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0055809145292740284,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.50175595"
  ],
  "wall_s_total": 9.465836670999124,
  "wall_s_per_eq": [
    9.465836670999124
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.50175595",
      "r2_train": 0.9951377090902568,
      "reward": null,
      "residual_heldout": 0.0055809145292740284,
      "pred_coeffs": {
        "u_xx": 0.50175595
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.465836670999124,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.0063254643072299475 cons=0.0 wall_s=10.292 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0063254643072299475,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.940792)"
  ],
  "wall_s_total": 10.292175595997833,
  "wall_s_per_eq": [
    10.292175595997833
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.940792)",
      "r2_train": 0.9950391486012709,
      "reward": null,
      "residual_heldout": 0.0063254643072299475,
      "pred_coeffs": {
        "u": -4.940792
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.292175595997833,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.004579370345786361 cons=0.0 wall_s=9.611 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004579370345786361,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49843788"
  ],
  "wall_s_total": 9.61058163800044,
  "wall_s_per_eq": [
    9.61058163800044
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49843788",
      "r2_train": 0.9951839504107756,
      "reward": null,
      "residual_heldout": 0.004579370345786361,
      "pred_coeffs": {
        "u_xx": 0.49843788
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.61058163800044,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.004687704402906276 cons=0.0 wall_s=9.066 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004687704402906276,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49989748"
  ],
  "wall_s_total": 9.065513076999196,
  "wall_s_per_eq": [
    9.065513076999196
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49989748",
      "r2_train": 0.9944047281850771,
      "reward": null,
      "residual_heldout": 0.004687704402906276,
      "pred_coeffs": {
        "u_xx": 0.49989748
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.065513076999196,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.006025970270318936 cons=0.0 wall_s=10.174 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006025970270318936,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.909819)"
  ],
  "wall_s_total": 10.173619214998325,
  "wall_s_per_eq": [
    10.173619214998325
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.909819)",
      "r2_train": 0.9955219532854122,
      "reward": null,
      "residual_heldout": 0.006025970270318936,
      "pred_coeffs": {
        "u": -4.909819
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 10.173619214998325,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.005397105209017911 cons=0.0 wall_s=9.237 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005397105209017911,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49857977"
  ],
  "wall_s_total": 9.23741727900051,
  "wall_s_per_eq": [
    9.23741727900051
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49857977",
      "r2_train": 0.9951577629174813,
      "reward": null,
      "residual_heldout": 0.005397105209017911,
      "pred_coeffs": {
        "u_xx": 0.49857977
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.23741727900051,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0044891012196012076 cons=0.0 wall_s=9.374 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0044891012196012076,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.5000762"
  ],
  "wall_s_total": 9.3740066140017,
  "wall_s_per_eq": [
    9.3740066140017
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.5000762",
      "r2_train": 0.9944621152857493,
      "reward": null,
      "residual_heldout": 0.0044891012196012076,
      "pred_coeffs": {
        "u_xx": 0.5000762
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.3740066140017,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.003976154515712206 cons=0.0 wall_s=9.571 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003976154515712206,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.8960266)"
  ],
  "wall_s_total": 9.571202072002052,
  "wall_s_per_eq": [
    9.571202072002052
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.8960266)",
      "r2_train": 0.9951524493673882,
      "reward": null,
      "residual_heldout": 0.003976154515712206,
      "pred_coeffs": {
        "u": -4.8960266
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.571202072002052,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004548856951136277 cons=0.0 wall_s=8.997 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004548856951136277,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49858448"
  ],
  "wall_s_total": 8.997256726997875,
  "wall_s_per_eq": [
    8.997256726997875
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49858448",
      "r2_train": 0.9960699751123815,
      "reward": null,
      "residual_heldout": 0.004548856951136277,
      "pred_coeffs": {
        "u_xx": 0.49858448
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.997256726997875,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.006004701276048522 cons=0.0 wall_s=9.227 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006004701276048522,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49941394"
  ],
  "wall_s_total": 9.22744337700351,
  "wall_s_per_eq": [
    9.22744337700351
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49941394",
      "r2_train": 0.9948549865803948,
      "reward": null,
      "residual_heldout": 0.006004701276048522,
      "pred_coeffs": {
        "u_xx": 0.49941394
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.22744337700351,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.00446981770917455 cons=0.0 wall_s=8.762 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00446981770917455,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.49802244"
  ],
  "wall_s_total": 8.762126184999943,
  "wall_s_per_eq": [
    8.762126184999943
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.49802244",
      "r2_train": 0.9960697819375764,
      "reward": null,
      "residual_heldout": 0.00446981770917455,
      "pred_coeffs": {
        "u_xx": 0.49802244
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.762126184999943,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.005604227981734687 cons=0.0 wall_s=9.566 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005604227981734687,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.904302)"
  ],
  "wall_s_total": 9.565973458997178,
  "wall_s_per_eq": [
    9.565973458997178
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.904302)",
      "r2_train": 0.9949172482330326,
      "reward": null,
      "residual_heldout": 0.005604227981734687,
      "pred_coeffs": {
        "u": -4.904302
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.565973458997178,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0044312445187265044 cons=0.0 wall_s=10.223 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0044312445187265044,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.5000911"
  ],
  "wall_s_total": 10.222716078002122,
  "wall_s_per_eq": [
    10.222716078002122
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.5000911",
      "r2_train": 0.9952197093159051,
      "reward": null,
      "residual_heldout": 0.0044312445187265044,
      "pred_coeffs": {
        "u_xx": 0.5000911
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 10.222716078002122,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.008240683253969509 cons=0.0 wall_s=9.201 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008240683253969509,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9228477)"
  ],
  "wall_s_total": 9.200730838998425,
  "wall_s_per_eq": [
    9.200730838998425
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9228477)",
      "r2_train": 0.9941432431692685,
      "reward": null,
      "residual_heldout": 0.008240683253969509,
      "pred_coeffs": {
        "u": -4.9228477
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.200730838998425,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.006316542108914941 cons=0.0 wall_s=9.477 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006316542108914941,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.898912)"
  ],
  "wall_s_total": 9.477330229001382,
  "wall_s_per_eq": [
    9.477330229001382
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.898912)",
      "r2_train": 0.9955607040230835,
      "reward": null,
      "residual_heldout": 0.006316542108914941,
      "pred_coeffs": {
        "u": -4.898912
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.477330229001382,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0049150674273211745 cons=0.0 wall_s=9.202 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0049150674273211745,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.4996166"
  ],
  "wall_s_total": 9.201654587999656,
  "wall_s_per_eq": [
    9.201654587999656
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.4996166",
      "r2_train": 0.9960625138788233,
      "reward": null,
      "residual_heldout": 0.0049150674273211745,
      "pred_coeffs": {
        "u_xx": 0.4996166
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.201654587999656,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.005853459608840441 cons=0.0 wall_s=9.224 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005853459608840441,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.5019356"
  ],
  "wall_s_total": 9.224452599999495,
  "wall_s_per_eq": [
    9.224452599999495
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.5019356",
      "r2_train": 0.9953963486658068,
      "reward": null,
      "residual_heldout": 0.005853459608840441,
      "pred_coeffs": {
        "u_xx": 0.5019356
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.224452599999495,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.005939769160639254 cons=0.0 wall_s=9.411 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005939769160639254,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9177938)"
  ],
  "wall_s_total": 9.410501038997609,
  "wall_s_per_eq": [
    9.410501038997609
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9177938)",
      "r2_train": 0.9948589905273784,
      "reward": null,
      "residual_heldout": 0.005939769160639254,
      "pred_coeffs": {
        "u": -4.9177938
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 9.410501038997609,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `diffusion_1d` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.007196937710389785 cons=0.0 wall_s=8.681 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007196937710389785,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-4.9117045)"
  ],
  "wall_s_total": 8.681169560000853,
  "wall_s_per_eq": [
    8.681169560000853
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-4.9117045)",
      "r2_train": 0.9940251188055966,
      "reward": null,
      "residual_heldout": 0.007196937710389785,
      "pred_coeffs": {
        "u": -4.9117045
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": false,
      "wall_s": 8.681169560000853,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.005033999328387778 cons=0.0 wall_s=9.364 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005033999328387778,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 9.364179332998901,
  "wall_s_per_eq": [
    9.364179332998901
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9948174880953886,
      "reward": null,
      "residual_heldout": 0.005033999328387778,
      "pred_coeffs": {
        "u_xx": 0.4983405897364059
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 9.364179332998901,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.364179332998901,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4983405897364059
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0055810851166893955 cons=0.0 wall_s=7.823 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0055810851166893955,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.82286363899766,
  "wall_s_per_eq": [
    7.82286363899766
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9951377090563124,
      "reward": null,
      "residual_heldout": 0.0055810851166893955,
      "pred_coeffs": {
        "u_xx": 0.5017597610720874
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.82286363899766,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.82286363899766,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5017597610720874
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0071785599835672955 cons=0.0 wall_s=8.103 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0071785599835672955,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.103072735000751,
  "wall_s_per_eq": [
    8.103072735000751
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9949837977936686,
      "reward": null,
      "residual_heldout": 0.0071785599835672955,
      "pred_coeffs": {
        "u_xx": 0.4998141437467435
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.103072735000751,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.103072735000751,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4998141437467435
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0045793689658542806 cons=0.0 wall_s=11.978 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0045793689658542806,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 11.978426908000984,
  "wall_s_per_eq": [
    11.978426908000984
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9951839503785496,
      "reward": null,
      "residual_heldout": 0.0045793689658542806,
      "pred_coeffs": {
        "u_xx": 0.4984378569132783
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 11.978426908000984,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.978426908000984,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4984378569132783
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0046876737904721025 cons=0.0 wall_s=8.572 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0046876737904721025,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.572002492001047,
  "wall_s_per_eq": [
    8.572002492001047
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9944047288708239,
      "reward": null,
      "residual_heldout": 0.0046876737904721025,
      "pred_coeffs": {
        "u_xx": 0.4998981014777449
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.572002492001047,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.572002492001047,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4998981014777449
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.005898845607720299 cons=0.0 wall_s=7.908 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005898845607720299,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.908264751000388,
  "wall_s_per_eq": [
    7.908264751000388
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9946904821947697,
      "reward": null,
      "residual_heldout": 0.005898845607720299,
      "pred_coeffs": {
        "u_xx": 0.500349756919912
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.908264751000388,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.908264751000388,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.500349756919912
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.00539736217385833 cons=0.0 wall_s=8.013 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00539736217385833,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.012710920000245,
  "wall_s_per_eq": [
    8.012710920000245
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9951577626379308,
      "reward": null,
      "residual_heldout": 0.00539736217385833,
      "pred_coeffs": {
        "u_xx": 0.4985769587126439
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.012710920000245,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.012710920000245,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4985769587126439
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.004488951692993865 cons=0.0 wall_s=7.711 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004488951692993865,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.711068871001771,
  "wall_s_per_eq": [
    7.711068871001771
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9944621153151869,
      "reward": null,
      "residual_heldout": 0.004488951692993865,
      "pred_coeffs": {
        "u_xx": 0.5000789092707416
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.711068871001771,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.711068871001771,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000789092707416
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.003932130023221843 cons=0.0 wall_s=12.801 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003932130023221843,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 12.80127857700063,
  "wall_s_per_eq": [
    12.80127857700063
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9949716687411454,
      "reward": null,
      "residual_heldout": 0.003932130023221843,
      "pred_coeffs": {
        "u_xx": 0.4987030981242159
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 12.80127857700063,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.80127857700063,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4987030981242159
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004548750459501419 cons=0.0 wall_s=8.478 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004548750459501419,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.477530247997493,
  "wall_s_per_eq": [
    8.477530247997493
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.996069974543146,
      "reward": null,
      "residual_heldout": 0.004548750459501419,
      "pred_coeffs": {
        "u_xx": 0.49858643674095526
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.477530247997493,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.477530247997493,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49858643674095526
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.006004701350651865 cons=0.0 wall_s=8.329 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006004701350651865,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.328977149998536,
  "wall_s_per_eq": [
    8.328977149998536
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9948549866492015,
      "reward": null,
      "residual_heldout": 0.006004701350651865,
      "pred_coeffs": {
        "u_xx": 0.4994138931681704
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.328977149998536,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.328977149998536,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4994138931681704
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.004469812162786968 cons=0.0 wall_s=7.925 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004469812162786968,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.925042506001773,
  "wall_s_per_eq": [
    7.925042506001773
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9960697823196857,
      "reward": null,
      "residual_heldout": 0.004469812162786968,
      "pred_coeffs": {
        "u_xx": 0.49802340242244886
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.925042506001773,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.925042506001773,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49802340242244886
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.005159216061976348 cons=0.0 wall_s=8.238 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005159216061976348,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.237526008000714,
  "wall_s_per_eq": [
    8.237526008000714
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9947025306305007,
      "reward": null,
      "residual_heldout": 0.005159216061976348,
      "pred_coeffs": {
        "u_xx": 0.4970427160345873
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.237526008000714,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.237526008000714,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4970427160345873
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.004431317922546592 cons=0.0 wall_s=13.226 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004431317922546592,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 13.225956664002297,
  "wall_s_per_eq": [
    13.225956664002297
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9952197100263935,
      "reward": null,
      "residual_heldout": 0.004431317922546592,
      "pred_coeffs": {
        "u_xx": 0.5000933240286816
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 13.225956664002297,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.225956664002297,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000933240286816
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.006964712726921813 cons=0.0 wall_s=8.515 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006964712726921813,
  "conservation_residual": 0.0,
  "equations": [
    "-D*uxx"
  ],
  "wall_s_total": 8.515144827000768,
  "wall_s_per_eq": [
    8.515144827000768
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-D*uxx",
      "r2_train": 0.9940438835399944,
      "reward": null,
      "residual_heldout": 0.006964712726921813,
      "pred_coeffs": {
        "u_xx": 0.49943300524510675
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.515144827000768,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.515144827000768,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.49943300524510675
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.006442753925637248 cons=0.0 wall_s=7.549 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006442753925637248,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.5488981700000295,
  "wall_s_per_eq": [
    7.5488981700000295
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.994980857114192,
      "reward": null,
      "residual_heldout": 0.006442753925637248,
      "pred_coeffs": {
        "u_xx": 0.49883998608797164
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.5488981700000295,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.5488981700000295,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.49883998608797164
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.004915069559388544 cons=0.0 wall_s=7.431 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004915069559388544,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 7.431163684999774,
  "wall_s_per_eq": [
    7.431163684999774
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9960625137809677,
      "reward": null,
      "residual_heldout": 0.004915069559388544,
      "pred_coeffs": {
        "u_xx": 0.4996165374660934
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 7.431163684999774,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.431163684999774,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4996165374660934
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.005853557039862773 cons=0.0 wall_s=8.803 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005853557039862773,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 8.803070396999829,
  "wall_s_per_eq": [
    8.803070396999829
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.995396348056669,
      "reward": null,
      "residual_heldout": 0.005853557039862773,
      "pred_coeffs": {
        "u_xx": 0.501936202872451
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 8.803070396999829,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.803070396999829,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.501936202872451
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.004200855591333036 cons=0.0 wall_s=15.069 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004200855591333036,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 15.069040874001075,
  "wall_s_per_eq": [
    15.069040874001075
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9945453193440228,
      "reward": null,
      "residual_heldout": 0.004200855591333036,
      "pred_coeffs": {
        "u_xx": 0.5000677486906598
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 15.069040874001075,
      "wall_pad_s": 0.0,
      "wall_raw_s": 15.069040874001075,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5000677486906598
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `diffusion_1d` / N=400 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0052823399915236866 cons=0.0 wall_s=15.224 ok=True

```json
{
  "law": "diffusion_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0052823399915236866,
  "conservation_residual": 0.0,
  "equations": [
    "D*uxx"
  ],
  "wall_s_total": 15.223911645000044,
  "wall_s_per_eq": [
    15.223911645000044
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "D*uxx",
      "r2_train": 0.9939590316585201,
      "reward": null,
      "residual_heldout": 0.0052823399915236866,
      "pred_coeffs": {
        "u_xx": 0.5003900051460632
      },
      "true_coeffs": {
        "u_xx": 0.5
      },
      "structure_ok": true,
      "wall_s": 15.223911645000044,
      "wall_pad_s": 0.0,
      "wall_raw_s": 15.223911645000044,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.5003900051460632
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=7.096016918912071e-11 cons=0.0 wall_s=31.538 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.096016918912071e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux - u_xx*(u*1.56504e-5*u_ux - 0.09999767)"
  ],
  "wall_s_total": 31.538319523999235,
  "wall_s_per_eq": [
    31.538319523999235
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux - u_xx*(u*1.56504e-5*u_ux - 0.09999767)",
      "r2_train": 0.9999999999420136,
      "reward": null,
      "residual_heldout": 7.096016918912071e-11,
      "pred_coeffs": {
        "1": -6.414183731134525e-07,
        "u": 6.357566142396424e-06,
        "u^2": 9.770810054959428e-07,
        "u^3": -6.00953416029831e-07,
        "u_x": 8.386641223713462e-08,
        "u_xx": 0.10000475924419168,
        "u*u_x": -0.9999947664879779
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 31.538319523999235,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=6.197865162218404e-11 cons=0.0 wall_s=8.350 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.197865162218404e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*((u_xx + 0.19999202)*u*(-2.8498023e-5) - 1.2123841e-5) - u_ux + u_xx*0.099998064"
  ],
  "wall_s_total": 8.350061790999462,
  "wall_s_per_eq": [
    8.350061790999462
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*((u_xx + 0.19999202)*u*(-2.8498023e-5) - 1.2123841e-5) - u_ux + u_xx*0.099998064",
      "r2_train": 0.9999999999670913,
      "reward": null,
      "residual_heldout": 6.197865162218404e-11,
      "pred_coeffs": {
        "1": -1.7933300483149309e-06,
        "u": -1.029158151080476e-05,
        "u^2": 3.339325163076329e-07,
        "u^3": 7.004750326601323e-06,
        "u_x": 3.1444804597003607e-07,
        "u_xx": 0.09999570143723155,
        "u*u_x": -0.9999927165116465
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.350061790999462,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=3.416116606554214e-11 cons=0.0 wall_s=8.376 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.416116606554214e-11,
  "conservation_residual": 0.0,
  "equations": [
    "(u_ux*(-0.53312) - (-0.053311262)*u_xx)*(u*u_xx*4.7049223e-5 + 1.8757675)"
  ],
  "wall_s_total": 8.376087685999664,
  "wall_s_per_eq": [
    8.376087685999664
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(u_ux*(-0.53312) - (-0.053311262)*u_xx)*(u*u_xx*4.7049223e-5 + 1.8757675)",
      "r2_train": 0.9999999999860186,
      "reward": null,
      "residual_heldout": 3.416116606554214e-11,
      "pred_coeffs": {
        "1": 4.930881847254641e-07,
        "u": -1.9884757556242666e-06,
        "u^2": 6.804150006738598e-07,
        "u^3": 4.908125075369879e-06,
        "u_x": -4.053465586717854e-07,
        "u_xx": 0.10000148914004942,
        "u*u_x": -0.9999987002834875
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.376087685999664,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=2.423637303110802e-11 cons=0.0 wall_s=8.650 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.423637303110802e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-2.6993623e-5*u_ux*(u*(-u + u_ux) - 1*(-0.3470937)) - u_ux + u_xx*0.09999717"
  ],
  "wall_s_total": 8.650176978000673,
  "wall_s_per_eq": [
    8.650176978000673
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2.6993623e-5*u_ux*(u*(-u + u_ux) - 1*(-0.3470937)) - u_ux + u_xx*0.09999717",
      "r2_train": 0.9999999999770519,
      "reward": null,
      "residual_heldout": 2.423637303110802e-11,
      "pred_coeffs": {
        "u_xx": 0.09999717
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.650176978000673,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=3.298626304596147e-11 cons=0.0 wall_s=8.735 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.298626304596147e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(u*(-2.6583064e-5)*(-u + u_ux) - 1*1.000008) - (-0.09999677)*u_xx"
  ],
  "wall_s_total": 8.735477835998608,
  "wall_s_per_eq": [
    8.735477835998608
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(u*(-2.6583064e-5)*(-u + u_ux) - 1*1.000008) - (-0.09999677)*u_xx",
      "r2_train": 0.9999999999750719,
      "reward": null,
      "residual_heldout": 3.298626304596147e-11,
      "pred_coeffs": {
        "u_xx": 0.09999677
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.735477835998608,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=1.7506710126997825e-11 cons=0.0 wall_s=8.392 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7506710126997825e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(u*(-u + u_ux)*(-3.2224787e-5) - 1.0000113) + u_xx*0.099995814"
  ],
  "wall_s_total": 8.391823330002808,
  "wall_s_per_eq": [
    8.391823330002808
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(u*(-u + u_ux)*(-3.2224787e-5) - 1.0000113) + u_xx*0.099995814",
      "r2_train": 0.9999999999872174,
      "reward": null,
      "residual_heldout": 1.7506710126997825e-11,
      "pred_coeffs": {
        "u_xx": 0.099995814
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.391823330002808,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=7.973413300958008e-12 cons=0.0 wall_s=8.096 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.973413300958008e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u*(-2.6035e-5*u_ux*u_xx - u_x - 9.067729e-6*(u_x + u_x*u_x)) - (-0.09999536)*u_xx"
  ],
  "wall_s_total": 8.095518768997863,
  "wall_s_per_eq": [
    8.095518768997863
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u*(-2.6035e-5*u_ux*u_xx - u_x - 9.067729e-6*(u_x + u_x*u_x)) - (-0.09999536)*u_xx",
      "r2_train": 0.9999999999794905,
      "reward": null,
      "residual_heldout": 7.973413300958008e-12,
      "pred_coeffs": {
        "u*u_x": -1.000009067729
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.095518768997863,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=5.845904213438005e-11 cons=0.0 wall_s=8.546 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.845904213438005e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*((-u + u_ux)*(-3.5527843e-5)*u - 1*1.0000135) - (-0.09999519)*u_xx"
  ],
  "wall_s_total": 8.546046023999224,
  "wall_s_per_eq": [
    8.546046023999224
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*((-u + u_ux)*(-3.5527843e-5)*u - 1*1.0000135) - (-0.09999519)*u_xx",
      "r2_train": 0.9999999999907352,
      "reward": null,
      "residual_heldout": 5.845904213438005e-11,
      "pred_coeffs": {
        "u_xx": 0.09999519
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.546046023999224,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=8.661839494863714e-12 cons=0.0 wall_s=8.403 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.661839494863714e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux*(u_x*8.671948e-6 + 6.8632653e-6) - u_ux + u_xx*(u*(-2.244075e-5)*u_ux - 1*(-0.09999463))"
  ],
  "wall_s_total": 8.402887897002074,
  "wall_s_per_eq": [
    8.402887897002074
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux*(u_x*8.671948e-6 + 6.8632653e-6) - u_ux + u_xx*(u*(-2.244075e-5)*u_ux - 1*(-0.09999463))",
      "r2_train": 0.9999999999933408,
      "reward": null,
      "residual_heldout": 8.661839494863714e-12,
      "pred_coeffs": {
        "u_x*u_ux": -8.671948e-06
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.402887897002074,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=6.549045862766078e-11 cons=0.0 wall_s=8.480 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.549045862766078e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(-2.3062508e-5)*u*u_xx - u_ux + u_ux*(-7.4988025e-6) + u_xx*0.099998"
  ],
  "wall_s_total": 8.479955659000552,
  "wall_s_per_eq": [
    8.479955659000552
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(-2.3062508e-5)*u*u_xx - u_ux + u_ux*(-7.4988025e-6) + u_xx*0.099998",
      "r2_train": 0.9999999999777938,
      "reward": null,
      "residual_heldout": 6.549045862766078e-11,
      "pred_coeffs": {
        "1": -7.063979811746934e-07,
        "u": -2.7572091541365133e-06,
        "u^2": 7.672288152007524e-07,
        "u^3": 3.1143017724175373e-06,
        "u_x": 7.079587503195722e-07,
        "u_xx": 0.10000012757149061,
        "u*u_x": -0.999996549289212
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.479955659000552,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=5.034763977189924e-11 cons=0.0 wall_s=8.374 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.034763977189924e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-2.4127103e-5*u_ux*(u*u_xx + 0.32121682) - u_ux + u_xx*0.099997886"
  ],
  "wall_s_total": 8.373554866000632,
  "wall_s_per_eq": [
    8.373554866000632
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2.4127103e-5*u_ux*(u*u_xx + 0.32121682) - u_ux + u_xx*0.099997886",
      "r2_train": 0.9999999999651434,
      "reward": null,
      "residual_heldout": 5.034763977189924e-11,
      "pred_coeffs": {
        "1": 4.288925296714209e-07,
        "u": 2.2777310737579185e-06,
        "u^2": -1.3041239615611269e-06,
        "u^3": 3.9485285338158524e-06,
        "u_x": -4.7085311309071646e-07,
        "u_xx": 0.1000038748689202,
        "u*u_x": -1.0000018275155405
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.373554866000632,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=4.705767705646712e-11 cons=0.0 wall_s=8.181 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.705767705646712e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(-7.5705157e-6) + (-u_ux - u_xx*(u*2.4064215e-5*u_ux - 0.09999723))"
  ],
  "wall_s_total": 8.181141686000046,
  "wall_s_per_eq": [
    8.181141686000046
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(-7.5705157e-6) + (-u_ux - u_xx*(u*2.4064215e-5*u_ux - 0.09999723))",
      "r2_train": 0.9999999999606641,
      "reward": null,
      "residual_heldout": 4.705767705646712e-11,
      "pred_coeffs": {
        "1": -6.624595596382785e-07,
        "u": -3.185001954624871e-06,
        "u^2": 1.4595673679693156e-06,
        "u^3": 4.341994111517013e-06,
        "u_x": 1.14455588831771e-06,
        "u_xx": 0.09999936070990867,
        "u*u_x": -0.9999944099700074
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.181141686000046,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=3.20225131816239e-11 cons=0.0 wall_s=8.347 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.20225131816239e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(u_xx*u*(-2.0429652e-5) - 1*5.801783e-6) - u_ux - (-0.09999761)*u_xx"
  ],
  "wall_s_total": 8.346945794997737,
  "wall_s_per_eq": [
    8.346945794997737
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(u_xx*u*(-2.0429652e-5) - 1*5.801783e-6) - u_ux - (-0.09999761)*u_xx",
      "r2_train": 0.9999999999785484,
      "reward": null,
      "residual_heldout": 3.20225131816239e-11,
      "pred_coeffs": {
        "1": -2.493449346827676e-07,
        "u": 2.9936149126326446e-06,
        "u^2": 1.694603677589373e-06,
        "u^3": 5.962673720203656e-07,
        "u_x": -1.9344714557011487e-07,
        "u_xx": 0.10000153608218164,
        "u*u_x": -0.9999991086419996
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.346945794997737,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=6.97284764555384e-11 cons=0.0 wall_s=8.501 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.97284764555384e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-(-2.1145053e-5)*u_ux*u_xx*(-u + u_ux) - 1.0000095*u_ux + u_xx*0.09999545"
  ],
  "wall_s_total": 8.501064013998985,
  "wall_s_per_eq": [
    8.501064013998985
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-(-2.1145053e-5)*u_ux*u_xx*(-u + u_ux) - 1.0000095*u_ux + u_xx*0.09999545",
      "r2_train": 0.9999999999591805,
      "reward": null,
      "residual_heldout": 6.97284764555384e-11,
      "pred_coeffs": {
        "1": 1.7326652395242293e-07,
        "u": -5.1291750625839914e-06,
        "u^2": -5.264377949912767e-07,
        "u^3": 8.242080446674097e-06,
        "u_x": -1.9879545693273893e-07,
        "u_xx": 0.0999998957225197,
        "u*u_x": -0.9999975721544612
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.501064013998985,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=6.717227318886137e-11 cons=0.0 wall_s=8.427 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.717227318886137e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000416 + (u + u_ux)*(u*u - 1*0.1807774)*9.901246e-6"
  ],
  "wall_s_total": 8.426788919998216,
  "wall_s_per_eq": [
    8.426788919998216
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000416 + (u + u_ux)*(u*u - 1*0.1807774)*9.901246e-6",
      "r2_train": 0.9999999999717367,
      "reward": null,
      "residual_heldout": 6.717227318886137e-11,
      "pred_coeffs": {
        "u_xx": 0.10000416,
        "u": -1.7899215086404e-06
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.426788919998216,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=2.2019297500785502e-11 cons=0.0 wall_s=8.513 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.2019297500785502e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux - (-0.10000226)*u_xx + (u_x + 0.40557206)*(u_ux*u_x*(-2.9842315e-5) - 1.6020445e-5*u_xx)"
  ],
  "wall_s_total": 8.512653556001169,
  "wall_s_per_eq": [
    8.512653556001169
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux - (-0.10000226)*u_xx + (u_x + 0.40557206)*(u_ux*u_x*(-2.9842315e-5) - 1.6020445e-5*u_xx)",
      "r2_train": 0.9999999999939005,
      "reward": null,
      "residual_heldout": 2.2019297500785502e-11,
      "pred_coeffs": {
        "u_x*u_ux": -1.2103209169718902e-05,
        "u_x*u_xx": -1.6020445e-05
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.512653556001169,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=4.553457989560858e-11 cons=0.0 wall_s=8.060 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.553457989560858e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-1.50030555e-5*u*u_ux*(-u + u_xx) - 1.0000117*u_ux + u_xx*0.099997856"
  ],
  "wall_s_total": 8.060405500000343,
  "wall_s_per_eq": [
    8.060405500000343
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-1.50030555e-5*u*u_ux*(-u + u_xx) - 1.0000117*u_ux + u_xx*0.099997856",
      "r2_train": 0.9999999999619904,
      "reward": null,
      "residual_heldout": 4.553457989560858e-11,
      "pred_coeffs": {
        "1": -7.577980464080265e-07,
        "u": 1.421834052227059e-06,
        "u^2": 1.4464422850239336e-06,
        "u^3": 3.894843114629752e-06,
        "u_x": 1.6761566286965852e-06,
        "u_xx": 0.10000422693310443,
        "u*u_x": -0.9999981713048733
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.060405500000343,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=4.178792617054579e-11 cons=0.0 wall_s=9.408 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.178792617054579e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(-(-3.0596555e-5)*u*(u - u_ux) - 1.1000069) + (u_ux + u_xx)*0.099996604"
  ],
  "wall_s_total": 9.408297054000286,
  "wall_s_per_eq": [
    9.408297054000286
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(-(-3.0596555e-5)*u*(u - u_ux) - 1.1000069) + (u_ux + u_xx)*0.099996604",
      "r2_train": 0.9999999999886385,
      "reward": null,
      "residual_heldout": 4.178792617054579e-11,
      "pred_coeffs": {
        "u_xx": 0.099996604
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.408297054000286,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=2.913118425634998e-11 cons=0.0 wall_s=8.734 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.913118425634998e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.09999574 - ((u_x*(-0.27302876) - (u*u_xx + 0.32293037))*(-2.3905539e-5)*u_ux + u_ux)"
  ],
  "wall_s_total": 8.734366132001014,
  "wall_s_per_eq": [
    8.734366132001014
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.09999574 - ((u_x*(-0.27302876) - (u*u_xx + 0.32293037))*(-2.3905539e-5)*u_ux + u_ux)",
      "r2_train": 0.9999999999739329,
      "reward": null,
      "residual_heldout": 2.913118425634998e-11,
      "pred_coeffs": {
        "u_x*u_ux": -6.5268996703016394e-06
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.734366132001014,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=2.0609256201896157e-11 cons=0.0 wall_s=8.217 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.0609256201896157e-11,
  "conservation_residual": 0.0,
  "equations": [
    "(u_ux + u_xx*(-0.09999739))*((u_x + u_x*u_x)*(-2.1654709e-5) - 0.9999816)"
  ],
  "wall_s_total": 8.216702761001216,
  "wall_s_per_eq": [
    8.216702761001216
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(u_ux + u_xx*(-0.09999739))*((u_x + u_x*u_x)*(-2.1654709e-5) - 0.9999816)",
      "r2_train": 0.9999999999763675,
      "reward": null,
      "residual_heldout": 2.0609256201896157e-11,
      "pred_coeffs": {
        "u_x*u_ux": -2.1654709e-05,
        "u_x*u_xx": 2.1654143812095102e-06
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.216702761001216,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=6.198631835273852e-11 cons=0.0 wall_s=9.526 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.198631835273852e-11,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 9.525537268000335,
  "wall_s_per_eq": [
    9.525537268000335
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9999999998436709,
      "reward": null,
      "residual_heldout": 6.198631835273852e-11,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000147184996257
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.525537268000335,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.525537268000335,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10000147184996257
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=1.8253418081913287e-10 cons=0.0 wall_s=7.604 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.8253418081913287e-10,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 7.6040079800004605,
  "wall_s_per_eq": [
    7.6040079800004605
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9999999998772146,
      "reward": null,
      "residual_heldout": 1.8253418081913287e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000046436665126
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 7.6040079800004605,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6040079800004605,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10000046436665126
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.013461385621638788 cons=0.0 wall_s=8.349 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.013461385621638788,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux + nu*uxx - uxx"
  ],
  "wall_s_total": 8.348980820999714,
  "wall_s_per_eq": [
    8.348980820999714
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux + nu*uxx - uxx",
      "r2_train": 0.9885266936308801,
      "reward": null,
      "residual_heldout": 0.013461385621638788,
      "pred_coeffs": {
        "u*u_x": -1.0977790886362815,
        "u_xx": 0.09777908863628149
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.348980820999714,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.348980820999714,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0977790886362815
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.04824657669672396 cons=0.0 wall_s=8.575 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.04824657669672396,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 8.575330342999223,
  "wall_s_per_eq": [
    8.575330342999223
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9673853290124639,
      "reward": null,
      "residual_heldout": 0.04824657669672396,
      "pred_coeffs": {
        "u*u_x": -1.0718091564860999,
        "u": -0.07180915648609987
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.575330342999223,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.575330342999223,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0718091564860999
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=1.3750413438505153e-10 cons=0.0 wall_s=8.656 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.3750413438505153e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-3*nu*uxx - uux"
  ],
  "wall_s_total": 8.656223108999257,
  "wall_s_per_eq": [
    8.656223108999257
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-3*nu*uxx - uux",
      "r2_train": 0.9999999998768276,
      "reward": null,
      "residual_heldout": 1.3750413438505153e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1000011238532367
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.656223108999257,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.656223108999257,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.0333337079510789
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.010361383605355783 cons=0.0 wall_s=8.480 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.010361383605355783,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*u + 2*u - uux"
  ],
  "wall_s_total": 8.480438181999489,
  "wall_s_per_eq": [
    8.480438181999489
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*u + 2*u - uux",
      "r2_train": 0.9914053580397373,
      "reward": null,
      "residual_heldout": 0.010361383605355783,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10590783783573121
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.480438181999489,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.480438181999489,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0529539189178656
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.007156811493305376 cons=0.0 wall_s=8.663 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007156811493305376,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u - u - uux"
  ],
  "wall_s_total": 8.663136508999742,
  "wall_s_per_eq": [
    8.663136508999742
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u - u - uux",
      "r2_train": 0.9895555530067078,
      "reward": null,
      "residual_heldout": 0.007156811493305376,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10808006283117544
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.663136508999742,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.663136508999742,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8919199371688246
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.09669214246225279 cons=0.0 wall_s=8.487 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.09669214246225279,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux"
  ],
  "wall_s_total": 8.487102177998167,
  "wall_s_per_eq": [
    8.487102177998167
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux",
      "r2_train": 0.9393361190292484,
      "reward": null,
      "residual_heldout": 0.09669214246225279,
      "pred_coeffs": {
        "u*u_x": -0.9668740637685543
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.487102177998167,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.487102177998167,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9668740637685543
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=6.993981391215424e-11 cons=0.0 wall_s=8.447 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 6.993981391215424e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-6*nu*uxx - uux"
  ],
  "wall_s_total": 8.4472498920004,
  "wall_s_per_eq": [
    8.4472498920004
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-6*nu*uxx - uux",
      "r2_train": 0.9999999998995902,
      "reward": null,
      "residual_heldout": 6.993981391215424e-11,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09999920684817655
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.4472498920004,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.4472498920004,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.01666653447469609
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=1.492766765569338e-10 cons=0.0 wall_s=8.667 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.492766765569338e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux"
  ],
  "wall_s_total": 8.667463079997106,
  "wall_s_per_eq": [
    8.667463079997106
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux",
      "r2_train": 0.9999999999233529,
      "reward": null,
      "residual_heldout": 1.492766765569338e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000113577673007
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.667463079997106,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.667463079997106,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.10000113577673007
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=1.8495209978279603e-10 cons=0.0 wall_s=8.855 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.8495209978279603e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux + uxx"
  ],
  "wall_s_total": 8.854770869998902,
  "wall_s_per_eq": [
    8.854770869998902
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux + uxx",
      "r2_train": 0.9999999999123783,
      "reward": null,
      "residual_heldout": 1.8495209978279603e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09999946207386856
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.854770869998902,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.854770869998902,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9000005379261314
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=1.1780132064540075e-10 cons=0.0 wall_s=8.686 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.1780132064540075e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 8.686128460998589,
  "wall_s_per_eq": [
    8.686128460998589
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.9999999998624871,
      "reward": null,
      "residual_heldout": 1.1780132064540075e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000069421165692
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.686128460998589,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.686128460998589,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.100000694211657
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.010844923969370495 cons=0.0 wall_s=8.527 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.010844923969370495,
  "conservation_residual": 0.0,
  "equations": [
    "nu**2*uux + nu*u - uux"
  ],
  "wall_s_total": 8.526694440999563,
  "wall_s_per_eq": [
    8.526694440999563
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu**2*uux + nu*u - uux",
      "r2_train": 0.9887953385120437,
      "reward": null,
      "residual_heldout": 0.010844923969370495,
      "pred_coeffs": {
        "u*u_x": -0.9863909819374211,
        "u": -0.1166576961137965
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.526694440999563,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.526694440999563,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.1166576961137965
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.051997557850899996 cons=0.0 wall_s=8.587 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.051997557850899996,
  "conservation_residual": 0.0,
  "equations": [
    "uux*(1 - nu)"
  ],
  "wall_s_total": 8.587118168001325,
  "wall_s_per_eq": [
    8.587118168001325
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "uux*(1 - nu)",
      "r2_train": 0.9460066180287073,
      "reward": null,
      "residual_heldout": 0.051997557850899996,
      "pred_coeffs": {
        "u*u_x": -0.9069062420146436
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.587118168001325,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.587118168001325,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.9069062420146436
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=1.4046433795386398e-10 cons=0.0 wall_s=8.575 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.4046433795386398e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uxx - uux"
  ],
  "wall_s_total": 8.575134880000405,
  "wall_s_per_eq": [
    8.575134880000405
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uxx - uux",
      "r2_train": 0.9999999998797399,
      "reward": null,
      "residual_heldout": 1.4046433795386398e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000079148138782
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.575134880000405,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.575134880000405,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.05000039574069391
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=1.7601768459161204e-10 cons=0.0 wall_s=8.566 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.7601768459161204e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx*(nu - 1) - uux"
  ],
  "wall_s_total": 8.566061958001228,
  "wall_s_per_eq": [
    8.566061958001228
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx*(nu - 1) - uux",
      "r2_train": 0.9999999998642789,
      "reward": null,
      "residual_heldout": 1.7601768459161204e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09999800843099921
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.566061958001228,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.566061958001228,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8873009057167318
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.07589909496307162 cons=0.0 wall_s=8.316 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.07589909496307162,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uux"
  ],
  "wall_s_total": 8.315667727998516,
  "wall_s_per_eq": [
    8.315667727998516
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uux",
      "r2_train": 0.9419919209016641,
      "reward": null,
      "residual_heldout": 0.07589909496307162,
      "pred_coeffs": {
        "u*u_x": -0.8530531889963687
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.315667727998516,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.315667727998516,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.42652659449818436
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.009069625749044262 cons=0.0 wall_s=8.602 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.009069625749044262,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u + 2*u - uux"
  ],
  "wall_s_total": 8.601923271999112,
  "wall_s_per_eq": [
    8.601923271999112
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u + 2*u - uux",
      "r2_train": 0.9895901668587485,
      "reward": null,
      "residual_heldout": 0.009069625749044262,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10352177574987742
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.601923271999112,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.601923271999112,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.1035217757498774
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.02196773814579811 cons=0.0 wall_s=8.995 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.02196773814579811,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 8.994535843001358,
  "wall_s_per_eq": [
    8.994535843001358
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9357100959553464,
      "reward": null,
      "residual_heldout": 0.02196773814579811,
      "pred_coeffs": {
        "u*u_x": -1.0762744826742943,
        "u": -0.07627448267429426
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.994535843001358,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.994535843001358,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0762744826742943
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=2.1891294413807962e-10 cons=0.0 wall_s=7.906 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.1891294413807962e-10,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 7.906451412000024,
  "wall_s_per_eq": [
    7.906451412000024
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9999999998167994,
      "reward": null,
      "residual_heldout": 2.1891294413807962e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000086205683847
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 7.906451412000024,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.906451412000024,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10000086205683847
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=3.290785721498471e-11 cons=0.0 wall_s=8.523 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.290785721498471e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-(-2.3693092e-5)*u*u_ux*(u*u*u - u_ux) - u_ux + u_xx*0.09999666"
  ],
  "wall_s_total": 8.522616223002842,
  "wall_s_per_eq": [
    8.522616223002842
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-(-2.3693092e-5)*u*u_ux*(u*u*u - u_ux) - u_ux + u_xx*0.09999666",
      "r2_train": 0.999999999974905,
      "reward": null,
      "residual_heldout": 3.290785721498471e-11,
      "pred_coeffs": {
        "u_xx": 0.09999666
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.522616223002842,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=3.586354358028347e-11 cons=0.0 wall_s=9.166 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.586354358028347e-11,
  "conservation_residual": 0.0,
  "equations": [
    "(0.33586875 - (-1)*u*u_xx)*u_ux*(-2.0431806e-5) - u_ux + u_xx*0.0999984"
  ],
  "wall_s_total": 9.165588043000753,
  "wall_s_per_eq": [
    9.165588043000753
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(0.33586875 - (-1)*u*u_xx)*u_ux*(-2.0431806e-5) - u_ux + u_xx*0.0999984",
      "r2_train": 0.9999999999618626,
      "reward": null,
      "residual_heldout": 3.586354358028347e-11,
      "pred_coeffs": {
        "1": -4.5070313322920533e-07,
        "u": 3.410785682677926e-06,
        "u^2": 5.508255116440811e-07,
        "u^3": 3.6693395049718965e-07,
        "u_x": 2.5256435115916595e-08,
        "u_xx": 0.1000039570746365,
        "u*u_x": -1.000000291405793
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.165588043000753,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=4.5127517488131886e-11 cons=0.0 wall_s=8.686 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.5127517488131886e-11,
  "conservation_residual": 0.0,
  "equations": [
    "(u*u_xx + u_x)*u_ux*(-1.2837948e-5) - u_ux - (-1)*0.09999549*u_xx"
  ],
  "wall_s_total": 8.68591789799757,
  "wall_s_per_eq": [
    8.68591789799757
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(u*u_xx + u_x)*u_ux*(-1.2837948e-5) - u_ux - (-1)*0.09999549*u_xx",
      "r2_train": 0.9999999999549022,
      "reward": null,
      "residual_heldout": 4.5127517488131886e-11,
      "pred_coeffs": {
        "u_x*u_ux": -1.2837948e-05
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.68591789799757,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=1.0873686238822926e-11 cons=0.0 wall_s=8.475 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.0873686238822926e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux*(1.1584651e-5 - (-(-3.2091528e-5)*u*u + u_x*(-1.4218688e-5))) - u_ux + u_xx*0.09999634"
  ],
  "wall_s_total": 8.474839807000535,
  "wall_s_per_eq": [
    8.474839807000535
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux*(1.1584651e-5 - (-(-3.2091528e-5)*u*u + u_x*(-1.4218688e-5))) - u_ux + u_xx*0.09999634",
      "r2_train": 0.9999999999929913,
      "reward": null,
      "residual_heldout": 1.0873686238822926e-11,
      "pred_coeffs": {
        "u_x*u_ux": -1.4218688e-05,
        "u_xx": 0.09999634
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.474839807000535,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=2.481565473695229e-11 cons=0.0 wall_s=8.597 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.481565473695229e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(-0.9999862) + u_x*(u_ux*u_x + u_ux)*(-2.0070507e-5) + u_xx*0.09999634"
  ],
  "wall_s_total": 8.597214984998573,
  "wall_s_per_eq": [
    8.597214984998573
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(-0.9999862) + u_x*(u_ux*u_x + u_ux)*(-2.0070507e-5) + u_xx*0.09999634",
      "r2_train": 0.999999999978709,
      "reward": null,
      "residual_heldout": 2.481565473695229e-11,
      "pred_coeffs": {
        "u_x*u_ux": -2.0070507e-05,
        "u_xx": 0.09999634
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.597214984998573,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=7.375271915186308e-12 cons=0.0 wall_s=8.443 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.375271915186308e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux*(u*(-u + u_ux)*3.1548574e-5 - 1*(-1.0831822e-5)) - u_ux + u_xx*0.09999603"
  ],
  "wall_s_total": 8.442809978998412,
  "wall_s_per_eq": [
    8.442809978998412
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux*(u*(-u + u_ux)*3.1548574e-5 - 1*(-1.0831822e-5)) - u_ux + u_xx*0.09999603",
      "r2_train": 0.9999999999862123,
      "reward": null,
      "residual_heldout": 7.375271915186308e-12,
      "pred_coeffs": {
        "u_xx": 0.09999603
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.442809978998412,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=1.9217284076660713e-11 cons=0.0 wall_s=8.398 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.9217284076660713e-11,
  "conservation_residual": 0.0,
  "equations": [
    "(-u_ux + u_xx*0.099997625)*(u_x*(u_x*2.4477618e-5 + 2.0570506e-5) + 0.99998236)"
  ],
  "wall_s_total": 8.397562461002963,
  "wall_s_per_eq": [
    8.397562461002963
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(-u_ux + u_xx*0.099997625)*(u_x*(u_x*2.4477618e-5 + 2.0570506e-5) + 0.99998236)",
      "r2_train": 0.9999999999792846,
      "reward": null,
      "residual_heldout": 1.9217284076660713e-11,
      "pred_coeffs": {
        "u_x*u_ux": -2.0570506e-05,
        "u_x*u_xx": 2.0570017450482502e-06
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.397562461002963,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=2.15839442163828e-11 cons=0.0 wall_s=8.591 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.15839442163828e-11,
  "conservation_residual": 0.0,
  "equations": [
    "(u*u - 1*0.37700152)*3.3033444e-5*u*(u_x + 0.21036494) - (u*u_x - 0.100001544*u_xx)"
  ],
  "wall_s_total": 8.591281993998564,
  "wall_s_per_eq": [
    8.591281993998564
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(u*u - 1*0.37700152)*3.3033444e-5*u*(u_x + 0.21036494) - (u*u_x - 0.100001544*u_xx)",
      "r2_train": 0.9999999999820345,
      "reward": null,
      "residual_heldout": 2.15839442163828e-11,
      "pred_coeffs": {
        "u*u_x": -1.0000124536585988,
        "u_xx": 0.100001544
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.591281993998564,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=2.435930447038837e-11 cons=0.0 wall_s=9.498 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.435930447038837e-11,
  "conservation_residual": 0.0,
  "equations": [
    "(u_x*(-u_x - 0.66043216) - 1*(-0.66043216))*u_ux*2.8400198e-5 - u_ux - (-0.09999625)*u_xx"
  ],
  "wall_s_total": 9.498133231001702,
  "wall_s_per_eq": [
    9.498133231001702
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(u_x*(-u_x - 0.66043216) - 1*(-0.66043216))*u_ux*2.8400198e-5 - u_ux - (-0.09999625)*u_xx",
      "r2_train": 0.9999999999843161,
      "reward": null,
      "residual_heldout": 2.435930447038837e-11,
      "pred_coeffs": {
        "u_x*u_ux": -1.8756404109567682e-05,
        "u_xx": 0.09999625
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.498133231001702,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=3.48496140238201e-11 cons=0.0 wall_s=8.421 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.48496140238201e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_ux*(-9.458021e-6) + u_xx*(u_ux*(-2.5690682e-5)*u + 0.09999754)"
  ],
  "wall_s_total": 8.42057954700067,
  "wall_s_per_eq": [
    8.42057954700067
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_ux*(-9.458021e-6) + u_xx*(u_ux*(-2.5690682e-5)*u + 0.09999754)",
      "r2_train": 0.9999999999578171,
      "reward": null,
      "residual_heldout": 3.48496140238201e-11,
      "pred_coeffs": {
        "1": 5.240127356290226e-07,
        "u": 1.7455568179299056e-06,
        "u^2": -1.094116530704836e-06,
        "u^3": 2.5930103710661194e-06,
        "u_x": 1.1442935609425942e-07,
        "u_xx": 0.10000325202995833,
        "u*u_x": -0.999999291511689
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.42057954700067,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=1.5839626337455253e-11 cons=0.0 wall_s=8.390 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.5839626337455253e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.099995136 - (u_ux - u_x*(u_ux*u_x*(-2.8069859e-5) + (u_ux + u_xx)*(-1.4538379e-5)))"
  ],
  "wall_s_total": 8.390078222000739,
  "wall_s_per_eq": [
    8.390078222000739
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.099995136 - (u_ux - u_x*(u_ux*u_x*(-2.8069859e-5) + (u_ux + u_xx)*(-1.4538379e-5)))",
      "r2_train": 0.9999999999802824,
      "reward": null,
      "residual_heldout": 1.5839626337455253e-11,
      "pred_coeffs": {
        "u_x*u_ux": -1.4538379e-05,
        "u_x*u_xx": -1.4538379e-05
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.390078222000739,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=8.083375790751788e-12 cons=0.0 wall_s=8.950 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.083375790751788e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(u*u*3.265922e-5 + u_x*(-1.3783008e-5) - 1.14448985e-5) - u_ux + u_xx*0.09999603"
  ],
  "wall_s_total": 8.949985270002799,
  "wall_s_per_eq": [
    8.949985270002799
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(u*u*3.265922e-5 + u_x*(-1.3783008e-5) - 1.14448985e-5) - u_ux + u_xx*0.09999603",
      "r2_train": 0.9999999999930784,
      "reward": null,
      "residual_heldout": 8.083375790751788e-12,
      "pred_coeffs": {
        "u_x*u_ux": -1.3783008e-05,
        "u_xx": 0.09999603
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.949985270002799,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=2.2252647823724074e-11 cons=0.0 wall_s=8.153 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.2252647823724074e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(-3.015287e-5*u*(-u + u_ux) - 1.0000094) + u_xx*0.09999629"
  ],
  "wall_s_total": 8.153278746001888,
  "wall_s_per_eq": [
    8.153278746001888
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(-3.015287e-5*u*(-u + u_ux) - 1.0000094) + u_xx*0.09999629",
      "r2_train": 0.9999999999844821,
      "reward": null,
      "residual_heldout": 2.2252647823724074e-11,
      "pred_coeffs": {
        "u_xx": 0.09999629
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.153278746001888,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=4.665173485992215e-11 cons=0.0 wall_s=8.479 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.665173485992215e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-1.8672947e-5*u*(u_ux*(u_ux + u_xx) + 0.295739) - u_ux + u_xx*0.09999038"
  ],
  "wall_s_total": 8.479178232999402,
  "wall_s_per_eq": [
    8.479178232999402
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-1.8672947e-5*u*(u_ux*(u_ux + u_xx) + 0.295739) - u_ux + u_xx*0.09999038",
      "r2_train": 0.9999999999714926,
      "reward": null,
      "residual_heldout": 4.665173485992215e-11,
      "pred_coeffs": {
        "1": 8.864480080726433e-07,
        "u": -8.691920985727152e-06,
        "u^2": -6.775091736745304e-08,
        "u^3": 8.575262777688838e-06,
        "u_x": -1.4043027997412599e-06,
        "u_xx": 0.09999669234422266,
        "u*u_x": -0.999992574979923
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.479178232999402,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=1.4079445303207578e-11 cons=0.0 wall_s=8.330 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.4079445303207578e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*((-u + u_ux)*u*0.29290342 - 1*(-0.09999624))*(-0.00010488342) - u_ux - (-0.09999622)*u_xx"
  ],
  "wall_s_total": 8.330120860999159,
  "wall_s_per_eq": [
    8.330120860999159
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*((-u + u_ux)*u*0.29290342 - 1*(-0.09999624))*(-0.00010488342) - u_ux - (-0.09999622)*u_xx",
      "r2_train": 0.9999999999713024,
      "reward": null,
      "residual_heldout": 1.4079445303207578e-11,
      "pred_coeffs": {
        "u_xx": 0.09999622
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.330120860999159,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=2.260244779687914e-11 cons=0.0 wall_s=8.675 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.260244779687914e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(u_xx*u*(-2.4269206e-5) - 1*8.486542e-6) - u_ux + u_xx*0.09999771"
  ],
  "wall_s_total": 8.674569468999834,
  "wall_s_per_eq": [
    8.674569468999834
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(u_xx*u*(-2.4269206e-5) - 1*8.486542e-6) - u_ux + u_xx*0.09999771",
      "r2_train": 0.9999999999599845,
      "reward": null,
      "residual_heldout": 2.260244779687914e-11,
      "pred_coeffs": {
        "1": 2.6255576802335205e-07,
        "u": 5.228186019206142e-06,
        "u^2": -5.322639354434975e-07,
        "u^3": 2.5203200292797313e-06,
        "u_x": 3.5596258425174737e-07,
        "u_xx": 0.10000606085553916,
        "u*u_x": -1.0000006884895962
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.674569468999834,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=6.951924485492562e-12 cons=0.0 wall_s=8.844 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.951924485492562e-12,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.09999624 - (u_ux*(-u_x + (u*u - 1*0.3383826)*2.6590502)*(-1.2946545e-5) + u_ux)"
  ],
  "wall_s_total": 8.84389920600006,
  "wall_s_per_eq": [
    8.84389920600006
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.09999624 - (u_ux*(-u_x + (u*u - 1*0.3383826)*2.6590502)*(-1.2946545e-5) + u_ux)",
      "r2_train": 0.9999999999898123,
      "reward": null,
      "residual_heldout": 6.951924485492562e-12,
      "pred_coeffs": {
        "u_x*u_ux": -1.2946545e-05,
        "u_xx": 0.09999624
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.84389920600006,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=2.4445630980442896e-11 cons=0.0 wall_s=8.293 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.4445630980442896e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(0.23045446 - u*(u - u_ux - u_ux))*(-1.9821622e-5) - u_ux + u_xx*0.099994995"
  ],
  "wall_s_total": 8.292522526997345,
  "wall_s_per_eq": [
    8.292522526997345
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(0.23045446 - u*(u - u_ux - u_ux))*(-1.9821622e-5) - u_ux + u_xx*0.099994995",
      "r2_train": 0.9999999999767724,
      "reward": null,
      "residual_heldout": 2.4445630980442896e-11,
      "pred_coeffs": {
        "u_xx": 0.099994995
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.292522526997345,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=5.230925896220727e-11 cons=0.0 wall_s=8.730 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.230925896220727e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*u*(-3.3337525e-5)*(-u + u_ux) - u_ux - 1.1542755e-5*u_ux + u_xx*0.09999571"
  ],
  "wall_s_total": 8.730457401001331,
  "wall_s_per_eq": [
    8.730457401001331
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*u*(-3.3337525e-5)*(-u + u_ux) - u_ux - 1.1542755e-5*u_ux + u_xx*0.09999571",
      "r2_train": 0.9999999999845164,
      "reward": null,
      "residual_heldout": 5.230925896220727e-11,
      "pred_coeffs": {
        "u_xx": 0.09999571
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.730457401001331,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=1.3676304313019912e-11 cons=0.0 wall_s=8.531 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.3676304313019912e-11,
  "conservation_residual": 0.0,
  "equations": [
    "u_ux*(-2.5547137e-5*u_x*(u_x - 1*(-0.80249417)) - 0.9999827) + u_xx*0.09999592"
  ],
  "wall_s_total": 8.531416132998856,
  "wall_s_per_eq": [
    8.531416132998856
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_ux*(-2.5547137e-5*u_x*(u_x - 1*(-0.80249417)) - 0.9999827) + u_xx*0.09999592",
      "r2_train": 0.9999999999848165,
      "reward": null,
      "residual_heldout": 1.3676304313019912e-11,
      "pred_coeffs": {
        "u_x*u_ux": -2.050142850269129e-05,
        "u_xx": 0.09999592
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.531416132998856,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=7.866515114579239e-11 cons=0.0 wall_s=10.086 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.866515114579239e-11,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 10.086493945000257,
  "wall_s_per_eq": [
    10.086493945000257
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9999999998893346,
      "reward": null,
      "residual_heldout": 7.866515114579239e-11,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000047496027352
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 10.086493945000257,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.086493945000257,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10000047496027352
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=1.646380085438203e-10 cons=0.0 wall_s=8.526 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.646380085438203e-10,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.526410776001285,
  "wall_s_per_eq": [
    8.526410776001285
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9999999998760718,
      "reward": null,
      "residual_heldout": 1.646380085438203e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09999943178343623
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.526410776001285,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.526410776001285,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.09999943178343623
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.01335106530779238 cons=0.0 wall_s=7.981 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01335106530779238,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux + nu*uxx - uxx"
  ],
  "wall_s_total": 7.980659119002667,
  "wall_s_per_eq": [
    7.980659119002667
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux + nu*uxx - uxx",
      "r2_train": 0.989983773544861,
      "reward": null,
      "residual_heldout": 0.01335106530779238,
      "pred_coeffs": {
        "u*u_x": -1.088297283071549,
        "u_xx": 0.08829728307154894
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 7.980659119002667,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.980659119002667,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.088297283071549
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.034567079731717416 cons=0.0 wall_s=8.531 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.034567079731717416,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 8.530994855002064,
  "wall_s_per_eq": [
    8.530994855002064
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9676430729144395,
      "reward": null,
      "residual_heldout": 0.034567079731717416,
      "pred_coeffs": {
        "u*u_x": -1.0666956911071552,
        "u": -0.06669569110715523
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.530994855002064,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.530994855002064,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0666956911071552
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=1.3038640126358013e-10 cons=0.0 wall_s=8.794 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.3038640126358013e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-3*nu*uxx - uux"
  ],
  "wall_s_total": 8.794241859999602,
  "wall_s_per_eq": [
    8.794241859999602
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-3*nu*uxx - uux",
      "r2_train": 0.9999999998464393,
      "reward": null,
      "residual_heldout": 1.3038640126358013e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09999979191076416
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.794241859999602,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.794241859999602,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.03333326397025472
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.01331312342264837 cons=0.0 wall_s=7.967 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.01331312342264837,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*u + 2*u - uux"
  ],
  "wall_s_total": 7.96650497399969,
  "wall_s_per_eq": [
    7.96650497399969
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*u + 2*u - uux",
      "r2_train": 0.9883529143903829,
      "reward": null,
      "residual_heldout": 0.01331312342264837,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10133099945932278
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 7.96650497399969,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.96650497399969,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0506654997296614
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.007537485044396537 cons=0.0 wall_s=8.516 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007537485044396537,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u - uux"
  ],
  "wall_s_total": 8.516443869997602,
  "wall_s_per_eq": [
    8.516443869997602
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u - uux",
      "r2_train": 0.9912503850022631,
      "reward": null,
      "residual_heldout": 0.007537485044396537,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10854138299946506
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.516443869997602,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.516443869997602,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10854138299946506
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.06779511204857151 cons=0.0 wall_s=7.997 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.06779511204857151,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux"
  ],
  "wall_s_total": 7.99664611299886,
  "wall_s_per_eq": [
    7.99664611299886
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux",
      "r2_train": 0.9490460109849678,
      "reward": null,
      "residual_heldout": 0.06779511204857151,
      "pred_coeffs": {
        "u*u_x": -0.9355850673838104
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 7.99664611299886,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.99664611299886,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9355850673838104
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=1.3599503208634747e-10 cons=0.0 wall_s=8.398 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.3599503208634747e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-6*nu*uxx - uux"
  ],
  "wall_s_total": 8.398389750000206,
  "wall_s_per_eq": [
    8.398389750000206
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-6*nu*uxx - uux",
      "r2_train": 0.9999999998476088,
      "reward": null,
      "residual_heldout": 1.3599503208634747e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09999930107139918
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.398389750000206,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.398389750000206,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.01666655017856653
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=1.2025741704225058e-10 cons=0.0 wall_s=9.240 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.2025741704225058e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux"
  ],
  "wall_s_total": 9.239783826000348,
  "wall_s_per_eq": [
    9.239783826000348
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux",
      "r2_train": 0.9999999998730846,
      "reward": null,
      "residual_heldout": 1.2025741704225058e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000030584357351
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.239783826000348,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.239783826000348,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.10000030584357351
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=1.8930230683162847e-10 cons=0.0 wall_s=8.984 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.8930230683162847e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux + uxx"
  ],
  "wall_s_total": 8.983769737998955,
  "wall_s_per_eq": [
    8.983769737998955
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux + uxx",
      "r2_train": 0.9999999998984326,
      "reward": null,
      "residual_heldout": 1.8930230683162847e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09999928487005072
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.983769737998955,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.983769737998955,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9000007151299493
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=1.2777129814382551e-10 cons=0.0 wall_s=9.595 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.2777129814382551e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 9.595452560999547,
  "wall_s_per_eq": [
    9.595452560999547
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.9999999998875122,
      "reward": null,
      "residual_heldout": 1.2777129814382551e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.0999996162190655
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.595452560999547,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.595452560999547,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0999996162190655
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.008871871204052296 cons=0.0 wall_s=8.856 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008871871204052296,
  "conservation_residual": 0.0,
  "equations": [
    "nu**2*uux + nu*u - uux"
  ],
  "wall_s_total": 8.856021727999178,
  "wall_s_per_eq": [
    8.856021727999178
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu**2*uux + nu*u - uux",
      "r2_train": 0.993828395533677,
      "reward": null,
      "residual_heldout": 0.008871871204052296,
      "pred_coeffs": {
        "u*u_x": -0.9894058115892101,
        "u": -0.10292807396813475
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.856021727999178,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.856021727999178,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.10292807396813475
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.0484614216599608 cons=0.0 wall_s=9.224 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0484614216599608,
  "conservation_residual": 0.0,
  "equations": [
    "2*nu*uux"
  ],
  "wall_s_total": 9.22413608199713,
  "wall_s_per_eq": [
    9.22413608199713
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "2*nu*uux",
      "r2_train": 0.950739936531526,
      "reward": null,
      "residual_heldout": 0.0484614216599608,
      "pred_coeffs": {
        "u*u_x": -0.9233955950046846
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.22413608199713,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.22413608199713,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4616977975023423
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=1.5913917956659313e-10 cons=0.0 wall_s=8.325 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 1.5913917956659313e-10,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uxx - uux"
  ],
  "wall_s_total": 8.324522751001496,
  "wall_s_per_eq": [
    8.324522751001496
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uxx - uux",
      "r2_train": 0.9999999998796903,
      "reward": null,
      "residual_heldout": 1.5913917956659313e-10,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09999982166514587
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.324522751001496,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.324522751001496,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.049999910832572936
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=9.273602343990076e-11 cons=0.0 wall_s=8.645 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 9.273602343990076e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx*(nu - 1) - uux"
  ],
  "wall_s_total": 8.645365714000945,
  "wall_s_per_eq": [
    8.645365714000945
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx*(nu - 1) - uux",
      "r2_train": 0.9999999998168172,
      "reward": null,
      "residual_heldout": 9.273602343990076e-11,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1000007767609719
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.645365714000945,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.645365714000945,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8872973318253408
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.05645097231930522 cons=0.0 wall_s=8.168 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.05645097231930522,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uux"
  ],
  "wall_s_total": 8.168497384001967,
  "wall_s_per_eq": [
    8.168497384001967
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uux",
      "r2_train": 0.9486957298851388,
      "reward": null,
      "residual_heldout": 0.05645097231930522,
      "pred_coeffs": {
        "u*u_x": -0.9100579016359934
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.168497384001967,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.168497384001967,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4550289508179967
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.01156475297872803 cons=0.0 wall_s=8.702 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.01156475297872803,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u + 2*u - uux"
  ],
  "wall_s_total": 8.702289405999181,
  "wall_s_per_eq": [
    8.702289405999181
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u + 2*u - uux",
      "r2_train": 0.9928129067123816,
      "reward": null,
      "residual_heldout": 0.01156475297872803,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.09913560968998736
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.702289405999181,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.702289405999181,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.0991356096899874
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.037082410718609536 cons=0.0 wall_s=8.482 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.037082410718609536,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 8.481553787001758,
  "wall_s_per_eq": [
    8.481553787001758
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9639203048482841,
      "reward": null,
      "residual_heldout": 0.037082410718609536,
      "pred_coeffs": {
        "u*u_x": -1.06705119031969,
        "u": -0.06705119031968998
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.481553787001758,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.481553787001758,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.06705119031969
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=7.459607158174314e-11 cons=0.0 wall_s=8.304 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 7.459607158174314e-11,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.303926222000882,
  "wall_s_per_eq": [
    8.303926222000882
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9999999998897531,
      "reward": null,
      "residual_heldout": 7.459607158174314e-11,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000061864804173
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.303926222000882,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.303926222000882,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10000061864804173
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=3.93227618731804e-12 cons=0.0 wall_s=37.216 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.93227618731804e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.100000024"
  ],
  "wall_s_total": 37.21605733999968,
  "wall_s_per_eq": [
    37.21605733999968
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.100000024",
      "r2_train": 0.9999999999970337,
      "reward": null,
      "residual_heldout": 3.93227618731804e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.100000024
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 37.21605733999968,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=3.247835861195993e-12 cons=0.0 wall_s=9.798 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.247835861195993e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.1000001"
  ],
  "wall_s_total": 9.798308551999071,
  "wall_s_per_eq": [
    9.798308551999071
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.1000001",
      "r2_train": 0.9999999999966043,
      "reward": null,
      "residual_heldout": 3.247835861195993e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.1000001
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.798308551999071,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=3.870965599908467e-12 cons=0.0 wall_s=9.886 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.870965599908467e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.1"
  ],
  "wall_s_total": 9.886409123999329,
  "wall_s_per_eq": [
    9.886409123999329
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.1",
      "r2_train": 0.9999999999960494,
      "reward": null,
      "residual_heldout": 3.870965599908467e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.1
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.886409123999329,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=4.128954417116312e-12 cons=0.0 wall_s=11.260 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.128954417116312e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000008"
  ],
  "wall_s_total": 11.26036705200022,
  "wall_s_per_eq": [
    11.26036705200022
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000008",
      "r2_train": 0.9999999999967463,
      "reward": null,
      "residual_heldout": 4.128954417116312e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000008
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 11.26036705200022,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=2.4380686408464674e-12 cons=0.0 wall_s=9.631 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.4380686408464674e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*(0.09999984 - 1.3773545e-6*u*u_ux)"
  ],
  "wall_s_total": 9.630650723000144,
  "wall_s_per_eq": [
    9.630650723000144
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*(0.09999984 - 1.3773545e-6*u*u_ux)",
      "r2_train": 0.9999999999975179,
      "reward": null,
      "residual_heldout": 2.4380686408464674e-12,
      "pred_coeffs": {
        "1": 1.9647677380338507e-08,
        "u": 2.2326624427557033e-07,
        "u^2": -3.625587312113889e-08,
        "u^3": 1.641500313180296e-07,
        "u_xx": 0.10000028429828005,
        "u*u_x": -0.999999515103055
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.630650723000144,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=3.626904440153641e-12 cons=0.0 wall_s=9.544 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.626904440153641e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09999996"
  ],
  "wall_s_total": 9.543851848000486,
  "wall_s_per_eq": [
    9.543851848000486
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09999996",
      "r2_train": 0.9999999999959668,
      "reward": null,
      "residual_heldout": 3.626904440153641e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09999996
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.543851848000486,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=4.7369991104424145e-12 cons=0.0 wall_s=9.609 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.7369991104424145e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09999999"
  ],
  "wall_s_total": 9.609232572998735,
  "wall_s_per_eq": [
    9.609232572998735
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09999999",
      "r2_train": 0.9999999999961025,
      "reward": null,
      "residual_heldout": 4.7369991104424145e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09999999
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.609232572998735,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=3.2208373406441546e-12 cons=0.0 wall_s=9.567 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.2208373406441546e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000004"
  ],
  "wall_s_total": 9.567010871000093,
  "wall_s_per_eq": [
    9.567010871000093
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000004",
      "r2_train": 0.9999999999964903,
      "reward": null,
      "residual_heldout": 3.2208373406441546e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000004
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.567010871000093,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=3.284453279506823e-12 cons=0.0 wall_s=9.570 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.284453279506823e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.100000024"
  ],
  "wall_s_total": 9.57014353699924,
  "wall_s_per_eq": [
    9.57014353699924
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.100000024",
      "r2_train": 0.999999999996236,
      "reward": null,
      "residual_heldout": 3.284453279506823e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.100000024
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.57014353699924,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=3.4159593267613142e-12 cons=0.0 wall_s=9.517 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.4159593267613142e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000009"
  ],
  "wall_s_total": 9.516896123001061,
  "wall_s_per_eq": [
    9.516896123001061
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000009",
      "r2_train": 0.9999999999962098,
      "reward": null,
      "residual_heldout": 3.4159593267613142e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000009
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.516896123001061,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=4.102023906301205e-12 cons=0.0 wall_s=10.245 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.102023906301205e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000005"
  ],
  "wall_s_total": 10.24461750699993,
  "wall_s_per_eq": [
    10.24461750699993
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000005",
      "r2_train": 0.9999999999957522,
      "reward": null,
      "residual_heldout": 4.102023906301205e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000005
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.24461750699993,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=3.6263469250720536e-12 cons=0.0 wall_s=10.094 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.6263469250720536e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.100000046"
  ],
  "wall_s_total": 10.09384588499961,
  "wall_s_per_eq": [
    10.09384588499961
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.100000046",
      "r2_train": 0.9999999999963403,
      "reward": null,
      "residual_heldout": 3.6263469250720536e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.100000046
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.09384588499961,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=4.158016377373664e-12 cons=0.0 wall_s=10.318 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.158016377373664e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.1"
  ],
  "wall_s_total": 10.317850292998628,
  "wall_s_per_eq": [
    10.317850292998628
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.1",
      "r2_train": 0.9999999999965471,
      "reward": null,
      "residual_heldout": 4.158016377373664e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.1
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.317850292998628,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=3.776342921668042e-12 cons=0.0 wall_s=10.407 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.776342921668042e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000005"
  ],
  "wall_s_total": 10.407356087001972,
  "wall_s_per_eq": [
    10.407356087001972
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000005",
      "r2_train": 0.9999999999965641,
      "reward": null,
      "residual_heldout": 3.776342921668042e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000005
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.407356087001972,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=2.81575247341824e-12 cons=0.0 wall_s=11.062 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.81575247341824e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000003"
  ],
  "wall_s_total": 11.062484158999723,
  "wall_s_per_eq": [
    11.062484158999723
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000003",
      "r2_train": 0.9999999999963047,
      "reward": null,
      "residual_heldout": 2.81575247341824e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000003
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 11.062484158999723,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=2.6243481159089785e-12 cons=0.0 wall_s=9.518 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.6243481159089785e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000001"
  ],
  "wall_s_total": 9.517585501002031,
  "wall_s_per_eq": [
    9.517585501002031
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000001",
      "r2_train": 0.9999999999959868,
      "reward": null,
      "residual_heldout": 2.6243481159089785e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000001
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.517585501002031,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=3.646980657324079e-12 cons=0.0 wall_s=10.420 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.646980657324079e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000004"
  ],
  "wall_s_total": 10.420400634000544,
  "wall_s_per_eq": [
    10.420400634000544
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000004",
      "r2_train": 0.9999999999960926,
      "reward": null,
      "residual_heldout": 3.646980657324079e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000004
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.420400634000544,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=3.71895720773771e-12 cons=0.0 wall_s=9.652 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.71895720773771e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000008"
  ],
  "wall_s_total": 9.651898796997557,
  "wall_s_per_eq": [
    9.651898796997557
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000008",
      "r2_train": 0.9999999999962813,
      "reward": null,
      "residual_heldout": 3.71895720773771e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000008
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.651898796997557,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=4.880769606409274e-12 cons=0.0 wall_s=10.733 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.880769606409274e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.099999994"
  ],
  "wall_s_total": 10.733187710000493,
  "wall_s_per_eq": [
    10.733187710000493
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.099999994",
      "r2_train": 0.9999999999967175,
      "reward": null,
      "residual_heldout": 4.880769606409274e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.099999994
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.733187710000493,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=2.798272421508994e-12 cons=0.0 wall_s=10.052 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.798272421508994e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10000003"
  ],
  "wall_s_total": 10.051938190001238,
  "wall_s_per_eq": [
    10.051938190001238
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10000003",
      "r2_train": 0.9999999999956968,
      "reward": null,
      "residual_heldout": 2.798272421508994e-12,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10000003
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.051938190001238,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=3.938008005126826e-12 cons=0.0 wall_s=8.634 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.938008005126826e-12,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.634120818998781,
  "wall_s_per_eq": [
    8.634120818998781
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9999999999970298,
      "reward": null,
      "residual_heldout": 3.938008005126826e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1000000355612699
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.634120818998781,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.634120818998781,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.1000000355612699
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=3.1986816064817073e-12 cons=0.0 wall_s=8.182 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.1986816064817073e-12,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.181704421000177,
  "wall_s_per_eq": [
    8.181704421000177
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9999999999966032,
      "reward": null,
      "residual_heldout": 3.1986816064817073e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000006772095552
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.181704421000177,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.181704421000177,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10000006772095552
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.01158364806980085 cons=0.0 wall_s=8.102 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01158364806980085,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux + nu*uxx - uxx"
  ],
  "wall_s_total": 8.102239875999658,
  "wall_s_per_eq": [
    8.102239875999658
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux + nu*uxx - uxx",
      "r2_train": 0.9886489930790655,
      "reward": null,
      "residual_heldout": 0.01158364806980085,
      "pred_coeffs": {
        "u*u_x": -1.0963925633233331,
        "u_xx": 0.09639256332333312
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.102239875999658,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.102239875999658,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0963925633233331
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.025368834009465123 cons=0.0 wall_s=9.329 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.025368834009465123,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 9.32888854599878,
  "wall_s_per_eq": [
    9.32888854599878
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9644358627603873,
      "reward": null,
      "residual_heldout": 0.025368834009465123,
      "pred_coeffs": {
        "u*u_x": -1.0692512497505984,
        "u": -0.06925124975059838
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.32888854599878,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.32888854599878,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0692512497505984
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=2.8172692176749886e-12 cons=0.0 wall_s=8.801 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.8172692176749886e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-3*nu*uxx - uux"
  ],
  "wall_s_total": 8.801053365998087,
  "wall_s_per_eq": [
    8.801053365998087
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-3*nu*uxx - uux",
      "r2_train": 0.999999999996733,
      "reward": null,
      "residual_heldout": 2.8172692176749886e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000007816608139
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.801053365998087,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.801053365998087,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.0333333593886938
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.00890119404323679 cons=0.0 wall_s=8.761 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00890119404323679,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*u + 2*u - uux"
  ],
  "wall_s_total": 8.761229646999709,
  "wall_s_per_eq": [
    8.761229646999709
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*u + 2*u - uux",
      "r2_train": 0.9920061945607767,
      "reward": null,
      "residual_heldout": 0.00890119404323679,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10252334845232092
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.761229646999709,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.761229646999709,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0512616742261605
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.010640947189447022 cons=0.0 wall_s=9.008 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.010640947189447022,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u - uux"
  ],
  "wall_s_total": 9.007633252000232,
  "wall_s_per_eq": [
    9.007633252000232
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u - uux",
      "r2_train": 0.9911789152833406,
      "reward": null,
      "residual_heldout": 0.010640947189447022,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10569755324815909
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.007633252000232,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.007633252000232,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10569755324815909
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.050927433114764956 cons=0.0 wall_s=8.415 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.050927433114764956,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux"
  ],
  "wall_s_total": 8.41492345000006,
  "wall_s_per_eq": [
    8.41492345000006
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux",
      "r2_train": 0.9499338003570629,
      "reward": null,
      "residual_heldout": 0.050927433114764956,
      "pred_coeffs": {
        "u*u_x": -0.9091999304099263
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.41492345000006,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.41492345000006,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9091999304099263
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=3.28421874140444e-12 cons=0.0 wall_s=9.949 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.28421874140444e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-6*nu*uxx - uux"
  ],
  "wall_s_total": 9.949159938998491,
  "wall_s_per_eq": [
    9.949159938998491
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-6*nu*uxx - uux",
      "r2_train": 0.9999999999962287,
      "reward": null,
      "residual_heldout": 3.28421874140444e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000002784366077
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.949159938998491,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.949159938998491,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.016666671307276795
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=3.398212187760912e-12 cons=0.0 wall_s=8.537 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.398212187760912e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux"
  ],
  "wall_s_total": 8.5374259909986,
  "wall_s_per_eq": [
    8.5374259909986
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux",
      "r2_train": 0.9999999999962189,
      "reward": null,
      "residual_heldout": 3.398212187760912e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000007531450544
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.5374259909986,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.5374259909986,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.10000007531450544
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=4.117593906125168e-12 cons=0.0 wall_s=8.761 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 4.117593906125168e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux + uxx"
  ],
  "wall_s_total": 8.760643519999576,
  "wall_s_per_eq": [
    8.760643519999576
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux + uxx",
      "r2_train": 0.9999999999957403,
      "reward": null,
      "residual_heldout": 4.117593906125168e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000003630839038
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.760643519999576,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.760643519999576,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8999999636916096
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=3.618796509655952e-12 cons=0.0 wall_s=8.748 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 3.618796509655952e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 8.748167024001305,
  "wall_s_per_eq": [
    8.748167024001305
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.9999999999963048,
      "reward": null,
      "residual_heldout": 3.618796509655952e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000006560831975
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.748167024001305,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.748167024001305,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.1000000656083198
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.006827225351912452 cons=0.0 wall_s=9.514 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006827225351912452,
  "conservation_residual": 0.0,
  "equations": [
    "nu**2*uux + nu*u - uux"
  ],
  "wall_s_total": 9.514091255001404,
  "wall_s_per_eq": [
    9.514091255001404
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu**2*uux + nu*u - uux",
      "r2_train": 0.9915627988365483,
      "reward": null,
      "residual_heldout": 0.006827225351912452,
      "pred_coeffs": {
        "u*u_x": -0.988021737568,
        "u": -0.10944524855835445
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.514091255001404,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.514091255001404,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.10944524855835445
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.05285384581479048 cons=0.0 wall_s=8.343 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.05285384581479048,
  "conservation_residual": 0.0,
  "equations": [
    "2*nu*uux"
  ],
  "wall_s_total": 8.342976931999146,
  "wall_s_per_eq": [
    8.342976931999146
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "2*nu*uux",
      "r2_train": 0.9441451275678971,
      "reward": null,
      "residual_heldout": 0.05285384581479048,
      "pred_coeffs": {
        "u*u_x": -0.9297975013383234
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.342976931999146,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.342976931999146,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.4648987506691617
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=2.8008718273745207e-12 cons=0.0 wall_s=8.569 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.8008718273745207e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uxx - uux"
  ],
  "wall_s_total": 8.568908851000742,
  "wall_s_per_eq": [
    8.568908851000742
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uxx - uux",
      "r2_train": 0.999999999996289,
      "reward": null,
      "residual_heldout": 2.8008718273745207e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1000000464162662
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.568908851000742,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.568908851000742,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.0500000232081331
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=5.780171031152837e-11 cons=0.0 wall_s=8.556 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 5.780171031152837e-11,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx*(nu - 1) - uux"
  ],
  "wall_s_total": 8.55590613700042,
  "wall_s_per_eq": [
    8.55590613700042
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx*(nu - 1) - uux",
      "r2_train": 0.9999999999253757,
      "reward": null,
      "residual_heldout": 5.780171031152837e-11,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000345159390914
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.55590613700042,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.55590613700042,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8872938786065316
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.05176219167447995 cons=0.0 wall_s=8.388 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.05176219167447995,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uux"
  ],
  "wall_s_total": 8.387833147000492,
  "wall_s_per_eq": [
    8.387833147000492
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uux",
      "r2_train": 0.950157728933781,
      "reward": null,
      "residual_heldout": 0.05176219167447995,
      "pred_coeffs": {
        "u*u_x": -0.9378546795241779
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.387833147000492,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.387833147000492,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.46892733976208895
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.009408380889970975 cons=0.0 wall_s=8.841 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.009408380889970975,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u + 2*u - uux"
  ],
  "wall_s_total": 8.841124959999433,
  "wall_s_per_eq": [
    8.841124959999433
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u + 2*u - uux",
      "r2_train": 0.9909289161119179,
      "reward": null,
      "residual_heldout": 0.009408380889970975,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.1063706275129701
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.841124959999433,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.841124959999433,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.10637062751297
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.036137563590248015 cons=0.0 wall_s=9.968 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.036137563590248015,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 9.968225061002158,
  "wall_s_per_eq": [
    9.968225061002158
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.967353721319935,
      "reward": null,
      "residual_heldout": 0.036137563590248015,
      "pred_coeffs": {
        "u*u_x": -1.0729125630695404,
        "u": -0.07291256306954041
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.968225061002158,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.968225061002158,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0729125630695404
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=2.809686974833545e-12 cons=0.0 wall_s=11.186 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 2.809686974833545e-12,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 11.186424767998687,
  "wall_s_per_eq": [
    11.186424767998687
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.9999999999957359,
      "reward": null,
      "residual_heldout": 2.809686974833545e-12,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10000004541985508
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 11.186424767998687,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.186424767998687,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.100000045419855
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.004913145947901584 cons=0.0 wall_s=10.048 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004913145947901584,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.101501"
  ],
  "wall_s_total": 10.047808371000428,
  "wall_s_per_eq": [
    10.047808371000428
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.101501",
      "r2_train": 0.9947905357685043,
      "reward": null,
      "residual_heldout": 0.004913145947901584,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.101501
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.047808371000428,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.004899797079012578 cons=0.0 wall_s=8.758 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004899797079012578,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09574877"
  ],
  "wall_s_total": 8.75823981600115,
  "wall_s_per_eq": [
    8.75823981600115
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09574877",
      "r2_train": 0.9935555560496011,
      "reward": null,
      "residual_heldout": 0.004899797079012578,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09574877
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.75823981600115,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.008595320953881729 cons=0.0 wall_s=9.507 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008595320953881729,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10453847"
  ],
  "wall_s_total": 9.507265405998623,
  "wall_s_per_eq": [
    9.507265405998623
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10453847",
      "r2_train": 0.9964492439056496,
      "reward": null,
      "residual_heldout": 0.008595320953881729,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10453847
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.507265405998623,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.011904163489522265 cons=0.0 wall_s=9.409 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.011904163489522265,
  "conservation_residual": 0.0,
  "equations": [
    "(u*(-0.11448069) - u_ux)*0.89813036"
  ],
  "wall_s_total": 9.409348290999333,
  "wall_s_per_eq": [
    9.409348290999333
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "(u*(-0.11448069) - u_ux)*0.89813036",
      "r2_train": 0.9919162214872183,
      "reward": null,
      "residual_heldout": 0.011904163489522265,
      "pred_coeffs": {
        "u_ux": -0.89813036,
        "u": -0.1028185833227484
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.409348290999333,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.006315879567797757 cons=0.0 wall_s=9.117 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006315879567797757,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.096437775"
  ],
  "wall_s_total": 9.116769435000606,
  "wall_s_per_eq": [
    9.116769435000606
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.096437775",
      "r2_train": 0.9947675379293021,
      "reward": null,
      "residual_heldout": 0.006315879567797757,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.096437775
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.116769435000606,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.007847621759248564 cons=0.0 wall_s=9.626 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007847621759248564,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09449114"
  ],
  "wall_s_total": 9.625560549000511,
  "wall_s_per_eq": [
    9.625560549000511
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09449114",
      "r2_train": 0.993543508809801,
      "reward": null,
      "residual_heldout": 0.007847621759248564,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09449114
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.625560549000511,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.007177497812490837 cons=0.0 wall_s=10.061 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007177497812490837,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09699951"
  ],
  "wall_s_total": 10.061264639000001,
  "wall_s_per_eq": [
    10.061264639000001
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09699951",
      "r2_train": 0.9951281632849087,
      "reward": null,
      "residual_heldout": 0.007177497812490837,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09699951
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.061264639000001,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.005155439315209526 cons=0.0 wall_s=9.610 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005155439315209526,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.1015004"
  ],
  "wall_s_total": 9.609782988001825,
  "wall_s_per_eq": [
    9.609782988001825
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.1015004",
      "r2_train": 0.9952100510497406,
      "reward": null,
      "residual_heldout": 0.005155439315209526,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.1015004
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.609782988001825,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.0059412189985913536 cons=0.0 wall_s=8.372 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0059412189985913536,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09731661"
  ],
  "wall_s_total": 8.371500895998906,
  "wall_s_per_eq": [
    8.371500895998906
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09731661",
      "r2_train": 0.9966204399722642,
      "reward": null,
      "residual_heldout": 0.0059412189985913536,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09731661
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.371500895998906,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.007944443480552519 cons=0.0 wall_s=8.475 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007944443480552519,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + (u_ux*(-u_x) + u_xx)*0.08812191"
  ],
  "wall_s_total": 8.474767210002028,
  "wall_s_per_eq": [
    8.474767210002028
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + (u_ux*(-u_x) + u_xx)*0.08812191",
      "r2_train": 0.9958571772958406,
      "reward": null,
      "residual_heldout": 0.007944443480552519,
      "pred_coeffs": {
        "u_x*u_ux": -0.08812191,
        "u_xx": 0.08812191
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.474767210002028,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.008611368857963512 cons=0.0 wall_s=8.563 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008611368857963512,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09930622"
  ],
  "wall_s_total": 8.562924306999776,
  "wall_s_per_eq": [
    8.562924306999776
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09930622",
      "r2_train": 0.9957449358823001,
      "reward": null,
      "residual_heldout": 0.008611368857963512,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09930622
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.562924306999776,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.026924176344898097 cons=0.0 wall_s=8.617 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.026924176344898097,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10705213"
  ],
  "wall_s_total": 8.617251648000092,
  "wall_s_per_eq": [
    8.617251648000092
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10705213",
      "r2_train": 0.9964354956319413,
      "reward": null,
      "residual_heldout": 0.026924176344898097,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10705213
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.617251648000092,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.005153038496131812 cons=0.0 wall_s=8.279 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005153038496131812,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.097702146 + (u*u_x - u_ux)*(-0.40363315)"
  ],
  "wall_s_total": 8.279018762998021,
  "wall_s_per_eq": [
    8.279018762998021
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.097702146 + (u*u_x - u_ux)*(-0.40363315)",
      "r2_train": 0.9949472365710347,
      "reward": null,
      "residual_heldout": 0.005153038496131812,
      "pred_coeffs": {
        "u*u_x": -0.40363315,
        "u_ux": -0.59636685,
        "u_xx": 0.097702146
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.279018762998021,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.003974601365478963 cons=0.0 wall_s=9.756 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003974601365478963,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10664317"
  ],
  "wall_s_total": 9.75571362899791,
  "wall_s_per_eq": [
    9.75571362899791
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10664317",
      "r2_train": 0.9951830175480513,
      "reward": null,
      "residual_heldout": 0.003974601365478963,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10664317
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.75571362899791,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.008628320587039513 cons=0.0 wall_s=8.683 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008628320587039513,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + (u*u*(u - 0.65246665)*(u + u_xx) - u_xx)*(-0.08969644)"
  ],
  "wall_s_total": 8.683496029996604,
  "wall_s_per_eq": [
    8.683496029996604
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + (u*u*(u - 0.65246665)*(u + u_xx) - u_xx)*(-0.08969644)",
      "r2_train": 0.9948601128390393,
      "reward": null,
      "residual_heldout": 0.008628320587039513,
      "pred_coeffs": {
        "u_ux": -1.0
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.683496029996604,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.0049098451658171754 cons=0.0 wall_s=9.006 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0049098451658171754,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09125533"
  ],
  "wall_s_total": 9.005828968001879,
  "wall_s_per_eq": [
    9.005828968001879
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09125533",
      "r2_train": 0.9949143861854629,
      "reward": null,
      "residual_heldout": 0.0049098451658171754,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09125533
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.005828968001879,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.005416868867102455 cons=0.0 wall_s=8.608 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005416868867102455,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09666625"
  ],
  "wall_s_total": 8.60843633300101,
  "wall_s_per_eq": [
    8.60843633300101
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09666625",
      "r2_train": 0.9956842363177423,
      "reward": null,
      "residual_heldout": 0.005416868867102455,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09666625
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.60843633300101,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.0057432655755513574 cons=0.0 wall_s=8.636 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0057432655755513574,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.101031825"
  ],
  "wall_s_total": 8.63597400999788,
  "wall_s_per_eq": [
    8.63597400999788
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.101031825",
      "r2_train": 0.9931319902260368,
      "reward": null,
      "residual_heldout": 0.0057432655755513574,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.101031825
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.63597400999788,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.003968098726723935 cons=0.0 wall_s=8.587 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003968098726723935,
  "conservation_residual": 0.0,
  "equations": [
    "u_xx*0.09988697 - (u_ux - 1*(-0.010225789))"
  ],
  "wall_s_total": 8.58650249999846,
  "wall_s_per_eq": [
    8.58650249999846
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "u_xx*0.09988697 - (u_ux - 1*(-0.010225789))",
      "r2_train": 0.9956964283210555,
      "reward": null,
      "residual_heldout": 0.003968098726723935,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09988697,
        "1": -0.010225789
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.58650249999846,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=50 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.006799635232174931 cons=0.0 wall_s=8.578 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006799635232174931,
  "conservation_residual": 0.0,
  "equations": [
    "-1*u*0.090689234 - u_ux - u_x*(u_xx*0.057886597 - 0.010844996)"
  ],
  "wall_s_total": 8.578189117000875,
  "wall_s_per_eq": [
    8.578189117000875
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-1*u*0.090689234 - u_ux - u_x*(u_xx*0.057886597 - 0.010844996)",
      "r2_train": 0.997607764056551,
      "reward": null,
      "residual_heldout": 0.006799635232174931,
      "pred_coeffs": {
        "u_x*u_xx": -0.057886597,
        "u_ux": -1.0,
        "u": -0.090689234
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.578189117000875,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0049131450121580765 cons=0.0 wall_s=8.798 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0049131450121580765,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.798408344999189,
  "wall_s_per_eq": [
    8.798408344999189
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9947905360947465,
      "reward": null,
      "residual_heldout": 0.0049131450121580765,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10150096935374728
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.798408344999189,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.798408344999189,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10150096935374728
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.004899776702321838 cons=0.0 wall_s=8.100 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004899776702321838,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.100041167999734,
  "wall_s_per_eq": [
    8.100041167999734
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9935555566528619,
      "reward": null,
      "residual_heldout": 0.004899776702321838,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09574896988393623
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.100041167999734,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.100041167999734,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.09574896988393623
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.08509319430795685 cons=0.0 wall_s=8.352 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.08509319430795685,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux"
  ],
  "wall_s_total": 8.352224434998789,
  "wall_s_per_eq": [
    8.352224434998789
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux",
      "r2_train": 0.9636118054877095,
      "reward": null,
      "residual_heldout": 0.08509319430795685,
      "pred_coeffs": {
        "u*u_x": -1.066951557457502
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.352224434998789,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.352224434998789,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.066951557457502
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.025047656434622693 cons=0.0 wall_s=8.593 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.025047656434622693,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 8.592940978000115,
  "wall_s_per_eq": [
    8.592940978000115
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9492547633703965,
      "reward": null,
      "residual_heldout": 0.025047656434622693,
      "pred_coeffs": {
        "u*u_x": -1.067814678404152,
        "u": -0.067814678404152
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.592940978000115,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.592940978000115,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.067814678404152
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0063158915369675595 cons=0.0 wall_s=8.341 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0063158915369675595,
  "conservation_residual": 0.0,
  "equations": [
    "-3*nu*uxx - uux"
  ],
  "wall_s_total": 8.340891793999617,
  "wall_s_per_eq": [
    8.340891793999617
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-3*nu*uxx - uux",
      "r2_train": 0.9947675384894533,
      "reward": null,
      "residual_heldout": 0.0063158915369675595,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09643797144627422
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.340891793999617,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.340891793999617,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.03214599048209141
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.023017684931963114 cons=0.0 wall_s=10.270 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.023017684931963114,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*u + 2*u - uux"
  ],
  "wall_s_total": 10.270231568996678,
  "wall_s_per_eq": [
    10.270231568996678
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*u + 2*u - uux",
      "r2_train": 0.9802723962645457,
      "reward": null,
      "residual_heldout": 0.023017684931963114,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10497499311041869
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.270231568996678,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.270231568996678,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0524874965552093
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.017904249882417178 cons=0.0 wall_s=10.812 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.017904249882417178,
  "conservation_residual": 0.0,
  "equations": [
    "nu*u - u - uux"
  ],
  "wall_s_total": 10.812160985999071,
  "wall_s_per_eq": [
    10.812160985999071
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*u - u - uux",
      "r2_train": 0.9906102971866534,
      "reward": null,
      "residual_heldout": 0.017904249882417178,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.1083969504356389
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.812160985999071,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.812160985999071,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8916030495643611
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.04929502321011498 cons=0.0 wall_s=11.814 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.04929502321011498,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux"
  ],
  "wall_s_total": 11.813713100000314,
  "wall_s_per_eq": [
    11.813713100000314
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux",
      "r2_train": 0.9334606861184043,
      "reward": null,
      "residual_heldout": 0.04929502321011498,
      "pred_coeffs": {
        "u*u_x": -0.8851705595778216
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 11.813713100000314,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.813713100000314,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8851705595778216
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.005941189853529868 cons=0.0 wall_s=8.949 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005941189853529868,
  "conservation_residual": 0.0,
  "equations": [
    "-6*nu*uxx - uux"
  ],
  "wall_s_total": 8.949457746999542,
  "wall_s_per_eq": [
    8.949457746999542
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-6*nu*uxx - uux",
      "r2_train": 0.996620438711594,
      "reward": null,
      "residual_heldout": 0.005941189853529868,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.0973169204700225
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.949457746999542,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.949457746999542,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.016219486745003748
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.008625677822645998 cons=0.0 wall_s=9.116 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008625677822645998,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(nu*(u + uux - ux) - 2*uxx) - uux"
  ],
  "wall_s_total": 9.11601475200223,
  "wall_s_per_eq": [
    9.11601475200223
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(nu*(u + uux - ux) - 2*uxx) - uux",
      "r2_train": 0.9947751165892881,
      "reward": null,
      "residual_heldout": 0.008625677822645998,
      "pred_coeffs": {
        "u*u_x": -1.0025735393550126,
        "u_xx": 0.1014601272424293,
        "u_x": 0.0025735393550124857,
        "u": -0.0025735393550124857
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.11601475200223,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.11601475200223,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.05073006362121465
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.008611369402925638 cons=0.0 wall_s=8.214 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.008611369402925638,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux + uxx"
  ],
  "wall_s_total": 8.214247341998998,
  "wall_s_per_eq": [
    8.214247341998998
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux + uxx",
      "r2_train": 0.9957449370994186,
      "reward": null,
      "residual_heldout": 0.008611369402925638,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09930611613283913
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.214247341998998,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.214247341998998,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9006938838671609
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.026924632369458308 cons=0.0 wall_s=8.627 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.026924632369458308,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 8.627002512002946,
  "wall_s_per_eq": [
    8.627002512002946
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.996435496423547,
      "reward": null,
      "residual_heldout": 0.026924632369458308,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10705344618926116
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.627002512002946,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.627002512002946,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.1070534461892612
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.010725717937650677 cons=0.0 wall_s=9.992 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.010725717937650677,
  "conservation_residual": 0.0,
  "equations": [
    "nu**2*uux + nu*u - uux"
  ],
  "wall_s_total": 9.9924884869979,
  "wall_s_per_eq": [
    9.9924884869979
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu**2*uux + nu*u - uux",
      "r2_train": 0.9849265990444448,
      "reward": null,
      "residual_heldout": 0.010725717937650677,
      "pred_coeffs": {
        "u*u_x": -0.9882387794139545,
        "u": -0.10844916129710469
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.9924884869979,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.9924884869979,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.10844916129710469
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.03656354537699639 cons=0.0 wall_s=9.333 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.03656354537699639,
  "conservation_residual": 0.0,
  "equations": [
    "uux*(1 - nu)"
  ],
  "wall_s_total": 9.333405555000354,
  "wall_s_per_eq": [
    9.333405555000354
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "uux*(1 - nu)",
      "r2_train": 0.9227502448450956,
      "reward": null,
      "residual_heldout": 0.03656354537699639,
      "pred_coeffs": {
        "u*u_x": -0.9558760050138393
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.333405555000354,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.333405555000354,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.9558760050138393
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0064498889600089915 cons=0.0 wall_s=9.568 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0064498889600089915,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uxx - uux"
  ],
  "wall_s_total": 9.56781196099837,
  "wall_s_per_eq": [
    9.56781196099837
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uxx - uux",
      "r2_train": 0.9921461520100353,
      "reward": null,
      "residual_heldout": 0.0064498889600089915,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09482257651677595
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.56781196099837,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.56781196099837,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.047411288258387974
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.004910584056921398 cons=0.0 wall_s=11.075 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004910584056921398,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx*(nu - 1) - uux"
  ],
  "wall_s_total": 11.075260679001076,
  "wall_s_per_eq": [
    11.075260679001076
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx*(nu - 1) - uux",
      "r2_train": 0.9949143855884038,
      "reward": null,
      "residual_heldout": 0.004910584056921398,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09124776292708796
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 11.075260679001076,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.075260679001076,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.898437243581611
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.04186111603236865 cons=0.0 wall_s=9.687 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.04186111603236865,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uux"
  ],
  "wall_s_total": 9.686877111002104,
  "wall_s_per_eq": [
    9.686877111002104
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uux",
      "r2_train": 0.9247849507551823,
      "reward": null,
      "residual_heldout": 0.04186111603236865,
      "pred_coeffs": {
        "u*u_x": -0.8992485625072903
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.686877111002104,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.686877111002104,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.4496242812536452
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.009765756793313827 cons=0.0 wall_s=9.674 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.009765756793313827,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u + 2*u - uux"
  ],
  "wall_s_total": 9.674456609998742,
  "wall_s_per_eq": [
    9.674456609998742
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u + 2*u - uux",
      "r2_train": 0.9818917131826521,
      "reward": null,
      "residual_heldout": 0.009765756793313827,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.11255535124295779
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.674456609998742,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.674456609998742,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.112555351242958
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.03900461442362427 cons=0.0 wall_s=8.298 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.03900461442362427,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 8.298311422000552,
  "wall_s_per_eq": [
    8.298311422000552
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9662955639122129,
      "reward": null,
      "residual_heldout": 0.03900461442362427,
      "pred_coeffs": {
        "u*u_x": -1.058489322185192,
        "u": -0.058489322185192094
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.298311422000552,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.298311422000552,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.058489322185192
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=50 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0037075093551793767 cons=0.0 wall_s=8.771 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0037075093551793767,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 8.770519157002127,
  "wall_s_per_eq": [
    8.770519157002127
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.9963419510753957,
      "reward": null,
      "residual_heldout": 0.0037075093551793767,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09832780536799457
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.770519157002127,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.770519157002127,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0983278053679946
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.006633996105170705 cons=0.0 wall_s=9.997 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006633996105170705,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09490413"
  ],
  "wall_s_total": 9.996875062999607,
  "wall_s_per_eq": [
    9.996875062999607
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09490413",
      "r2_train": 0.9942929073986174,
      "reward": null,
      "residual_heldout": 0.006633996105170705,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09490413
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.996875062999607,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.006698072446535599 cons=0.0 wall_s=9.599 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006698072446535599,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09573822"
  ],
  "wall_s_total": 9.599026271000184,
  "wall_s_per_eq": [
    9.599026271000184
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09573822",
      "r2_train": 0.9956244797638389,
      "reward": null,
      "residual_heldout": 0.006698072446535599,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09573822
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.599026271000184,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.0039061264260533803 cons=0.0 wall_s=9.252 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0039061264260533803,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.099511616"
  ],
  "wall_s_total": 9.252251772002637,
  "wall_s_per_eq": [
    9.252251772002637
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.099511616",
      "r2_train": 0.9929901268505362,
      "reward": null,
      "residual_heldout": 0.0039061264260533803,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.099511616
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.252251772002637,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.003539218720806094 cons=0.0 wall_s=8.690 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003539218720806094,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.100397356"
  ],
  "wall_s_total": 8.689556180001091,
  "wall_s_per_eq": [
    8.689556180001091
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.100397356",
      "r2_train": 0.9937544038201176,
      "reward": null,
      "residual_heldout": 0.003539218720806094,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.100397356
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.689556180001091,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.0052353639258447505 cons=0.0 wall_s=8.708 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0052353639258447505,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.094620064"
  ],
  "wall_s_total": 8.708409590999509,
  "wall_s_per_eq": [
    8.708409590999509
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.094620064",
      "r2_train": 0.9944934988606747,
      "reward": null,
      "residual_heldout": 0.0052353639258447505,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.094620064
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.708409590999509,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.006669511491661542 cons=0.0 wall_s=9.261 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006669511491661542,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.099584386"
  ],
  "wall_s_total": 9.260810656000103,
  "wall_s_per_eq": [
    9.260810656000103
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.099584386",
      "r2_train": 0.9941437605005302,
      "reward": null,
      "residual_heldout": 0.006669511491661542,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.099584386
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.260810656000103,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.0055676152613688456 cons=0.0 wall_s=9.381 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0055676152613688456,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10391536"
  ],
  "wall_s_total": 9.380822279999848,
  "wall_s_per_eq": [
    9.380822279999848
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10391536",
      "r2_train": 0.9942045651134876,
      "reward": null,
      "residual_heldout": 0.0055676152613688456,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10391536
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.380822279999848,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.004716335447157923 cons=0.0 wall_s=8.906 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004716335447157923,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10134175"
  ],
  "wall_s_total": 8.905561215000489,
  "wall_s_per_eq": [
    8.905561215000489
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10134175",
      "r2_train": 0.9939429562067228,
      "reward": null,
      "residual_heldout": 0.004716335447157923,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10134175
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.905561215000489,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.005521383842575517 cons=0.0 wall_s=8.937 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005521383842575517,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10148547"
  ],
  "wall_s_total": 8.936889748001704,
  "wall_s_per_eq": [
    8.936889748001704
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10148547",
      "r2_train": 0.9948563791080239,
      "reward": null,
      "residual_heldout": 0.005521383842575517,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10148547
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.936889748001704,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.00944149476133688 cons=0.0 wall_s=9.098 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00944149476133688,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09952157"
  ],
  "wall_s_total": 9.09808154199709,
  "wall_s_per_eq": [
    9.09808154199709
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09952157",
      "r2_train": 0.9948322716331107,
      "reward": null,
      "residual_heldout": 0.00944149476133688,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09952157
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.09808154199709,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.0038158572045410067 cons=0.0 wall_s=8.846 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0038158572045410067,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.099027336"
  ],
  "wall_s_total": 8.845561374000681,
  "wall_s_per_eq": [
    8.845561374000681
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.099027336",
      "r2_train": 0.9937313722467415,
      "reward": null,
      "residual_heldout": 0.0038158572045410067,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.099027336
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.845561374000681,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.004085942030167417 cons=0.0 wall_s=8.529 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004085942030167417,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10183715"
  ],
  "wall_s_total": 8.528535574998386,
  "wall_s_per_eq": [
    8.528535574998386
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10183715",
      "r2_train": 0.9953848802437508,
      "reward": null,
      "residual_heldout": 0.004085942030167417,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10183715
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.528535574998386,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.007667274845484109 cons=0.0 wall_s=10.204 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007667274845484109,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09458075"
  ],
  "wall_s_total": 10.204188777999661,
  "wall_s_per_eq": [
    10.204188777999661
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09458075",
      "r2_train": 0.9946547523734822,
      "reward": null,
      "residual_heldout": 0.007667274845484109,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09458075
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.204188777999661,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.007768366267307607 cons=0.0 wall_s=9.183 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007768366267307607,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09368287"
  ],
  "wall_s_total": 9.182935175998864,
  "wall_s_per_eq": [
    9.182935175998864
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09368287",
      "r2_train": 0.9953775600728255,
      "reward": null,
      "residual_heldout": 0.007768366267307607,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09368287
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.182935175998864,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.007299288391140702 cons=0.0 wall_s=9.239 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007299288391140702,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10060423"
  ],
  "wall_s_total": 9.239152501999342,
  "wall_s_per_eq": [
    9.239152501999342
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10060423",
      "r2_train": 0.9950474597410973,
      "reward": null,
      "residual_heldout": 0.007299288391140702,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10060423
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.239152501999342,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.005894681088046217 cons=0.0 wall_s=8.620 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005894681088046217,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.104605"
  ],
  "wall_s_total": 8.619576663997577,
  "wall_s_per_eq": [
    8.619576663997577
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.104605",
      "r2_train": 0.993266272723502,
      "reward": null,
      "residual_heldout": 0.005894681088046217,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.104605
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.619576663997577,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.006221339371649347 cons=0.0 wall_s=10.099 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006221339371649347,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09462111"
  ],
  "wall_s_total": 10.099418319001416,
  "wall_s_per_eq": [
    10.099418319001416
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09462111",
      "r2_train": 0.9956693024063583,
      "reward": null,
      "residual_heldout": 0.006221339371649347,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09462111
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.099418319001416,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.003219089832018862 cons=0.0 wall_s=9.124 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003219089832018862,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10192155"
  ],
  "wall_s_total": 9.123771945000044,
  "wall_s_per_eq": [
    9.123771945000044
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10192155",
      "r2_train": 0.9935942641853354,
      "reward": null,
      "residual_heldout": 0.003219089832018862,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10192155
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.123771945000044,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.004669303164212684 cons=0.0 wall_s=9.276 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004669303164212684,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.099311754"
  ],
  "wall_s_total": 9.275593408001441,
  "wall_s_per_eq": [
    9.275593408001441
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.099311754",
      "r2_train": 0.9945760915034912,
      "reward": null,
      "residual_heldout": 0.004669303164212684,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.099311754
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.275593408001441,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.0075014838283303815 cons=0.0 wall_s=11.005 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0075014838283303815,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.0907933"
  ],
  "wall_s_total": 11.00521026199931,
  "wall_s_per_eq": [
    11.00521026199931
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.0907933",
      "r2_train": 0.9952910077480791,
      "reward": null,
      "residual_heldout": 0.0075014838283303815,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.0907933
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 11.00521026199931,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.006633949877807651 cons=0.0 wall_s=8.689 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006633949877807651,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.689429474001372,
  "wall_s_per_eq": [
    8.689429474001372
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9942929072717313,
      "reward": null,
      "residual_heldout": 0.006633949877807651,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.0949049311434463
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.689429474001372,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.689429474001372,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.0949049311434463
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.006698190898940029 cons=0.0 wall_s=8.199 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006698190898940029,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.19914559999961,
  "wall_s_per_eq": [
    8.19914559999961
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.995624479841684,
      "reward": null,
      "residual_heldout": 0.006698190898940029,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09573578068485886
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.19914559999961,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.19914559999961,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.09573578068485886
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.021122648587003367 cons=0.0 wall_s=8.900 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.021122648587003367,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux + nu*uxx - uxx"
  ],
  "wall_s_total": 8.90009630699933,
  "wall_s_per_eq": [
    8.90009630699933
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux + nu*uxx - uxx",
      "r2_train": 0.9812372543933048,
      "reward": null,
      "residual_heldout": 0.021122648587003367,
      "pred_coeffs": {
        "u*u_x": -1.086820097204329,
        "u_xx": 0.08682009720432893
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.90009630699933,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.90009630699933,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.086820097204329
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.03533942419755907 cons=0.0 wall_s=8.302 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.03533942419755907,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 8.301977692000946,
  "wall_s_per_eq": [
    8.301977692000946
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.957144014671621,
      "reward": null,
      "residual_heldout": 0.03533942419755907,
      "pred_coeffs": {
        "u*u_x": -1.0660362471660754,
        "u": -0.06603624716607537
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.301977692000946,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.301977692000946,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0660362471660754
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0052353691221675895 cons=0.0 wall_s=8.182 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0052353691221675895,
  "conservation_residual": 0.0,
  "equations": [
    "-3*nu*uxx - uux"
  ],
  "wall_s_total": 8.182214495998778,
  "wall_s_per_eq": [
    8.182214495998778
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-3*nu*uxx - uux",
      "r2_train": 0.9944934998428319,
      "reward": null,
      "residual_heldout": 0.0052353691221675895,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09461996531278971
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.182214495998778,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.182214495998778,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.03153998843759657
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.04596981811360051 cons=0.0 wall_s=8.292 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.04596981811360051,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + ux) - uux"
  ],
  "wall_s_total": 8.29184270100086,
  "wall_s_per_eq": [
    8.29184270100086
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + ux) - uux",
      "r2_train": 0.9362806792651698,
      "reward": null,
      "residual_heldout": 0.04596981811360051,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_x": -0.0477286248194146,
        "u": -0.0477286248194146
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.29184270100086,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.29184270100086,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.0477286248194146
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.016991432258874933 cons=0.0 wall_s=8.593 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.016991432258874933,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u - uux"
  ],
  "wall_s_total": 8.592825566000101,
  "wall_s_per_eq": [
    8.592825566000101
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u - uux",
      "r2_train": 0.9828682950425716,
      "reward": null,
      "residual_heldout": 0.016991432258874933,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10882166328778055
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.592825566000101,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.592825566000101,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10882166328778055
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.06152471171163996 cons=0.0 wall_s=8.520 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.06152471171163996,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux"
  ],
  "wall_s_total": 8.520242612001311,
  "wall_s_per_eq": [
    8.520242612001311
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux",
      "r2_train": 0.9422677179419423,
      "reward": null,
      "residual_heldout": 0.06152471171163996,
      "pred_coeffs": {
        "u*u_x": -0.8765196612514763
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.520242612001311,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.520242612001311,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8765196612514763
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.00552137959952097 cons=0.0 wall_s=8.193 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00552137959952097,
  "conservation_residual": 0.0,
  "equations": [
    "-6*nu*uxx - uux"
  ],
  "wall_s_total": 8.193127667000226,
  "wall_s_per_eq": [
    8.193127667000226
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-6*nu*uxx - uux",
      "r2_train": 0.9948563794854526,
      "reward": null,
      "residual_heldout": 0.00552137959952097,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10148534416783578
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.193127667000226,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.193127667000226,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.01691422402797263
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.009441425909831965 cons=0.0 wall_s=8.805 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.009441425909831965,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux"
  ],
  "wall_s_total": 8.805113903003075,
  "wall_s_per_eq": [
    8.805113903003075
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux",
      "r2_train": 0.9948322703840208,
      "reward": null,
      "residual_heldout": 0.009441425909831965,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09952199495581582
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.805113903003075,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.805113903003075,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.09952199495581582
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0038158584707235353 cons=0.0 wall_s=9.954 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0038158584707235353,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux + uxx"
  ],
  "wall_s_total": 9.953588779997517,
  "wall_s_per_eq": [
    9.953588779997517
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux + uxx",
      "r2_train": 0.9937313738963721,
      "reward": null,
      "residual_heldout": 0.0038158584707235353,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09902737849875198
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.953588779997517,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.953588779997517,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.900972621501248
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.004085950531578008 cons=0.0 wall_s=9.047 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004085950531578008,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 9.047405097000592,
  "wall_s_per_eq": [
    9.047405097000592
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.995384882866431,
      "reward": null,
      "residual_heldout": 0.004085950531578008,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10183749570843381
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.047405097000592,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.047405097000592,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.1018374957084338
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.011759215855230116 cons=0.0 wall_s=8.414 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.011759215855230116,
  "conservation_residual": 0.0,
  "equations": [
    "nu**2*uux + nu*u - uux"
  ],
  "wall_s_total": 8.414430734999769,
  "wall_s_per_eq": [
    8.414430734999769
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu**2*uux + nu*u - uux",
      "r2_train": 0.9863768558436234,
      "reward": null,
      "residual_heldout": 0.011759215855230116,
      "pred_coeffs": {
        "u*u_x": -0.9898652156385238,
        "u": -0.10067166613042727
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.414430734999769,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.414430734999769,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.10067166613042727
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.0795524165895354 cons=0.0 wall_s=9.068 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0795524165895354,
  "conservation_residual": 0.0,
  "equations": [
    "2*nu*uux"
  ],
  "wall_s_total": 9.06846729800236,
  "wall_s_per_eq": [
    9.06846729800236
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "2*nu*uux",
      "r2_train": 0.9547044564661333,
      "reward": null,
      "residual_heldout": 0.0795524165895354,
      "pred_coeffs": {
        "u*u_x": -0.936061964630612
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.06846729800236,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.06846729800236,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.468030982315306
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0072992962267123766 cons=0.0 wall_s=8.650 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0072992962267123766,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uxx - uux"
  ],
  "wall_s_total": 8.649986897999042,
  "wall_s_per_eq": [
    8.649986897999042
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uxx - uux",
      "r2_train": 0.9950474585670698,
      "reward": null,
      "residual_heldout": 0.0072992962267123766,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1006046051716606
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.649986897999042,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.649986897999042,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.0503023025858303
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.005894347891178808 cons=0.0 wall_s=8.941 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005894347891178808,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx*(nu - 1) - uux"
  ],
  "wall_s_total": 8.941362986002787,
  "wall_s_per_eq": [
    8.941362986002787
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx*(nu - 1) - uux",
      "r2_train": 0.9932662729982449,
      "reward": null,
      "residual_heldout": 0.005894347891178808,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10460790957574931
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.941362986002787,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.941362986002787,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8813031476715747
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.057336770480601505 cons=0.0 wall_s=8.325 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.057336770480601505,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uux"
  ],
  "wall_s_total": 8.325431646000652,
  "wall_s_per_eq": [
    8.325431646000652
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uux",
      "r2_train": 0.9512304141825568,
      "reward": null,
      "residual_heldout": 0.057336770480601505,
      "pred_coeffs": {
        "u*u_x": -0.9293626190334857
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.325431646000652,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.325431646000652,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.46468130951674286
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.01348312831527072 cons=0.0 wall_s=8.459 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.01348312831527072,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u + 2*u - uux"
  ],
  "wall_s_total": 8.459032040998864,
  "wall_s_per_eq": [
    8.459032040998864
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u + 2*u - uux",
      "r2_train": 0.9826823777783662,
      "reward": null,
      "residual_heldout": 0.01348312831527072,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10417409005930978
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.459032040998864,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.459032040998864,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.1041740900593098
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.044079901751026655 cons=0.0 wall_s=8.643 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.044079901751026655,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 8.64327924600002,
  "wall_s_per_eq": [
    8.64327924600002
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9522947870020223,
      "reward": null,
      "residual_heldout": 0.044079901751026655,
      "pred_coeffs": {
        "u*u_x": -1.0707179233907769,
        "u": -0.07071792339077687
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.64327924600002,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.64327924600002,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0707179233907769
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=100 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.007501513708477582 cons=0.0 wall_s=8.545 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007501513708477582,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 8.545296428997972,
  "wall_s_per_eq": [
    8.545296428997972
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.9952910080777807,
      "reward": null,
      "residual_heldout": 0.007501513708477582,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09079305254672021
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.545296428997972,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.545296428997972,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0907930525467202
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.005945222100765442 cons=0.0 wall_s=11.097 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005945222100765442,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.099173434"
  ],
  "wall_s_total": 11.0971757719999,
  "wall_s_per_eq": [
    11.0971757719999
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.099173434",
      "r2_train": 0.9945797539440159,
      "reward": null,
      "residual_heldout": 0.005945222100765442,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.099173434
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 11.0971757719999,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.004311568377395129 cons=0.0 wall_s=9.396 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004311568377395129,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.099929444"
  ],
  "wall_s_total": 9.39582923800117,
  "wall_s_per_eq": [
    9.39582923800117
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.099929444",
      "r2_train": 0.9953501444365492,
      "reward": null,
      "residual_heldout": 0.004311568377395129,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.099929444
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.39582923800117,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.004928810554606463 cons=0.0 wall_s=9.940 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004928810554606463,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09942652"
  ],
  "wall_s_total": 9.94009506799921,
  "wall_s_per_eq": [
    9.94009506799921
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09942652",
      "r2_train": 0.9942076842417783,
      "reward": null,
      "residual_heldout": 0.004928810554606463,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09942652
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.94009506799921,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.005842259127512067 cons=0.0 wall_s=9.785 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005842259127512067,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10073631"
  ],
  "wall_s_total": 9.785139718998835,
  "wall_s_per_eq": [
    9.785139718998835
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10073631",
      "r2_train": 0.9950376349612233,
      "reward": null,
      "residual_heldout": 0.005842259127512067,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10073631
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.785139718998835,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.005983913726256576 cons=0.0 wall_s=9.454 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005983913726256576,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09636683"
  ],
  "wall_s_total": 9.45449649299917,
  "wall_s_per_eq": [
    9.45449649299917
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09636683",
      "r2_train": 0.9936212130147334,
      "reward": null,
      "residual_heldout": 0.005983913726256576,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09636683
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.45449649299917,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.006023617452597428 cons=0.0 wall_s=10.566 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006023617452597428,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09833365"
  ],
  "wall_s_total": 10.566082331999496,
  "wall_s_per_eq": [
    10.566082331999496
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09833365",
      "r2_train": 0.9946737355430175,
      "reward": null,
      "residual_heldout": 0.006023617452597428,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09833365
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.566082331999496,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.005915483814925921 cons=0.0 wall_s=9.640 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005915483814925921,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + 0.09865667*u_xx"
  ],
  "wall_s_total": 9.640455090000614,
  "wall_s_per_eq": [
    9.640455090000614
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + 0.09865667*u_xx",
      "r2_train": 0.9948876284128362,
      "reward": null,
      "residual_heldout": 0.005915483814925921,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09865667
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.640455090000614,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.005825194549037016 cons=0.0 wall_s=9.539 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005825194549037016,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09492518"
  ],
  "wall_s_total": 9.538563618996704,
  "wall_s_per_eq": [
    9.538563618996704
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09492518",
      "r2_train": 0.9943937222702692,
      "reward": null,
      "residual_heldout": 0.005825194549037016,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09492518
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.538563618996704,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.005795831930159044 cons=0.0 wall_s=9.222 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005795831930159044,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.100461274"
  ],
  "wall_s_total": 9.222137077998923,
  "wall_s_per_eq": [
    9.222137077998923
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.100461274",
      "r2_train": 0.9949765151073687,
      "reward": null,
      "residual_heldout": 0.005795831930159044,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.100461274
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.222137077998923,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.004988687977455612 cons=0.0 wall_s=9.446 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004988687977455612,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09856034"
  ],
  "wall_s_total": 9.446080367000832,
  "wall_s_per_eq": [
    9.446080367000832
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09856034",
      "r2_train": 0.9937473377876729,
      "reward": null,
      "residual_heldout": 0.004988687977455612,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09856034
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.446080367000832,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.005370705927463077 cons=0.0 wall_s=9.834 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005370705927463077,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09848896"
  ],
  "wall_s_total": 9.833674656998483,
  "wall_s_per_eq": [
    9.833674656998483
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09848896",
      "r2_train": 0.9935415731355993,
      "reward": null,
      "residual_heldout": 0.005370705927463077,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09848896
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.833674656998483,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.005407978525955866 cons=0.0 wall_s=10.407 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005407978525955866,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10188676"
  ],
  "wall_s_total": 10.406697859001724,
  "wall_s_per_eq": [
    10.406697859001724
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10188676",
      "r2_train": 0.9954120152351207,
      "reward": null,
      "residual_heldout": 0.005407978525955866,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10188676
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.406697859001724,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.008864675645949073 cons=0.0 wall_s=10.329 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008864675645949073,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10009963"
  ],
  "wall_s_total": 10.329054789999645,
  "wall_s_per_eq": [
    10.329054789999645
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10009963",
      "r2_train": 0.9933431701012099,
      "reward": null,
      "residual_heldout": 0.008864675645949073,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10009963
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.329054789999645,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.004732726876383137 cons=0.0 wall_s=11.011 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004732726876383137,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10013846"
  ],
  "wall_s_total": 11.01108391100206,
  "wall_s_per_eq": [
    11.01108391100206
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10013846",
      "r2_train": 0.9950969976524624,
      "reward": null,
      "residual_heldout": 0.004732726876383137,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10013846
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 11.01108391100206,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.006136255855497046 cons=0.0 wall_s=10.014 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006136255855497046,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09930657"
  ],
  "wall_s_total": 10.01369099799922,
  "wall_s_per_eq": [
    10.01369099799922
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09930657",
      "r2_train": 0.9947834488833404,
      "reward": null,
      "residual_heldout": 0.006136255855497046,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09930657
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.01369099799922,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.00753865656343952 cons=0.0 wall_s=9.859 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00753865656343952,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10071284"
  ],
  "wall_s_total": 9.858754643999418,
  "wall_s_per_eq": [
    9.858754643999418
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10071284",
      "r2_train": 0.9946460173995582,
      "reward": null,
      "residual_heldout": 0.00753865656343952,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10071284
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.858754643999418,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.00553004496040194 cons=0.0 wall_s=9.997 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00553004496040194,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.10173644"
  ],
  "wall_s_total": 9.996874226999353,
  "wall_s_per_eq": [
    9.996874226999353
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.10173644",
      "r2_train": 0.9945580033437003,
      "reward": null,
      "residual_heldout": 0.00553004496040194,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.10173644
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.996874226999353,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.004930561923647135 cons=0.0 wall_s=9.484 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004930561923647135,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09884765"
  ],
  "wall_s_total": 9.483906411001954,
  "wall_s_per_eq": [
    9.483906411001954
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09884765",
      "r2_train": 0.9942123653579851,
      "reward": null,
      "residual_heldout": 0.004930561923647135,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09884765
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.483906411001954,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.005230092163854993 cons=0.0 wall_s=10.101 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005230092163854993,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09810077"
  ],
  "wall_s_total": 10.101341574998514,
  "wall_s_per_eq": [
    10.101341574998514
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09810077",
      "r2_train": 0.9940859532274963,
      "reward": null,
      "residual_heldout": 0.005230092163854993,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09810077
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 10.101341574998514,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `burgers_1d` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.006110987723857336 cons=0.0 wall_s=9.159 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006110987723857336,
  "conservation_residual": 0.0,
  "equations": [
    "-u_ux + u_xx*0.09890448"
  ],
  "wall_s_total": 9.158652701000392,
  "wall_s_per_eq": [
    9.158652701000392
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-u_ux + u_xx*0.09890448",
      "r2_train": 0.9950402185542289,
      "reward": null,
      "residual_heldout": 0.006110987723857336,
      "pred_coeffs": {
        "u_ux": -1.0,
        "u_xx": 0.09890448
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.158652701000392,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.005945190241034287 cons=0.0 wall_s=8.625 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005945190241034287,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.624956139999995,
  "wall_s_per_eq": [
    8.624956139999995
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9945797541412774,
      "reward": null,
      "residual_heldout": 0.005945190241034287,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09917630929714184
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.624956139999995,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.624956139999995,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.09917630929714184
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.00431152141591761 cons=0.0 wall_s=8.685 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.00431152141591761,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.685137313997984,
  "wall_s_per_eq": [
    8.685137313997984
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9953501450799874,
      "reward": null,
      "residual_heldout": 0.00431152141591761,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09992803555289123
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.685137313997984,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.685137313997984,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.09992803555289123
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.01774140974975499 cons=0.0 wall_s=9.915 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.01774140974975499,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux + nu*uxx - uxx"
  ],
  "wall_s_total": 9.915094544001477,
  "wall_s_per_eq": [
    9.915094544001477
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux + nu*uxx - uxx",
      "r2_train": 0.9832591351142393,
      "reward": null,
      "residual_heldout": 0.01774140974975499,
      "pred_coeffs": {
        "u*u_x": -1.0907984537116029,
        "u_xx": 0.09079845371160289
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.915094544001477,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.915094544001477,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0907984537116029
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.036453476797326606 cons=0.0 wall_s=9.098 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.036453476797326606,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 9.098438687000453,
  "wall_s_per_eq": [
    9.098438687000453
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9623326268256132,
      "reward": null,
      "residual_heldout": 0.036453476797326606,
      "pred_coeffs": {
        "u*u_x": -1.0743420223074631,
        "u": -0.07434202230746312
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.098438687000453,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.098438687000453,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0743420223074631
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.005984056730756231 cons=0.0 wall_s=8.303 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005984056730756231,
  "conservation_residual": 0.0,
  "equations": [
    "-3*nu*uxx - uux"
  ],
  "wall_s_total": 8.30286452099972,
  "wall_s_per_eq": [
    8.30286452099972
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-3*nu*uxx - uux",
      "r2_train": 0.9936212130155392,
      "reward": null,
      "residual_heldout": 0.005984056730756231,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09636356003995145
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.30286452099972,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.30286452099972,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.032121186679983815
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.014006244817481738 cons=0.0 wall_s=8.695 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.014006244817481738,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*u + 2*u - uux"
  ],
  "wall_s_total": 8.695068833996629,
  "wall_s_per_eq": [
    8.695068833996629
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*u + 2*u - uux",
      "r2_train": 0.9852644919815147,
      "reward": null,
      "residual_heldout": 0.014006244817481738,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10428465602825021
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.695068833996629,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.695068833996629,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.052142328014125
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.015368675182963263 cons=0.0 wall_s=9.622 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.015368675182963263,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u - uux"
  ],
  "wall_s_total": 9.622088006999547,
  "wall_s_per_eq": [
    9.622088006999547
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u - uux",
      "r2_train": 0.9845162502944091,
      "reward": null,
      "residual_heldout": 0.015368675182963263,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10861248793711
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.622088006999547,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.622088006999547,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.10861248793711
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.06014717728655813 cons=0.0 wall_s=9.454 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.06014717728655813,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uux"
  ],
  "wall_s_total": 9.453742916997726,
  "wall_s_per_eq": [
    9.453742916997726
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uux",
      "r2_train": 0.9489477385225098,
      "reward": null,
      "residual_heldout": 0.06014717728655813,
      "pred_coeffs": {
        "u*u_x": -0.9070043103149453
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.453742916997726,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.453742916997726,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9070043103149453
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.005795824085259038 cons=0.0 wall_s=8.536 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005795824085259038,
  "conservation_residual": 0.0,
  "equations": [
    "-6*nu*uxx - uux"
  ],
  "wall_s_total": 8.535580856001616,
  "wall_s_per_eq": [
    8.535580856001616
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-6*nu*uxx - uux",
      "r2_train": 0.9949765153672022,
      "reward": null,
      "residual_heldout": 0.005795824085259038,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10046148680805869
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.535580856001616,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.535580856001616,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.016743581134676448
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.004955234282686523 cons=0.0 wall_s=8.685 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.004955234282686523,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(nu*(u + uux - ux) - 2*uxx) - uux"
  ],
  "wall_s_total": 8.685201116000826,
  "wall_s_per_eq": [
    8.685201116000826
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(nu*(u + uux - ux) - 2*uxx) - uux",
      "r2_train": 0.9937568787504156,
      "reward": null,
      "residual_heldout": 0.004955234282686523,
      "pred_coeffs": {
        "u*u_x": -1.0023489865391833,
        "u_xx": 0.09693268879347812,
        "u_x": 0.0023489865391833195,
        "u": -0.0023489865391833195
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.685201116000826,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.685201116000826,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.04846634439673906
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.005370535380970081 cons=0.0 wall_s=11.552 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005370535380970081,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux + uxx"
  ],
  "wall_s_total": 11.551947064999695,
  "wall_s_per_eq": [
    11.551947064999695
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux + uxx",
      "r2_train": 0.9935415724370501,
      "reward": null,
      "residual_heldout": 0.005370535380970081,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09849154462147713
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 11.551947064999695,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.551947064999695,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9015084553785229
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.005407978535437972 cons=0.0 wall_s=8.778 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005407978535437972,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx - uux - uxx"
  ],
  "wall_s_total": 8.7778939359996,
  "wall_s_per_eq": [
    8.7778939359996
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx - uux - uxx",
      "r2_train": 0.9954120161710749,
      "reward": null,
      "residual_heldout": 0.005407978535437972,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10188506056364965
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.7778939359996,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.7778939359996,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.1018850605636497
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.01829115116120264 cons=0.0 wall_s=8.700 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.01829115116120264,
  "conservation_residual": 0.0,
  "equations": [
    "nu**2*uux + nu*u - uux"
  ],
  "wall_s_total": 8.699648736001109,
  "wall_s_per_eq": [
    8.699648736001109
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu**2*uux + nu*u - uux",
      "r2_train": 0.9856410793309287,
      "reward": null,
      "residual_heldout": 0.01829115116120264,
      "pred_coeffs": {
        "u*u_x": -0.9881538267111685,
        "u": -0.10884012719962953
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.699648736001109,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.699648736001109,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.10884012719962953
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.060658358741801276 cons=0.0 wall_s=8.804 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.060658358741801276,
  "conservation_residual": 0.0,
  "equations": [
    "uux*(1 - nu)"
  ],
  "wall_s_total": 8.804424153997388,
  "wall_s_per_eq": [
    8.804424153997388
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "uux*(1 - nu)",
      "r2_train": 0.943153794389276,
      "reward": null,
      "residual_heldout": 0.060658358741801276,
      "pred_coeffs": {
        "u*u_x": -0.9170458738408738
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.804424153997388,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.804424153997388,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.9170458738408738
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.006136238169472581 cons=0.0 wall_s=9.519 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006136238169472581,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uxx - uux"
  ],
  "wall_s_total": 9.518623250998644,
  "wall_s_per_eq": [
    9.518623250998644
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uxx - uux",
      "r2_train": 0.99478344905716,
      "reward": null,
      "residual_heldout": 0.006136238169472581,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.09930572268111718
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 9.518623250998644,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.518623250998644,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.04965286134055859
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.007538700839032416 cons=0.0 wall_s=8.575 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.007538700839032416,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*uxx*(nu - 1) - uux"
  ],
  "wall_s_total": 8.574512348001008,
  "wall_s_per_eq": [
    8.574512348001008
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*uxx*(nu - 1) - uux",
      "r2_train": 0.994646017342187,
      "reward": null,
      "residual_heldout": 0.007538700839032416,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.10071462150054022
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.574512348001008,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.574512348001008,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8863746607885405
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.057350251805552706 cons=0.0 wall_s=8.484 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.057350251805552706,
  "conservation_residual": 0.0,
  "equations": [
    "-2*nu*uux"
  ],
  "wall_s_total": 8.483843902002263,
  "wall_s_per_eq": [
    8.483843902002263
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-2*nu*uux",
      "r2_train": 0.9382724913012145,
      "reward": null,
      "residual_heldout": 0.057350251805552706,
      "pred_coeffs": {
        "u*u_x": -0.9302825156865733
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.483843902002263,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.483843902002263,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.46514125784328664
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.014477407155091394 cons=0.0 wall_s=8.268 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.014477407155091394,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*u + 2*u - uux"
  ],
  "wall_s_total": 8.267808594999224,
  "wall_s_per_eq": [
    8.267808594999224
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*u + 2*u - uux",
      "r2_train": 0.9810548372490285,
      "reward": null,
      "residual_heldout": 0.014477407155091394,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u": -0.10697263069903373
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 8.267808594999224,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.267808594999224,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        2.1069726306990337
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.0341210854476927 cons=0.0 wall_s=9.163 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0341210854476927,
  "conservation_residual": 0.0,
  "equations": [
    "-nu*(u + uux) + u"
  ],
  "wall_s_total": 9.162620307000907,
  "wall_s_per_eq": [
    9.162620307000907
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "-nu*(u + uux) + u",
      "r2_train": 0.9655166345471006,
      "reward": null,
      "residual_heldout": 0.0341210854476927,
      "pred_coeffs": {
        "u*u_x": -1.0690603710875128,
        "u": -0.06906037108751284
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": false,
      "wall_s": 9.162620307000907,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.162620307000907,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0690603710875128
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `burgers_1d` / N=400 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.006110988942137651 cons=0.0 wall_s=8.655 ok=True

```json
{
  "law": "burgers_1d",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.006110988942137651,
  "conservation_residual": 0.0,
  "equations": [
    "nu*uxx - uux"
  ],
  "wall_s_total": 8.65509039799872,
  "wall_s_per_eq": [
    8.65509039799872
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "du/dt",
      "equation": "nu*uxx - uux",
      "r2_train": 0.9950402187149695,
      "reward": null,
      "residual_heldout": 0.006110988942137651,
      "pred_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.098904361797495
      },
      "true_coeffs": {
        "u*u_x": -1.0,
        "u_xx": 0.1
      },
      "structure_ok": true,
      "wall_s": 8.65509039799872,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.65509039799872,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.098904361797495
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.179 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.17881826500161,
  "wall_s_per_eq": [
    10.021722392000811,
    10.157095873000799
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.021722392000811,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.157095873000799,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.819 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.819089654996787,
  "wall_s_per_eq": [
    10.306627827998454,
    9.512461826998333
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.306627827998454,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.512461826998333,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.591 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.591477224999835,
  "wall_s_per_eq": [
    9.914152004999778,
    10.677325220000057
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.914152004999778,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.677325220000057,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=21.625 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 21.625490118003654,
  "wall_s_per_eq": [
    9.984519310000906,
    11.640970808002749
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.984519310000906,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 11.640970808002749,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.556 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.556494283002394,
  "wall_s_per_eq": [
    9.64546144900305,
    10.911032833999343
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.64546144900305,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.911032833999343,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.751 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.750540336000995,
  "wall_s_per_eq": [
    9.685716462998244,
    10.064823873002751
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.685716462998244,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.064823873002751,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.873 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.87257792600576,
  "wall_s_per_eq": [
    9.651882361002208,
    10.220695565003552
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.651882361002208,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.220695565003552,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.371 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.37067276000016,
  "wall_s_per_eq": [
    9.98786360700251,
    10.382809152997652
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.98786360700251,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.382809152997652,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.147 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.14733835899824,
  "wall_s_per_eq": [
    9.796362443998078,
    10.350975915000163
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.796362443998078,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.350975915000163,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=22.174 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 22.17393774699667,
  "wall_s_per_eq": [
    10.22251060599956,
    11.951427140997112
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.22251060599956,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 11.951427140997112,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.878 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 18.877906015000917,
  "wall_s_per_eq": [
    8.90268671100057,
    9.975219304000348
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.90268671100057,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.975219304000348,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.671 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 18.67140795299565,
  "wall_s_per_eq": [
    9.20151844299835,
    9.469889509997302
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.20151844299835,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.469889509997302,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.610 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 18.60971333999987,
  "wall_s_per_eq": [
    9.031539170999167,
    9.578174169000704
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.031539170999167,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.578174169000704,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.035 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.034881168998254,
  "wall_s_per_eq": [
    9.051020597999013,
    9.98386057099924
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.051020597999013,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.98386057099924,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.385 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.385008052999183,
  "wall_s_per_eq": [
    10.10124016500049,
    10.283767887998692
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.10124016500049,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.283767887998692,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.697 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.696697571002005,
  "wall_s_per_eq": [
    10.188329148000776,
    9.50836842300123
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.188329148000776,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.50836842300123,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.560 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 18.55956876900018,
  "wall_s_per_eq": [
    9.188106830999459,
    9.37146193800072
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.188106830999459,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.37146193800072,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=21.559 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 21.55855828300264,
  "wall_s_per_eq": [
    9.960793701000512,
    11.597764582002128
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.960793701000512,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 11.597764582002128,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.718 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.717895753001358,
  "wall_s_per_eq": [
    9.80601533600202,
    9.911880416999338
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.80601533600202,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.911880416999338,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.484 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.484078053999838,
  "wall_s_per_eq": [
    9.521766036999907,
    9.962312016999931
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.521766036999907,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.962312016999931,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.813 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.81277190000037,
  "wall_s_per_eq": [
    7.914791717001208,
    7.897980182999163
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.914791717001208,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.914791717001208,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.897980182999163,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.897980182999163,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.572 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.571608148999076,
  "wall_s_per_eq": [
    7.353920851997827,
    7.217687297001248
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.353920851997827,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.353920851997827,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.217687297001248,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.217687297001248,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.623 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.623223556001903,
  "wall_s_per_eq": [
    7.922166697000648,
    7.701056859001255
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999319,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.922166697000648,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.922166697000648,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999979,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.701056859001255,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.701056859001255,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=1.2459539380671176 cons=1.2796748176364732 wall_s=15.180 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.2459539380671176,
  "conservation_residual": 1.2796748176364732,
  "equations": [
    "2*v",
    "invx2*k"
  ],
  "wall_s_total": 15.179833284004417,
  "wall_s_per_eq": [
    7.853297722002026,
    7.326535562002391
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -1.0514810553720393,
      "reward": null,
      "residual_heldout": 2.4919078761342353,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 7.853297722002026,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.853297722002026,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.326535562002391,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.326535562002391,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.184 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 16.18438675499783,
  "wall_s_per_eq": [
    7.962136426998768,
    8.222250327999063
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.962136426998768,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.962136426998768,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.222250327999063,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.222250327999063,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.723 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.722567935998086,
  "wall_s_per_eq": [
    7.558594959999027,
    7.163972975999059
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999981,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.558594959999027,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.558594959999027,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.163972975999059,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.163972975999059,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.931 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 14.930916203000379,
  "wall_s_per_eq": [
    7.459277084999485,
    7.471639118000894
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.459277084999485,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.459277084999485,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.471639118000894,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.471639118000894,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.456 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.456498319003003,
  "wall_s_per_eq": [
    7.046409104001214,
    7.41008921500179
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.046409104001214,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.046409104001214,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.41008921500179,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.41008921500179,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.370 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 16.370250884003326,
  "wall_s_per_eq": [
    7.672312096001406,
    8.69793878800192
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.672312096001406,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.672312096001406,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.69793878800192,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.69793878800192,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.693 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.693118428996968,
  "wall_s_per_eq": [
    7.7731899689970305,
    7.919928459999937
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999983,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.7731899689970305,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.7731899689970305,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.919928459999937,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.919928459999937,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.366 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.366091845000483,
  "wall_s_per_eq": [
    7.172047965999809,
    7.194043879000674
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.172047965999809,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.172047965999809,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.194043879000674,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.194043879000674,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.549 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.549116173002403,
  "wall_s_per_eq": [
    7.397855626000819,
    7.151260547001584
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999983,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.397855626000819,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.397855626000819,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.151260547001584,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.151260547001584,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.923 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.92310174999875,
  "wall_s_per_eq": [
    7.814385898000182,
    8.108715851998568
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.814385898000182,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.814385898000182,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.108715851998568,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.108715851998568,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.699 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 14.698732924000069,
  "wall_s_per_eq": [
    7.337459927999589,
    7.36127299600048
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.337459927999589,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.337459927999589,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.36127299600048,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.36127299600048,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.981 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.980912904004072,
  "wall_s_per_eq": [
    7.810371800002031,
    7.170541104002041
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999982,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.810371800002031,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.810371800002031,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.170541104002041,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.170541104002041,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.604 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 17.60397580999779,
  "wall_s_per_eq": [
    7.459352490997844,
    10.144623318999948
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.459352490997844,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.459352490997844,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.144623318999948,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.144623318999948,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.950 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.950126719002583,
  "wall_s_per_eq": [
    7.6652951130017755,
    8.284831606000807
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.6652951130017755,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6652951130017755,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.284831606000807,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.284831606000807,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.903 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.902859908997925,
  "wall_s_per_eq": [
    8.466563227000734,
    7.436296681997192
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999976,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.466563227000734,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.466563227000734,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.436296681997192,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.436296681997192,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.275 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.275145191000775,
  "wall_s_per_eq": [
    7.083547594000265,
    7.191597597000509
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.999999999999998,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.083547594000265,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.083547594000265,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.191597597000509,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.191597597000509,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.721 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.721171451001283,
  "wall_s_per_eq": [
    8.058305070000642,
    7.66286638100064
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.058305070000642,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.058305070000642,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.66286638100064,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.66286638100064,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.664 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.664082130002498,
  "wall_s_per_eq": [
    9.901533291002124,
    9.762548839000374
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.901533291002124,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.762548839000374,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.151 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.150596939001844,
  "wall_s_per_eq": [
    9.117984231001174,
    10.03261270800067
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.117984231001174,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.03261270800067,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.784 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 18.784468002999347,
  "wall_s_per_eq": [
    9.171380338000745,
    9.613087664998602
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.171380338000745,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.613087664998602,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.823 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.82288174200221,
  "wall_s_per_eq": [
    9.348723464001523,
    10.474158278000687
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.348723464001523,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.474158278000687,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.909 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.90922651699657,
  "wall_s_per_eq": [
    9.93957460999809,
    9.969651906998479
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.93957460999809,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.969651906998479,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.040 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.04028862299674,
  "wall_s_per_eq": [
    9.310292095997283,
    10.729996526999457
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.310292095997283,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.729996526999457,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.675 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.674557577003725,
  "wall_s_per_eq": [
    9.387022770002659,
    10.287534807001066
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.387022770002659,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.287534807001066,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.680 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.67983644099877,
  "wall_s_per_eq": [
    9.026442426998983,
    10.653394013999787
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.026442426998983,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.653394013999787,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.309 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.309198783998,
  "wall_s_per_eq": [
    9.545762719997583,
    9.763436064000416
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.545762719997583,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.763436064000416,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.211 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.21115141500195,
  "wall_s_per_eq": [
    9.481480297999951,
    9.729671117001999
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.481480297999951,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.729671117001999,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.877 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 18.87702238699785,
  "wall_s_per_eq": [
    8.929961446996458,
    9.947060940001393
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.929961446996458,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.947060940001393,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=18.500 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 18.4997484839987,
  "wall_s_per_eq": [
    9.34107866100021,
    9.15866982299849
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.34107866100021,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.15866982299849,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.408 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.40769843000089,
  "wall_s_per_eq": [
    9.160630868998851,
    10.24706756100204
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.160630868998851,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.24706756100204,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.872 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.871789181997883,
  "wall_s_per_eq": [
    10.754652208001062,
    10.117136973996821
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.754652208001062,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.117136973996821,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.816 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.816118298997026,
  "wall_s_per_eq": [
    9.646366726999986,
    10.16975157199704
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.646366726999986,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.16975157199704,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.071 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.071210214995517,
  "wall_s_per_eq": [
    9.122074760998657,
    9.94913545399686
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.122074760998657,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.94913545399686,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.777 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.776518284001213,
  "wall_s_per_eq": [
    9.28907533399979,
    10.487442950001423
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.28907533399979,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.487442950001423,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.507 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.50673046999873,
  "wall_s_per_eq": [
    10.108352716000809,
    9.39837775399792
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.108352716000809,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.39837775399792,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.887 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.88749632100007,
  "wall_s_per_eq": [
    9.754428640000697,
    10.133067680999375
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.754428640000697,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.133067680999375,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.387 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.387328984001215,
  "wall_s_per_eq": [
    10.907317515000614,
    9.480011469000601
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.907317515000614,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.480011469000601,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.027 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.02744401399832,
  "wall_s_per_eq": [
    7.652636545997666,
    7.374807468000654
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.652636545997666,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.652636545997666,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.374807468000654,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.374807468000654,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.911 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.91139233099966,
  "wall_s_per_eq": [
    7.4537993330013705,
    7.45759299799829
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.4537993330013705,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.4537993330013705,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.45759299799829,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.45759299799829,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.281 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.280866900000547,
  "wall_s_per_eq": [
    6.863856534000661,
    7.417010365999886
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999631,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.863856534000661,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.863856534000661,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.417010365999886,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.417010365999886,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=1.1685522549833676 cons=1.5291413982604334 wall_s=15.940 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.1685522549833676,
  "conservation_residual": 1.5291413982604334,
  "equations": [
    "2*v",
    "invx2*k"
  ],
  "wall_s_total": 15.939736101001472,
  "wall_s_per_eq": [
    8.458012899001915,
    7.481723201999557
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.7339907396676957,
      "reward": null,
      "residual_heldout": 2.337104509966735,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.458012899001915,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.458012899001915,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.481723201999557,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.481723201999557,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.176 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.17624095699648,
  "wall_s_per_eq": [
    7.675044035997416,
    7.501196920999064
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.675044035997416,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.675044035997416,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.501196920999064,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.501196920999064,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.759 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 14.758914750000258,
  "wall_s_per_eq": [
    6.938123838001047,
    7.820790911999211
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.938123838001047,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.938123838001047,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.820790911999211,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.820790911999211,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.787 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.787217858000076,
  "wall_s_per_eq": [
    8.069114624999202,
    7.718103233000875
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.069114624999202,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.069114624999202,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.718103233000875,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.718103233000875,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.748 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.7484328549981,
  "wall_s_per_eq": [
    7.277554272000998,
    7.470878582997102
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.277554272000998,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.277554272000998,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.470878582997102,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.470878582997102,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.194 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 16.19442504900144,
  "wall_s_per_eq": [
    8.606427434002399,
    7.58799761499904
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.606427434002399,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.606427434002399,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.58799761499904,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.58799761499904,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.134 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.134161938000034,
  "wall_s_per_eq": [
    7.531255432000762,
    7.602906505999272
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.531255432000762,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.531255432000762,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.602906505999272,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.602906505999272,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.530 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.529791495002428,
  "wall_s_per_eq": [
    6.845390727001359,
    7.684400768001069
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.845390727001359,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.845390727001359,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.684400768001069,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.684400768001069,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.145 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 19.144664799001475,
  "wall_s_per_eq": [
    11.007544839998445,
    8.13711995900303
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 11.007544839998445,
      "wall_pad_s": 0.0,
      "wall_raw_s": 11.007544839998445,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.13711995900303,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.13711995900303,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.002 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.002001009997912,
  "wall_s_per_eq": [
    7.582789225998567,
    7.419211783999344
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.582789225998567,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.582789225998567,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.419211783999344,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.419211783999344,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.510 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.510024493003584,
  "wall_s_per_eq": [
    7.4578476210008375,
    7.052176872002747
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.4578476210008375,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.4578476210008375,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.052176872002747,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.052176872002747,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.099 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.098871014004544,
  "wall_s_per_eq": [
    7.867016269003216,
    7.231854745001328
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.867016269003216,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.867016269003216,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.231854745001328,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.231854745001328,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.926 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.926302979998582,
  "wall_s_per_eq": [
    7.749408192998089,
    7.176894787000492
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.749408192998089,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.749408192998089,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.176894787000492,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.176894787000492,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.478 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 14.477960745000019,
  "wall_s_per_eq": [
    7.594378140001936,
    6.883582604998082
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.594378140001936,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.594378140001936,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 6.883582604998082,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.883582604998082,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.808 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.808087238001463,
  "wall_s_per_eq": [
    7.449765959001525,
    7.358321278999938
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999983,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.449765959001525,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.449765959001525,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.358321278999938,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.358321278999938,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.807 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 14.807167582999682,
  "wall_s_per_eq": [
    6.947738340000797,
    7.8594292429988855
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.947738340000797,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.947738340000797,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.8594292429988855,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.8594292429988855,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.976 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.976493514997856,
  "wall_s_per_eq": [
    7.686570722999022,
    7.289922791998833
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.686570722999022,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.686570722999022,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.289922791998833,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.289922791998833,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=23.923 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 23.92252287500014,
  "wall_s_per_eq": [
    12.81966866899893,
    11.102854206001211
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 12.81966866899893,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 11.102854206001211,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.749 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.749493232997338,
  "wall_s_per_eq": [
    10.301573978998931,
    10.447919253998407
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.301573978998931,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.447919253998407,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.195 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.194654535000154,
  "wall_s_per_eq": [
    9.68173564999961,
    10.512918885000545
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.68173564999961,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.512918885000545,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=3

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.414 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.41363124900454,
  "wall_s_per_eq": [
    9.137930288001371,
    10.275700961003167
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.137930288001371,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.275700961003167,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=22.095 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 22.094513374002418,
  "wall_s_per_eq": [
    10.644877636001183,
    11.449635738001234
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.644877636001183,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 11.449635738001234,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.891 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.89093081000101,
  "wall_s_per_eq": [
    9.284036747001664,
    11.606894062999345
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.284036747001664,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 11.606894062999345,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=21.199 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 21.198648379002407,
  "wall_s_per_eq": [
    10.368997137000406,
    10.829651242002
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.368997137000406,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.829651242002,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=21.467 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 21.466610002997186,
  "wall_s_per_eq": [
    10.858172239997657,
    10.608437762999529
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.858172239997657,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.608437762999529,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.127 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.126782680999895,
  "wall_s_per_eq": [
    9.67682651799987,
    10.449956163000024
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.67682651799987,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.449956163000024,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=21.632 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 21.632392783001706,
  "wall_s_per_eq": [
    10.823864300000423,
    10.808528483001282
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.823864300000423,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.808528483001282,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=22.026 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 22.02582139900187,
  "wall_s_per_eq": [
    11.277929093001148,
    10.747892306000722
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 11.277929093001148,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.747892306000722,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.850 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.850402247000602,
  "wall_s_per_eq": [
    9.449433666002733,
    10.40096858099787
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.449433666002733,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.40096858099787,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.749 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.749136225000257,
  "wall_s_per_eq": [
    9.526309261000279,
    10.222826963999978
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.526309261000279,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.222826963999978,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.306 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.306223135994514,
  "wall_s_per_eq": [
    10.116381467996689,
    10.189841667997825
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.116381467996689,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.189841667997825,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.611 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.61142252099671,
  "wall_s_per_eq": [
    9.31135494299815,
    10.300067577998561
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.31135494299815,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.300067577998561,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.506 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.50569751599687,
  "wall_s_per_eq": [
    9.548295204996975,
    10.957402310999896
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.548295204996975,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.957402310999896,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.212 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.21182045599926,
  "wall_s_per_eq": [
    10.034967577001225,
    10.176852878998034
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.034967577001225,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.176852878998034,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=21.609 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 21.609395890998712,
  "wall_s_per_eq": [
    10.402036408999265,
    11.207359481999447
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.402036408999265,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 11.207359481999447,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=19.866 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 19.86625679500139,
  "wall_s_per_eq": [
    9.687956269001006,
    10.178300526000385
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.687956269001006,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.178300526000385,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=20.204 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-inv_x2"
  ],
  "wall_s_total": 20.203787102000206,
  "wall_s_per_eq": [
    9.395151527001872,
    10.808635574998334
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.395151527001872,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.808635574998334,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.416 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.415695248997508,
  "wall_s_per_eq": [
    7.630533541996556,
    7.7851617070009524
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.630533541996556,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.630533541996556,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.7851617070009524,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.7851617070009524,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.472 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.471635490001063,
  "wall_s_per_eq": [
    7.220631117001176,
    7.251004372999887
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.220631117001176,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.220631117001176,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.251004372999887,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.251004372999887,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.762 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.761948824998399,
  "wall_s_per_eq": [
    7.165293349000422,
    8.596655475997977
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999478,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.165293349000422,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.165293349000422,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.596655475997977,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.596655475997977,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=1.194153468183876 cons=1.081621579283728 wall_s=15.313 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.194153468183876,
  "conservation_residual": 1.081621579283728,
  "equations": [
    "2*v",
    "invx2*k"
  ],
  "wall_s_total": 15.313172001002386,
  "wall_s_per_eq": [
    8.090299931001937,
    7.222872070000449
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.7133804452242467,
      "reward": null,
      "residual_heldout": 2.388306936367752,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.090299931001937,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.090299931001937,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.222872070000449,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.222872070000449,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.390 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.389592807001463,
  "wall_s_per_eq": [
    7.678174915999989,
    7.711417891001474
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.678174915999989,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.678174915999989,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.711417891001474,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.711417891001474,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=5

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.324 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.323633979001897,
  "wall_s_per_eq": [
    7.223756785999285,
    8.099877193002612
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.223756785999285,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.223756785999285,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.999999999999999,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.099877193002612,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.099877193002612,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.269 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 17.26932423800463,
  "wall_s_per_eq": [
    7.628321121002955,
    9.641003117001674
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.628321121002955,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.628321121002955,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.641003117001674,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.641003117001674,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=17.570 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 17.57038376100172,
  "wall_s_per_eq": [
    7.804760122002335,
    9.765623638999386
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.804760122002335,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.804760122002335,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.765623638999386,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.765623638999386,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=8

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=16.268 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 16.267542923000292,
  "wall_s_per_eq": [
    8.167396177999763,
    8.10014674500053
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.167396177999763,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.167396177999763,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.10014674500053,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.10014674500053,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.961 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.960718703001476,
  "wall_s_per_eq": [
    8.252336311001272,
    6.708382392000203
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.252336311001272,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.252336311001272,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 6.708382392000203,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.708382392000203,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.037 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.037167037000472,
  "wall_s_per_eq": [
    6.790913423999882,
    7.24625361300059
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.790913423999882,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.790913423999882,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.24625361300059,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.24625361300059,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.588 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.588148424998508,
  "wall_s_per_eq": [
    7.421957716000179,
    7.166190708998329
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.421957716000179,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.421957716000179,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.166190708998329,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.166190708998329,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=12

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.794 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.793862256003194,
  "wall_s_per_eq": [
    7.385887660002481,
    7.407974596000713
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.385887660002481,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.385887660002481,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.407974596000713,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.407974596000713,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=13

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.568 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.568250583000918,
  "wall_s_per_eq": [
    7.618117085999984,
    6.950133497000934
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.618117085999984,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.618117085999984,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 6.950133497000934,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.950133497000934,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.579 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.57946061199982,
  "wall_s_per_eq": [
    7.622052922000876,
    6.957407689998945
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.622052922000876,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.622052922000876,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 6.957407689998945,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.957407689998945,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=15

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.583 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.58336420699925,
  "wall_s_per_eq": [
    7.926619111000036,
    7.656745095999213
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.926619111000036,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.926619111000036,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.656745095999213,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.656745095999213,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.260 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.260368246003054,
  "wall_s_per_eq": [
    7.479397765000613,
    7.780970481002441
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.479397765000613,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.479397765000613,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9999999999999989,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.780970481002441,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.780970481002441,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.490 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.48958660900098,
  "wall_s_per_eq": [
    7.209818711002299,
    7.279767897998681
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.209818711002299,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.209818711002299,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.279767897998681,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.279767897998681,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=14.118 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.118215605001751,
  "wall_s_per_eq": [
    6.983034632001363,
    7.135180973000388
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999988,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.983034632001363,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.983034632001363,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999984,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.135180973000388,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.135180973000388,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.0 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.0 cons=0.0 wall_s=15.315 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.315099966999696,
  "wall_s_per_eq": [
    7.512249911000254,
    7.802850055999443
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.512249911000254,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.512249911000254,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9999999999999993,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.802850055999443,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.802850055999443,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.11423976034355653 cons=1.1469758358351436 wall_s=17.615 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.11423976034355653,
  "conservation_residual": 1.1469758358351436,
  "equations": [
    "(-v + x)*(x*(0.08936249*v*x + 0.6547055) - 1.0380396)",
    "v*v*v"
  ],
  "wall_s_total": 17.61497856099959,
  "wall_s_per_eq": [
    9.098916391001694,
    8.516062169997895
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(-v + x)*(x*(0.08936249*v*x + 0.6547055) - 1.0380396)",
      "r2_train": 0.9959352100150343,
      "reward": null,
      "residual_heldout": 0.0010633048501163158,
      "pred_coeffs": {
        "x*v": -0.6547055
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 9.098916391001694,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.936959831360973,
      "reward": null,
      "residual_heldout": 0.22741621583699673,
      "pred_coeffs": {
        "v^3": 1.000000000000016
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.516062169997895,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=False residual=0.2751354689773932 cons=0.3989432605783291 wall_s=16.989 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.2751354689773932,
  "conservation_residual": 0.3989432605783291,
  "equations": [
    "v + (x*(-v*x - v) - 1.5145017)*x*(x - 1.472428)*(-0.34148213)",
    "inv_x2*(x - 0.049766082) - inv_x2 - 1.7806777"
  ],
  "wall_s_total": 16.989376616998925,
  "wall_s_per_eq": [
    8.69225823799934,
    8.297118378999585
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + (x*(-v*x - v) - 1.5145017)*x*(x - 1.472428)*(-0.34148213)",
      "r2_train": 0.9988605828476544,
      "reward": null,
      "residual_heldout": 0.011552763434195095,
      "pred_coeffs": {
        "x": -0.7615033431616234
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.69225823799934,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 0.049766082) - inv_x2 - 1.7806777",
      "r2_train": 0.9995602087993137,
      "reward": null,
      "residual_heldout": 0.5387181745205913,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
        "1": -1.7806777
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.297118378999585,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.015334936607809728 cons=5260.227798694594 wall_s=18.386 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.015334936607809728,
  "conservation_residual": 5260.227798694594,
  "equations": [
    "v - x*(x*(v*v*(-0.39681512) - 0.527513) + 0.7963765)",
    "inv_x2*(x - 1.1338351) - 0.88418746"
  ],
  "wall_s_total": 18.386412326002755,
  "wall_s_per_eq": [
    9.197734886001854,
    9.188677440000902
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - x*(x*(v*v*(-0.39681512) - 0.527513) + 0.7963765)",
      "r2_train": 0.9970643189519875,
      "reward": null,
      "residual_heldout": 0.003357129490732854,
      "pred_coeffs": {
        "v": 1.0,
        "x": -0.7963765
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 9.197734886001854,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.1338351) - 0.88418746",
      "r2_train": 0.9889784701605656,
      "reward": null,
      "residual_heldout": 0.027312743724886603,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
        "1": -0.88418746
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.188677440000902,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.2813272073433877 cons=55.696655143872384 wall_s=16.444 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.2813272073433877,
  "conservation_residual": 55.696655143872384,
  "equations": [
    "v - x*(-0.30262932*v*v - 1*0.38082895) - 1*0.57780725",
    "inv_x2*(x - 1*1.0225407) + v"
  ],
  "wall_s_total": 16.44368164199841,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - x*(-0.30262932*v*v - 1*0.38082895) - 1*0.57780725",
      "r2_train": 0.9987991838482547,
      "reward": null,
      "residual_heldout": 0.009243236597525316,
      "pred_coeffs": {
        "1": -0.57780725,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.095059900999331,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.0225407) + v",
      "r2_train": 0.9993887633083156,
      "reward": null,
      "residual_heldout": 0.55341117808925,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
        "v": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.348621740999079,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=False residual=1.0068717151667634 cons=15888084.86925455 wall_s=16.601 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.0068717151667634,
  "conservation_residual": 15888084.86925455,
  "equations": [
    "v + x*(-v + x + x - 3.042033)*0.14034458",
    "v*(inv_x2 + 12.814334)*0.19947231"
  ],
  "wall_s_total": 16.601016243999766,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v + x*(-v + x + x - 3.042033)*0.14034458",
      "r2_train": 0.9973573303159693,
      "reward": null,
      "residual_heldout": 0.010000084841820862,
      "pred_coeffs": {
        "x*v": -0.14034458,
        "x^2": 0.28068916
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.066057271000318,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(inv_x2 + 12.814334)*0.19947231",
      "r2_train": 0.9894824272946003,
      "reward": null,
      "residual_heldout": 2.003743345491706,
      "pred_coeffs": {
        "v*inv_x2": 0.19947231
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.534958972999448,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=False residual=0.44268125972908295 cons=3.0949354244945235 wall_s=19.109 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.44268125972908295,
  "conservation_residual": 3.0949354244945235,
  "equations": [
    "-v*((v - 1*0.8962812)*(-0.38147402)*(x - 1*(-0.39434883)) - 1.8615098)",
    "inv_x2*inv_x2*(-0.05285098) + v"
  ],
  "wall_s_total": 19.109441476004577,
  "wall_s_per_eq": [
    8.736088288002065,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-v*((v - 1*0.8962812)*(-0.38147402)*(x - 1*(-0.39434883)) - 1.8615098)",
      "r2_train": 0.9918369054548498,
      "reward": null,
      "residual_heldout": 0.017633232316371712,
      "pred_coeffs": {
        "x*v": -0.34190799241442404
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.736088288002065,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*inv_x2*(-0.05285098) + v",
      "r2_train": 0.750971077030526,
      "reward": null,
      "residual_heldout": 0.8677292871417942,
      "pred_coeffs": {
        "inv_x2^2": -0.05285098,
        "v": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 10.373353188002511,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.15613487274162127 cons=244.29637748466334 wall_s=19.233 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.15613487274162127,
  "conservation_residual": 244.29637748466334,
  "equations": [
    "v - x*(-v*x*v*0.3568868 + x*(-0.4320768) + 0.6644998)",
    "-inv_x2*(1.065086 - x) - 1.0330925"
  ],
  "wall_s_total": 19.233465557001182,
  "wall_s_per_eq": [
    8.15998881500127,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - x*(-v*x*v*0.3568868 + x*(-0.4320768) + 0.6644998)",
      "r2_train": 0.9992155710666057,
      "reward": null,
      "residual_heldout": 0.005388205027596419,
      "pred_coeffs": {
        "v": 1.0,
        "x": -0.6644998
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.15998881500127,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2*(1.065086 - x) - 1.0330925",
      "r2_train": 0.9996787442952701,
      "reward": null,
      "residual_heldout": 0.30688154045564614,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
        "1": -1.0330925
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 11.073476741999912,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.17875524927038286 cons=1.1733335884433613 wall_s=16.120 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.17875524927038286,
  "conservation_residual": 1.1733335884433613,
  "equations": [
    "v*x*(-0.12296772) + v - 1*0.08005005",
    "v*v*(-1.5835246)"
  ],
  "wall_s_total": 16.119589523001196,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v*x*(-0.12296772) + v - 1*0.08005005",
      "r2_train": 0.9933737620337689,
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        "x*v": -0.12296772,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.30281760700018,
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      "wall_raw_s": null,
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        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*(-1.5835246)",
      "r2_train": 0.5866458330873743,
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        "v^2": -1.5835246
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 7.8167719160010165,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=False residual=0.25736426168699517 cons=1.386158579884307 wall_s=17.011 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.25736426168699517,
  "conservation_residual": 1.386158579884307,
  "equations": [
    "v + (v + x*(v*(-0.5211014) - 0.25907066))*x*(-1.1673777) - 0.76101327",
    "v*v*v"
  ],
  "wall_s_total": 17.0107845120001,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "equation": "v + (v + x*(v*(-0.5211014) - 0.25907066))*x*(-1.1673777) - 0.76101327",
      "r2_train": 0.9915976939318449,
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      "structure_ok": false,
      "wall_s": 7.929471346000355,
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    },
    {
      "eq_i": 1,
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      "wall_s": 9.081313165999745,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=False residual=0.5953715290483022 cons=6.564849079538136 wall_s=17.380 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5953715290483022,
  "conservation_residual": 6.564849079538136,
  "equations": [
    "1.0210239*(v + (-x)*(-x - (-0.33616737*v + (1.1239067 - x)*0.52658296) + 1.3282311))",
    "-inv_x2*(1.0598369 - x) + v"
  ],
  "wall_s_total": 17.379794095999387,
  "wall_s_per_eq": [
    8.045987146000698,
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "1.0210239*(v + (-x)*(-x - (-0.33616737*v + (1.1239067 - x)*0.52658296) + 1.3282311))",
      "r2_train": 0.998163468185607,
      "reward": null,
      "residual_heldout": 0.017456110097849732,
      "pred_coeffs": {
        "x*v": -0.34323491917014304,
        "x^2": 0.483370112507256
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.045987146000698,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2*(1.0598369 - x) + v",
      "r2_train": 0.9994391498648315,
      "reward": null,
      "residual_heldout": 1.1732869479987547,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
        "v": 1.0
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.333806949998689,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=False residual=0.3592624926896748 cons=10.974907884403866 wall_s=17.708 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.3592624926896748,
  "conservation_residual": 10.974907884403866,
  "equations": [
    "x*inv_x2*(-0.0048289383) + v - x*(0.37221444 + x*(-0.20593153)) + 0.1121338",
    "inv_x2*(x - 1.0394561) + v"
  ],
  "wall_s_total": 17.7083131540021,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*inv_x2*(-0.0048289383) + v - x*(0.37221444 + x*(-0.20593153)) + 0.1121338",
      "r2_train": 0.9989733470730799,
      "reward": null,
      "residual_heldout": 0.014496877498968887,
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        "x*inv_x2": -0.0048289383,
        "x^2": 0.20593153,
        "1": 0.1121338,
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      "true_coeffs": {
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      },
      "structure_ok": true,
      "wall_s": 8.938252359999751,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.0394561) + v",
      "r2_train": 0.9993699142228529,
      "reward": null,
      "residual_heldout": 0.7040281078803807,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
        "v": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.770060794002347,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=False residual=0.4306644923305892 cons=564490965.6183903 wall_s=16.666 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.4306644923305892,
  "conservation_residual": 564490965.6183903,
  "equations": [
    "v - ((v - 0.19183502)*x*(-0.679588)*v - x) - 1.5395737",
    "inv_x2*(x - 1.5447351)"
  ],
  "wall_s_total": 16.665606227001263,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - ((v - 0.19183502)*x*(-0.679588)*v - x) - 1.5395737",
      "r2_train": 0.9945384538906669,
      "reward": null,
      "residual_heldout": 0.009445546835609116,
      "pred_coeffs": {
        "x*v": -0.13036877757176,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 7.799900070000149,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.5447351)",
      "r2_train": 0.7742420868006248,
      "reward": null,
      "residual_heldout": 0.8518834378255692,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.865706157001114,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=False residual=0.9385220605219288 cons=6.054554082875567 wall_s=16.870 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.9385220605219288,
  "conservation_residual": 6.054554082875567,
  "equations": [
    "(x*0.43852445*x + (-v + x)*(x - 1*2.2638338))*0.44924307",
    "inv_x2*(x - 0.99637264) + v"
  ],
  "wall_s_total": 16.87015127900304,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(x*0.43852445*x + (-v + x)*(x - 1*2.2638338))*0.44924307",
      "r2_train": 0.9986857100919965,
      "reward": null,
      "residual_heldout": 0.00851538723564009,
      "pred_coeffs": {
        "x*v": -0.44924307,
        "x^2": 0.6462471401880615
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.458154103002016,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 0.99637264) + v",
      "r2_train": 0.9996707785842698,
      "reward": null,
      "residual_heldout": 1.8685287338082175,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
        "v": 1.0
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.411997176001023,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=False residual=0.4918726684602733 cons=17.693925434161997 wall_s=17.281 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.4918726684602733,
  "conservation_residual": 17.693925434161997,
  "equations": [
    "inv_x2*(-0.0066430974) + v*0.7401116 - (-0.45159325)*x - 0.67977226",
    "inv_x2*(x - 1*1.1675404) - 1*1.2265713"
  ],
  "wall_s_total": 17.281149329999607,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "inv_x2*(-0.0066430974) + v*0.7401116 - (-0.45159325)*x - 0.67977226",
      "r2_train": 0.9953030938088001,
      "reward": null,
      "residual_heldout": 0.01278449465935778,
      "pred_coeffs": {
        "inv_x2": -0.0066430974,
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        "v": 0.7401116,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.108951250000246,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.1675404) - 1*1.2265713",
      "r2_train": 0.9750167627296352,
      "reward": null,
      "residual_heldout": 0.9709608422611887,
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        "x*inv_x2": 1.0,
        "1": -1.2265713
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.172198079999362,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=False residual=0.5997127229489798 cons=95628.20475955172 wall_s=16.596 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5997127229489798,
  "conservation_residual": 95628.20475955172,
  "equations": [
    "x*v*(-0.0874938) + v - 0.050854567",
    "v*(inv_x2*0.21617532 + 1.6878994)"
  ],
  "wall_s_total": 16.59617722799885,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "x*v*(-0.0874938) + v - 0.050854567",
      "r2_train": 0.9962220152548786,
      "reward": null,
      "residual_heldout": 0.017032665784491238,
      "pred_coeffs": {
        "x*v": -0.0874938,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.189206750997982,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(inv_x2*0.21617532 + 1.6878994)",
      "r2_train": 0.9886100526942071,
      "reward": null,
      "residual_heldout": 1.1823927801134684,
      "pred_coeffs": {
        "v*inv_x2": 0.21617532
      },
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        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 8.406970477000868,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=False residual=1.4139641959127722 cons=0.5496052417425721 wall_s=16.788 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.4139641959127722,
  "conservation_residual": 0.5496052417425721,
  "equations": [
    "(-v + x*(-0.30466026) + 0.4769815)*(-0.8421343)",
    "v*3.288102"
  ],
  "wall_s_total": 16.788303850000375,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(-v + x*(-0.30466026) + 0.4769815)*(-0.8421343)",
      "r2_train": 0.9926859956161588,
      "reward": null,
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      "pred_coeffs": {
        "1": -0.40168248161545,
        "v": 0.8421343,
        "x": 0.256564854792918
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.389186704000167,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*3.288102",
      "r2_train": 0.4113369843878989,
      "reward": null,
      "residual_heldout": 2.805980795210218,
      "pred_coeffs": {
        "v": 3.288102
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 8.399117146000208,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=False residual=0.3990032893274181 cons=0.012750506928991285 wall_s=16.485 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.3990032893274181,
  "conservation_residual": 0.012750506928991285,
  "equations": [
    "inv_x2*x*x*(x*x*v*(-0.02587881) - 0.016013645) + v",
    "v*v*v"
  ],
  "wall_s_total": 16.485436476996256,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "inv_x2*x*x*(x*x*v*(-0.02587881) - 0.016013645) + v",
      "r2_train": 0.9959672401323273,
      "reward": null,
      "residual_heldout": 0.012464857639334494,
      "pred_coeffs": {
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        "x*v": 26.01232380998326,
        "x^2": -34.203292737388985,
        "v^3": -0.3698322746741815,
        "x*v^2": 4.235371643415004,
        "x^2*v": -11.618382612154742,
        "x^3": 9.317017942262208,
        "inv_x2": -0.0036635512736884275
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.169522795997182,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.9405579015530969,
      "reward": null,
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        "v^3": 0.9999999999999925
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.315913680999074,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=False residual=0.5181964106858322 cons=0.1661191934763591 wall_s=16.246 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5181964106858322,
  "conservation_residual": 0.1661191934763591,
  "equations": [
    "(v + x - 1.5835642)*0.59663206",
    "v*v*v"
  ],
  "wall_s_total": 16.246398281000438,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "r2_train": 0.993516254153232,
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        "x": 0.59663206
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.398063578999427,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.2780871135597045,
      "reward": null,
      "residual_heldout": 1.0159283161892236,
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        "v^3": 1.0000000000002809
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 7.8483347020010115,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=False residual=45.52437859182814 cons=1.0526166424442132 wall_s=15.934 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 45.52437859182814,
  "conservation_residual": 1.0526166424442132,
  "equations": [
    "v*(inv_x2*0.014508745 - 1*(-0.24630116)) + x - 1.6123432",
    "v*(v + x - 0.632803)*(v + x*(-(-1.8280964)*inv_x2 + x*6.5354085) - 6.3093476)"
  ],
  "wall_s_total": 15.934219301998382,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v*(inv_x2*0.014508745 - 1*(-0.24630116)) + x - 1.6123432",
      "r2_train": 0.9914021529284667,
      "reward": null,
      "residual_heldout": 88.00770799947003,
      "pred_coeffs": {
        "v*inv_x2": 0.014508745,
        "1": -1.6123432,
        "x": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 7.937902861998737,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
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        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*(v + x - 0.632803)*(v + x*(-(-1.8280964)*inv_x2 + x*6.5354085) - 6.3093476)",
      "r2_train": 0.6227105888885736,
      "reward": null,
      "residual_heldout": 3.041049184186246,
      "pred_coeffs": {
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        "v": 15031.508868308096,
        "x": -22955.14590307886,
        "v^2": 6098.152575406214,
        "x*v": -18783.246488858484,
        "x^2": 14327.042444346336,
        "v^3": 819.9431230994743,
        "x*v^2": -3807.577600490538,
        "x^2*v": 5866.629993090782,
        "x^3": -2979.463840171618,
        "inv_x2": -0.20715692620045678
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.996316439999646,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=50 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=False residual=5.432002024184775 cons=0.9506376412775264 wall_s=16.133 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 5.432002024184775,
  "conservation_residual": 0.9506376412775264,
  "equations": [
    "v*x*0.4428281*v + v + x*0.6004914 - 0.90157634",
    "((v*(v + 3.30115) - 1*(-2.7381752))*3.480054*(v*(v + 2.0213795) - v) + 1.5330606)*(-2.1037352)"
  ],
  "wall_s_total": 16.133303408998472,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*x*0.4428281*v + v + x*0.6004914 - 0.90157634",
      "r2_train": 0.994518234057157,
      "reward": null,
      "residual_heldout": 0.00513769357027337,
      "pred_coeffs": {
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        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.15093739599979,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "((v*(v + 3.30115) - 1*(-2.7381752))*3.480054*(v*(v + 2.0213795) - v) + 1.5330606)*(-2.1037352)",
      "r2_train": 0.8701855648147514,
      "reward": null,
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        "v^2": -44.73127844674903,
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 7.982366012998682,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.001606738774726587 cons=0.42462627989044927 wall_s=15.566 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.001606738774726587,
  "conservation_residual": 0.42462627989044927,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.566154016003566,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.623932384001819,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.623932384001819,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.8841923674486356,
      "reward": null,
      "residual_heldout": 0.002272230348021593,
      "pred_coeffs": {
        "inv_x2": -0.9459111481730188
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.942221632001747,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.942221632001747,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9459111481730188
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=1

- recovered=True structure_ok=True accepted=True residual=0.15910429599144513 cons=0.03898429719128744 wall_s=15.304 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.15910429599144513,
  "conservation_residual": 0.03898429719128744,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.304088485998363,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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        "v": 1.0
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      "true_coeffs": {
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      "structure_ok": true,
      "wall_s": 7.421417030000157,
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      "wall_raw_s": 7.421417030000157,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9990408738306765,
      "reward": null,
      "residual_heldout": 0.3079486980963122,
      "pred_coeffs": {
        "inv_x2": -1.0009844247774835
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.8826714559982065,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.8826714559982065,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0009844247774835
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=2

- recovered=True structure_ok=True accepted=True residual=0.02953289226227336 cons=0.006725576775712663 wall_s=14.543 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.02953289226227336,
  "conservation_residual": 0.006725576775712663,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.542664290001994,
  "wall_s_per_eq": [
    6.930702968998958,
    7.611961321003037
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9958385012808142,
      "reward": null,
      "residual_heldout": 0.0026229314600283425,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.930702968998958,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.930702968998958,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9739558422017167,
      "reward": null,
      "residual_heldout": 0.05644285306451838,
      "pred_coeffs": {
        "inv_x2": -1.0079769545655664
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.611961321003037,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.611961321003037,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0079769545655664
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=1.3071825370847185 cons=1.609288653509423 wall_s=15.055 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.3071825370847185,
  "conservation_residual": 1.609288653509423,
  "equations": [
    "2*v",
    "invx2*k"
  ],
  "wall_s_total": 15.055495974000223,
  "wall_s_per_eq": [
    7.364165879000211,
    7.691330095000012
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.4572476446625091,
      "reward": null,
      "residual_heldout": 1.8687381427443177,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 7.364165879000211,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.364165879000211,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.998980907614665,
      "reward": null,
      "residual_heldout": 0.7456269314251195,
      "pred_coeffs": {
        "inv_x2": -0.995528742585047
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.691330095000012,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.691330095000012,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.995528742585047
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=True accepted=False residual=2.3354488488242318 cons=0.4919088162099259 wall_s=15.993 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 2.3354488488242318,
  "conservation_residual": 0.4919088162099259,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.992928195002605,
  "wall_s_per_eq": [
    7.460377376999531,
    8.532550818003074
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9967109774341912,
      "reward": null,
      "residual_heldout": 0.013656752851652302,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.460377376999531,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.460377376999531,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9697852487587507,
      "reward": null,
      "residual_heldout": 4.657240944796811,
      "pred_coeffs": {
        "inv_x2": -0.9801946665519844
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.532550818003074,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.532550818003074,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9801946665519844
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=True accepted=False residual=0.572191911098382 cons=0.4080284975903719 wall_s=15.828 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.572191911098382,
  "conservation_residual": 0.4080284975903719,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.828048528997897,
  "wall_s_per_eq": [
    7.06074441599776,
    8.767304113000137
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9893370245354693,
      "reward": null,
      "residual_heldout": 0.01687507310703258,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.06074441599776,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.06074441599776,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.4676462774207806,
      "reward": null,
      "residual_heldout": 1.1275087490897313,
      "pred_coeffs": {
        "inv_x2": -0.8170841296202167
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.767304113000137,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.767304113000137,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8170841296202167
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.18720035542850133 cons=0.057637487118777114 wall_s=15.059 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.18720035542850133,
  "conservation_residual": 0.057637487118777114,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.058581058001437,
  "wall_s_per_eq": [
    8.07393915799912,
    6.984641900002316
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.998728944790369,
      "reward": null,
      "residual_heldout": 0.0048443400624522326,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.07393915799912,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.07393915799912,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9994002660223185,
      "reward": null,
      "residual_heldout": 0.36955637079455045,
      "pred_coeffs": {
        "inv_x2": -1.0030234516852239
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 6.984641900002316,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.984641900002316,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0030234516852239
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=False residual=0.3006640904445013 cons=0.06368509323352303 wall_s=14.512 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.3006640904445013,
  "conservation_residual": 0.06368509323352303,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.51223124000171,
  "wall_s_per_eq": [
    6.851506238999718,
    7.6607250010019925
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9900908233584566,
      "reward": null,
      "residual_heldout": 0.007343657167944514,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.851506238999718,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.851506238999718,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.38690255035687293,
      "reward": null,
      "residual_heldout": 0.5939845237210581,
      "pred_coeffs": {
        "inv_x2": -0.6724911457788335
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.6607250010019925,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6607250010019925,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.6724911457788335
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=False residual=0.2615559036080643 cons=1.0154103755854866 wall_s=15.102 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.2615559036080643,
  "conservation_residual": 1.0154103755854866,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.102288474001398,
  "wall_s_per_eq": [
    7.519333107000421,
    7.582955367000977
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9820960047918478,
      "reward": null,
      "residual_heldout": 0.001792538301484791,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.519333107000421,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.519333107000421,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.3078247357629328,
      "reward": null,
      "residual_heldout": 0.5213192689146439,
      "pred_coeffs": {
        "inv_x2": -0.7138616389795933
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.582955367000977,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.582955367000977,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7138616389795933
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=True accepted=False residual=0.8612224441521293 cons=0.604014758095574 wall_s=15.080 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.8612224441521293,
  "conservation_residual": 0.604014758095574,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.080092922002223,
  "wall_s_per_eq": [
    7.459375406000618,
    7.620717516001605
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.997323655713841,
      "reward": null,
      "residual_heldout": 0.019498151421692797,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.459375406000618,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.459375406000618,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9987590927696529,
      "reward": null,
      "residual_heldout": 1.702946736882566,
      "pred_coeffs": {
        "inv_x2": -1.0022609817269437
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.620717516001605,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.620717516001605,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0022609817269437
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=10

- recovered=False structure_ok=True accepted=False residual=0.7419047828199968 cons=0.13853077488931476 wall_s=14.588 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.7419047828199968,
  "conservation_residual": 0.13853077488931476,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.588088476997655,
  "wall_s_per_eq": [
    7.078382971998508,
    7.509705504999147
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9981166176131141,
      "reward": null,
      "residual_heldout": 0.014473001276138249,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.078382971998508,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.078382971998508,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9991358531019693,
      "reward": null,
      "residual_heldout": 1.4693365643638554,
      "pred_coeffs": {
        "inv_x2": -0.9967546557561607
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.509705504999147,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.509705504999147,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9967546557561607
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=True accepted=False residual=0.6616195423335535 cons=0.29260439727377724 wall_s=15.386 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.6616195423335535,
  "conservation_residual": 0.29260439727377724,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.386023079998267,
  "wall_s_per_eq": [
    7.995898340999702,
    7.390124738998566
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.99183047042378,
      "reward": null,
      "residual_heldout": 0.008008873469038147,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.995898340999702,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.995898340999702,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.5958951875210237,
      "reward": null,
      "residual_heldout": 1.3152302111980687,
      "pred_coeffs": {
        "inv_x2": -1.0288414047104764
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.390124738998566,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.390124738998566,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0288414047104764
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=True accepted=False residual=1.4734516167475464 cons=0.5702881532542503 wall_s=16.024 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 1.4734516167475464,
  "conservation_residual": 0.5702881532542503,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 16.024119117999362,
  "wall_s_per_eq": [
    7.653765956001735,
    8.370353161997627
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9974737927720038,
      "reward": null,
      "residual_heldout": 0.010764694537082172,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.653765956001735,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.653765956001735,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9994294506035036,
      "reward": null,
      "residual_heldout": 2.936138538958011,
      "pred_coeffs": {
        "inv_x2": -0.9963705117973434
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.370353161997627,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.370353161997627,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9963705117973434
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=True accepted=False residual=0.979082075729002 cons=0.1644497653679077 wall_s=14.978 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.979082075729002,
  "conservation_residual": 0.1644497653679077,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.977764989002026,
  "wall_s_per_eq": [
    7.489672850999341,
    7.488092138002685
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.994143060705403,
      "reward": null,
      "residual_heldout": 0.009301823322350557,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.489672850999341,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.489672850999341,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9097005751086716,
      "reward": null,
      "residual_heldout": 1.9488623281356534,
      "pred_coeffs": {
        "inv_x2": -0.9978301249669226
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.488092138002685,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.488092138002685,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9978301249669226
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=True accepted=False residual=1.6917107762142545 cons=0.380642520907476 wall_s=14.885 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 1.6917107762142545,
  "conservation_residual": 0.380642520907476,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.884607129002688,
  "wall_s_per_eq": [
    7.4045871490016,
    7.480019980001089
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9951605921450705,
      "reward": null,
      "residual_heldout": 0.016483362843564713,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.4045871490016,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.4045871490016,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9784216516375709,
      "reward": null,
      "residual_heldout": 3.3669381895849444,
      "pred_coeffs": {
        "inv_x2": -1.0056279270252508
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.480019980001089,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.480019980001089,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0056279270252508
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=False residual=1.533958448568152 cons=0.8951254808396495 wall_s=14.535 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.533958448568152,
  "conservation_residual": 0.8951254808396495,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.53510340000139,
  "wall_s_per_eq": [
    7.250777983001171,
    7.284325417000218
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9918540808940277,
      "reward": null,
      "residual_heldout": 0.018811868460132455,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.250777983001171,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.250777983001171,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.20470529486859157,
      "reward": null,
      "residual_heldout": 3.0491050286761716,
      "pred_coeffs": {
        "inv_x2": -0.6720467908102354
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.284325417000218,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.284325417000218,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.6720467908102354
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=True accepted=False residual=0.9491813044741527 cons=0.7382369271666424 wall_s=16.526 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.9491813044741527,
  "conservation_residual": 0.7382369271666424,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 16.525918913997884,
  "wall_s_per_eq": [
    7.848880501998792,
    8.677038411999092
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9951785145067473,
      "reward": null,
      "residual_heldout": 0.01067529445349643,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.848880501998792,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.848880501998792,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.890274474813896,
      "reward": null,
      "residual_heldout": 1.887687314494809,
      "pred_coeffs": {
        "inv_x2": -0.9552527144802048
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.677038411999092,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.677038411999092,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9552527144802048
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=False residual=0.7828147352055728 cons=0.4990918730724703 wall_s=14.723 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.7828147352055728,
  "conservation_residual": 0.4990918730724703,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.722793965003802,
  "wall_s_per_eq": [
    7.036244095001166,
    7.6865498700026365
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9886584274105056,
      "reward": null,
      "residual_heldout": 0.021440503851491426,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.036244095001166,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.036244095001166,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": -0.03983348401807607,
      "reward": null,
      "residual_heldout": 1.5441889665596542,
      "pred_coeffs": {
        "inv_x2": -0.40959129868215427
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.6865498700026365,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6865498700026365,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.40959129868215427
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=False residual=0.14913744801951576 cons=82.9747193588538 wall_s=14.482 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.14913744801951576,
  "conservation_residual": 82.9747193588538,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.482232441998349,
  "wall_s_per_eq": [
    7.020683465998445,
    7.461548975999904
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9821145038544441,
      "reward": null,
      "residual_heldout": 0.0009869066753454593,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.020683465998445,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.020683465998445,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.2398798759760593,
      "reward": null,
      "residual_heldout": 0.29728798936368606,
      "pred_coeffs": {
        "inv_x2": -0.47391196467862357
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.461548975999904,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.461548975999904,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.47391196467862357
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=50 / σ=0.05 / seed=19

- recovered=True structure_ok=True accepted=True residual=0.04365548771762003 cons=0.1411606719303658 wall_s=14.864 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.04365548771762003,
  "conservation_residual": 0.1411606719303658,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.864126655000291,
  "wall_s_per_eq": [
    7.367324341001222,
    7.496802313999069
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.992725737745189,
      "reward": null,
      "residual_heldout": 0.002583951393468888,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.367324341001222,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.367324341001222,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.4637388240169148,
      "reward": null,
      "residual_heldout": 0.08472702404177118,
      "pred_coeffs": {
        "inv_x2": -0.9224940521691889
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.496802313999069,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.496802313999069,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9224940521691889
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.040401516749188154 cons=1.146939040744577 wall_s=17.354 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.040401516749188154,
  "conservation_residual": 1.146939040744577,
  "equations": [
    "v - x*(x*(-0.43159214) - (-0.29104722*(v - 1*0.06261284) - 0.6931705))",
    "v*v*v"
  ],
  "wall_s_total": 17.3540714869996,
  "wall_s_per_eq": [
    8.778458488999604,
    8.575612997999997
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - x*(x*(-0.43159214) - (-0.29104722*(v - 1*0.06261284) - 0.6931705))",
      "r2_train": 0.9943906066594084,
      "reward": null,
      "residual_heldout": 0.001964354425683619,
      "pred_coeffs": {
        "x*v": -0.29104722,
        "x^2": 0.43159214
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.778458488999604,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.7484681489644236,
      "reward": null,
      "residual_heldout": 0.0788386790726927,
      "pred_coeffs": {
        "v^3": 1.000000000000068
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.575612997999997,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.10638512225894112 cons=0.04647336224488368 wall_s=17.427 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.10638512225894112,
  "conservation_residual": 0.04647336224488368,
  "equations": [
    "v*0.39727262*v*x + v + x*0.5331412 - 0.8041754",
    "v*v*v"
  ],
  "wall_s_total": 17.42724024200288,
  "wall_s_per_eq": [
    8.14894016100152,
    9.278300081001362
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*0.39727262*v*x + v + x*0.5331412 - 0.8041754",
      "r2_train": 0.9956258933068901,
      "reward": null,
      "residual_heldout": 0.0024236538910472603,
      "pred_coeffs": {
        "1": -0.8041754,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.14894016100152,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.7151246453203194,
      "reward": null,
      "residual_heldout": 0.21034659062683497,
      "pred_coeffs": {
        "v^3": 1.0000000000000313
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.278300081001362,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=False residual=0.3660897646385355 cons=0.642932920971474 wall_s=17.119 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.3660897646385355,
  "conservation_residual": 0.642932920971474,
  "equations": [
    "-v*(v*x*(-0.43491375) - 1*0.9687321) + x*0.64118904 - 1*0.5409797 - 0.42796767",
    "-inv_x2"
  ],
  "wall_s_total": 17.118559037000523,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-v*(v*x*(-0.43491375) - 1*0.9687321) + x*0.64118904 - 1*0.5409797 - 0.42796767",
      "r2_train": 0.9978359521881972,
      "reward": null,
      "residual_heldout": 0.0061811566580810655,
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        "1": -0.96894737,
        "v": 0.9687321
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.078736406001553,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-inv_x2",
      "r2_train": 0.9988345099504731,
      "reward": null,
      "residual_heldout": 0.7259983726189899,
      "pred_coeffs": {
        "inv_x2": -1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.03982263099897,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.41031114186502177 cons=35193527.84830731 wall_s=16.834 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.41031114186502177,
  "conservation_residual": 35193527.84830731,
  "equations": [
    "v*0.9329684 + x*(0.19744956 + v*(-0.11091794)) - 1*0.33246943",
    "inv_x2*(x - 1*1.1424699)"
  ],
  "wall_s_total": 16.833708721998846,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "v*0.9329684 + x*(0.19744956 + v*(-0.11091794)) - 1*0.33246943",
      "r2_train": 0.9962774185681151,
      "reward": null,
      "residual_heldout": 0.01287769122258626,
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        "x*v": -0.11091794,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.15149583099992,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.1424699)",
      "r2_train": 0.9119259057349374,
      "reward": null,
      "residual_heldout": 0.8077445925074572,
      "pred_coeffs": {
        "x*inv_x2": 1.0
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        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 8.682212890998926,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.22996300433534972 cons=1.3551910120306045 wall_s=16.277 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
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  "structure_ok": false,
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  "residual": 0.22996300433534972,
  "conservation_residual": 1.3551910120306045,
  "equations": [
    "v - 0.45167187*x - (x*v*0.19924803 - 1*x*0.2856416*x)",
    "v*v*v"
  ],
  "wall_s_total": 16.2772743179994,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "wall_raw_s": null,
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      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.796509872519386,
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        "v^3": 1.0000000000000107
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 7.818020177001017,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.18258736030994205 cons=7387116.94937953 wall_s=18.122 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.18258736030994205,
  "conservation_residual": 7387116.94937953,
  "equations": [
    "v - x*((v + x*x*(-0.28806275))*x*0.17765976 + 0.20518406)",
    "inv_x2*(x - 1*1.0454342)"
  ],
  "wall_s_total": 18.12191633099792,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v - x*((v + x*x*(-0.28806275))*x*0.17765976 + 0.20518406)",
      "r2_train": 0.9980959143494378,
      "reward": null,
      "residual_heldout": 0.005892346325641787,
      "pred_coeffs": {
        "x": -0.20518406
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.690554716999031,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.0454342)",
      "r2_train": 0.9989070150346795,
      "reward": null,
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      "pred_coeffs": {
        "x*inv_x2": 1.0
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 9.431361613998888,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=False residual=0.5325716289764988 cons=0.07592728359299515 wall_s=18.278 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5325716289764988,
  "conservation_residual": 0.07592728359299515,
  "equations": [
    "v - 0.1859397*x*x*(v - x*x + x - 1*(-0.8287284))",
    "v*1.2600578*v*v"
  ],
  "wall_s_total": 18.27818321700397,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v - 0.1859397*x*x*(v - x*x + x - 1*(-0.8287284))",
      "r2_train": 0.9961282198765686,
      "reward": null,
      "residual_heldout": 0.010031394095912197,
      "pred_coeffs": {
        "1": -0.9741497084660884,
        "v": 0.405704918722494,
        "x": 2.6055587499946156,
        "v^2": -0.12373231817543405,
        "x*v": 0.9507326014962271,
        "x^2": -2.709683778601732,
        "v^3": -0.008591835108846028,
        "x*v^2": 0.09769636707605585,
        "x^2*v": -0.5537276927680101,
        "x^3": 0.9269369698210427,
        "inv_x2": 2.4439792630576196e-05
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 9.652588248001848,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*1.2600578*v*v",
      "r2_train": 0.9725959225899475,
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        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 8.625594969002123,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
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  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.03773942971763915 cons=0.017240974591758808 wall_s=17.325 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.03773942971763915,
  "conservation_residual": 0.017240974591758808,
  "equations": [
    "v*(-0.075611584)*v + (v + x)*0.5262559 - 0.8531988",
    "v*v*v"
  ],
  "wall_s_total": 17.32456352999725,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
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  "eq_results": [
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      "equation": "v*(-0.075611584)*v + (v + x)*0.5262559 - 0.8531988",
      "r2_train": 0.9953820069629281,
      "reward": null,
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      "wall_s": 8.942762953000056,
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      "wall_raw_s": null,
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        "wall_cap_s": 120,
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      "free_const_values": null,
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    {
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      "equation": "v*v*v",
      "r2_train": 0.8078254189545816,
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      "structure_ok": false,
      "wall_s": 8.381800576997193,
      "wall_pad_s": 0.0,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=False residual=0.42921820270560906 cons=0.5099407004414641 wall_s=16.879 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.42921820270560906,
  "conservation_residual": 0.5099407004414641,
  "equations": [
    "-(-0.48499438)*v*v*x + v - (-0.64378804)*x - 0.9652266",
    "v*v*v"
  ],
  "wall_s_total": 16.879374568998173,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "target": "dx/dt",
      "equation": "-(-0.48499438)*v*v*x + v - (-0.64378804)*x - 0.9652266",
      "r2_train": 0.9950915402052352,
      "reward": null,
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      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.8213628785935645,
      "reward": null,
      "residual_heldout": 0.8399843219822838,
      "pred_coeffs": {
        "v^3": 0.9999999999999903
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.210035968997545,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=False residual=0.3696029009345618 cons=6.001469393282272 wall_s=17.095 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.3696029009345618,
  "conservation_residual": 6.001469393282272,
  "equations": [
    "v*(v*x*0.13938929 + 1.1017764)",
    "v*2.0934534"
  ],
  "wall_s_total": 17.094752574001177,
  "wall_s_per_eq": [
    8.410656636999192,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(v*x*0.13938929 + 1.1017764)",
      "r2_train": 0.9912588193524658,
      "reward": null,
      "residual_heldout": 0.01384809743357112,
      "pred_coeffs": {
        "v": 1.1017764
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.410656636999192,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*2.0934534",
      "r2_train": 0.2953295008848944,
      "reward": null,
      "residual_heldout": 0.7253577044355525,
      "pred_coeffs": {
        "v": 2.0934534
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.684095937001985,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=False residual=0.4060110182358906 cons=13.368528904971955 wall_s=17.235 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.4060110182358906,
  "conservation_residual": 13.368528904971955,
  "equations": [
    "-0.112273395*v + v - x*(v*v*(-0.3093287) - 1*0.5796562) - 1*0.8875019",
    "v*v*(-1.6199398)"
  ],
  "wall_s_total": 17.23467620000156,
  "wall_s_per_eq": [
    8.311917717001052,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-0.112273395*v + v - x*(v*v*(-0.3093287) - 1*0.5796562) - 1*0.8875019",
      "r2_train": 0.9927008436250087,
      "reward": null,
      "residual_heldout": 0.013216591681311065,
      "pred_coeffs": {
        "1": -0.8875019,
        "v": 0.887726605
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.311917717001052,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*(-1.6199398)",
      "r2_train": 0.45540455630209487,
      "reward": null,
      "residual_heldout": 0.7988054447904701,
      "pred_coeffs": {
        "v^2": -1.6199398
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.922758483000507,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.03677871049703254 cons=209.150494373679 wall_s=16.897 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.03677871049703254,
  "conservation_residual": 209.150494373679,
  "equations": [
    "v - x*((v*v + 1.3019912)*x*(-0.590223) + 1.1568264)",
    "v - (inv_x2*x*(-0.5465561)*x + inv_x2)"
  ],
  "wall_s_total": 16.89709090099859,
  "wall_s_per_eq": [
    7.989601854998909,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - x*((v*v + 1.3019912)*x*(-0.590223) + 1.1568264)",
      "r2_train": 0.9982791061520326,
      "reward": null,
      "residual_heldout": 0.00622990148267612,
      "pred_coeffs": {
        "v": 1.0,
        "x": -1.1568264
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 7.989601854998909,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v - (inv_x2*x*(-0.5465561)*x + inv_x2)",
      "r2_train": 0.9990929378819418,
      "reward": null,
      "residual_heldout": 0.06732751951138896,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.907489045999682,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=False residual=0.5330596227769829 cons=90354806.90060261 wall_s=17.318 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5330596227769829,
  "conservation_residual": 90354806.90060261,
  "equations": [
    "inv_x2*(-0.00016298858) + v",
    "inv_x2*(x - 1.0062459)"
  ],
  "wall_s_total": 17.317899679997936,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "inv_x2*(-0.00016298858) + v",
      "r2_train": 0.9969418684334824,
      "reward": null,
      "residual_heldout": 0.04125838580772755,
      "pred_coeffs": {
        "inv_x2": -0.00016298858,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.578754088997812,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.0062459)",
      "r2_train": 0.9988841443569645,
      "reward": null,
      "residual_heldout": 1.0248608597462383,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.739145591000124,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.1284525783121298 cons=1.3692847405817636 wall_s=17.797 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.1284525783121298,
  "conservation_residual": 1.3692847405817636,
  "equations": [
    "v - x*(v*v*(-0.45808393) - 1*0.5776819) - 0.8822701",
    "v*v*(-2.2343097)"
  ],
  "wall_s_total": 17.79675671500081,
  "wall_s_per_eq": [
    9.087438471000496,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - x*(v*v*(-0.45808393) - 1*0.5776819) - 0.8822701",
      "r2_train": 0.992037259517723,
      "reward": null,
      "residual_heldout": 0.0063366120614972,
      "pred_coeffs": {
        "1": -0.8822701,
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 9.087438471000496,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*(-2.2343097)",
      "r2_train": 0.6818567213993736,
      "reward": null,
      "residual_heldout": 0.2505685445627624,
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        "v^2": -2.2343097
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.709318244000315,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.03653944197455167 cons=939897906.0009191 wall_s=17.699 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.03653944197455167,
  "conservation_residual": 939897906.0009191,
  "equations": [
    "v + (-v + v*v + x)*0.14072803*(x + 0.04785717) - 0.36501074",
    "inv_x2*(x - 1.0713975)"
  ],
  "wall_s_total": 17.698861635995854,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + (-v + v*v + x)*0.14072803*(x + 0.04785717) - 0.36501074",
      "r2_train": 0.9955249169177681,
      "reward": null,
      "residual_heldout": 0.005104773935565599,
      "pred_coeffs": {
        "x*v": -0.14072803,
        "x^2": 0.14072803,
        "1": -0.36501074
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.216009128998849,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.0713975)",
      "r2_train": 0.9485683990866606,
      "reward": null,
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      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
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        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.482852506997006,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.11905192517210758 cons=0.841951713117178 wall_s=19.545 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.11905192517210758,
  "conservation_residual": 0.841951713117178,
  "equations": [
    "v*(0.9381 + x*(-0.116844304)) - (x*(-0.17748983) - 1*(-0.30898213))",
    "v*v*v"
  ],
  "wall_s_total": 19.544824346001406,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(0.9381 + x*(-0.116844304)) - (x*(-0.17748983) - 1*(-0.30898213))",
      "r2_train": 0.9934506335635013,
      "reward": null,
      "residual_heldout": 0.007985194638716433,
      "pred_coeffs": {
        "x*v": -0.116844304,
        "1": -0.30898213
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 10.029858727000828,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.870411563729566,
      "reward": null,
      "residual_heldout": 0.23011865570549872,
      "pred_coeffs": {
        "v^3": 0.9999999999999929
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.514965619000577,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=False residual=0.25470477314259204 cons=0.00797721099753253 wall_s=17.587 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.25470477314259204,
  "conservation_residual": 0.00797721099753253,
  "equations": [
    "-(-1)*inv_x2*(inv_x2*x*(-0.0011985574) + 0.008580081) + v",
    "v*v*v"
  ],
  "wall_s_total": 17.586820792999788,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-(-1)*inv_x2*(inv_x2*x*(-0.0011985574) + 0.008580081) + v",
      "r2_train": 0.9959627244016231,
      "reward": null,
      "residual_heldout": 0.012689488185933325,
      "pred_coeffs": {
        "inv_x2": 0.008580081,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.008178537998901,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.9037946582613252,
      "reward": null,
      "residual_heldout": 0.49672005809925074,
      "pred_coeffs": {
        "v^3": 0.9999999999999923
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.578642255000887,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.009677359087237838 cons=22417308939.956112 wall_s=17.247 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.009677359087237838,
  "conservation_residual": 22417308939.956112,
  "equations": [
    "v - x*(v*0.0772918 - 0.050376583) - 0.095880575",
    "inv_x2*(x - 1*1.1579646)"
  ],
  "wall_s_total": 17.246543497996754,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - x*(v*0.0772918 - 0.050376583) - 0.095880575",
      "r2_train": 0.9954308279045826,
      "reward": null,
      "residual_heldout": 0.0018990645408126828,
      "pred_coeffs": {
        "x*v": -0.0772918,
        "1": -0.095880575
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        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.447325051998632,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.1579646)",
      "r2_train": 0.9719424296194393,
      "reward": null,
      "residual_heldout": 0.017455653633662995,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.799218445998122,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.0731265073090768 cons=48909770777.78338 wall_s=16.303 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0731265073090768,
  "conservation_residual": 48909770777.78338,
  "equations": [
    "v + x*(0.01027829 + inv_x2*(-0.003275157))",
    "inv_x2*(x - 1*1.1363215)"
  ],
  "wall_s_total": 16.30299562000073,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + x*(0.01027829 + inv_x2*(-0.003275157))",
      "r2_train": 0.9942212913977515,
      "reward": null,
      "residual_heldout": 0.007913189346211451,
      "pred_coeffs": {
        "x*inv_x2": -0.003275157,
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.167502426000283,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.1363215)",
      "r2_train": 0.7769240513776408,
      "reward": null,
      "residual_heldout": 0.13833982527194214,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.135493194000446,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=False residual=0.5314114202770125 cons=0.0234499974976626 wall_s=16.914 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.5314114202770125,
  "conservation_residual": 0.0234499974976626,
  "equations": [
    "(-v + x*(-0.15468372))*(-0.9109532) - 0.21992949",
    "v*v*v"
  ],
  "wall_s_total": 16.913691435001965,
  "wall_s_per_eq": [
    8.42741040400142,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "(-v + x*(-0.15468372))*(-0.9109532) - 0.21992949",
      "r2_train": 0.9912945770887349,
      "reward": null,
      "residual_heldout": 0.021281159611154402,
      "pred_coeffs": {
        "1": -0.21992949,
        "v": 0.9109532,
        "x": 0.140909629721904
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.42741040400142,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "v*v*v",
      "r2_train": 0.8591746407781322,
      "reward": null,
      "residual_heldout": 1.0415416809428706,
      "pred_coeffs": {
        "v^3": 0.9999999999999989
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.486281031000544,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.037566407522471645 cons=0.21872422927970808 wall_s=16.415 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.037566407522471645,
  "conservation_residual": 0.21872422927970808,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 16.414657237004576,
  "wall_s_per_eq": [
    7.806536692001828,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.993019940085661,
      "reward": null,
      "residual_heldout": 0.002851902218388178,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.806536692001828,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.806536692001828,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.49593917508731356,
      "reward": null,
      "residual_heldout": 0.07228091282655512,
      "pred_coeffs": {
        "inv_x2": -0.8107044578059289
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.608120545002748,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.608120545002748,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8107044578059289
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.04047865057949167 cons=0.03157429455036322 wall_s=15.601 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.04047865057949167,
  "conservation_residual": 0.03157429455036322,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.601467936005065,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "reward": null,
      "residual_heldout": 0.0017648107548651967,
      "pred_coeffs": {
        "v": 1.0
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.583260186002008,
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      "wall_raw_s": 7.583260186002008,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.4558357065118469,
      "reward": null,
      "residual_heldout": 0.07919249040411813,
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        "inv_x2": -0.7267617526874502
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 8.018207750003057,
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      "wall_raw_s": 8.018207750003057,
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      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7267617526874502
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=True accepted=False residual=0.36630663101276784 cons=0.22519130753376496 wall_s=14.932 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.36630663101276784,
  "conservation_residual": 0.22519130753376496,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.931548684995505,
  "wall_s_per_eq": [
    7.236238137997134,
    7.695310546998371
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9971091728020103,
      "reward": null,
      "residual_heldout": 0.006431960760790758,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.236238137997134,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.236238137997134,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9988346766179739,
      "reward": null,
      "residual_heldout": 0.7261813012647449,
      "pred_coeffs": {
        "inv_x2": -1.0004041402799904
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.695310546998371,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.695310546998371,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0004041402799904
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=1.9984854104265377 cons=1.6178120275002263 wall_s=14.939 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.9984854104265377,
  "conservation_residual": 1.6178120275002263,
  "equations": [
    "2*v",
    "invx2*k"
  ],
  "wall_s_total": 14.938554078002198,
  "wall_s_per_eq": [
    7.368933540001308,
    7.5696205380008905
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.9281840124843361,
      "reward": null,
      "residual_heldout": 2.977724371297911,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 7.368933540001308,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.368933540001308,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.8520136273891887,
      "reward": null,
      "residual_heldout": 1.0192464495551643,
      "pred_coeffs": {
        "inv_x2": -0.9171704747807443
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.5696205380008905,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.5696205380008905,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9171704747807443
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=False residual=0.39180510486647124 cons=0.3071439595205791 wall_s=15.379 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.39180510486647124,
  "conservation_residual": 0.3071439595205791,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.378765317997022,
  "wall_s_per_eq": [
    7.503718118998222,
    7.8750471989988
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9940300311237237,
      "reward": null,
      "residual_heldout": 0.005386308387364017,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.503718118998222,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.503718118998222,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.511434194623136,
      "reward": null,
      "residual_heldout": 0.7782239013455785,
      "pred_coeffs": {
        "inv_x2": -0.7726228429829908
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.8750471989988,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.8750471989988,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7726228429829908
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=True accepted=False residual=0.26967956003822025 cons=0.08804388390143254 wall_s=16.801 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.26967956003822025,
  "conservation_residual": 0.08804388390143254,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 16.801157803001843,
  "wall_s_per_eq": [
    7.7774618650000775,
    9.023695938001765
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9975874590492643,
      "reward": null,
      "residual_heldout": 0.004203462334147922,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.7774618650000775,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.7774618650000775,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9985800994292623,
      "reward": null,
      "residual_heldout": 0.5351556577422926,
      "pred_coeffs": {
        "inv_x2": -0.9981482045266085
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 9.023695938001765,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.023695938001765,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9981482045266085
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=True accepted=False residual=0.8293119048017084 cons=0.299156841810609 wall_s=18.063 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.8293119048017084,
  "conservation_residual": 0.299156841810609,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 18.06317676800245,
  "wall_s_per_eq": [
    10.62714105499981,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9952185849226973,
      "reward": null,
      "residual_heldout": 0.010017371765493091,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 10.62714105499981,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.62714105499981,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9298640595593086,
      "reward": null,
      "residual_heldout": 1.6486064378379237,
      "pred_coeffs": {
        "inv_x2": -1.004911289273264
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.436035713002639,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.436035713002639,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.004911289273264
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.07402126075059601 cons=0.010918616282793102 wall_s=15.598 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.07402126075059601,
  "conservation_residual": 0.010918616282793102,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.59756888999982,
  "wall_s_per_eq": [
    7.895521401998849,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9931754217047195,
      "reward": null,
      "residual_heldout": 0.008320689146753471,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.895521401998849,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.895521401998849,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.6595861174723163,
      "reward": null,
      "residual_heldout": 0.13972183235443855,
      "pred_coeffs": {
        "inv_x2": -0.8057185879213147
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.7020474880009715,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.7020474880009715,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8057185879213147
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=True accepted=False residual=1.1461792214348663 cons=0.4279752493536777 wall_s=15.345 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 1.1461792214348663,
  "conservation_residual": 0.4279752493536777,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.345330605003255,
  "wall_s_per_eq": [
    7.501029285002005,
    7.84430132000125
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "reward": null,
      "residual_heldout": 0.021464155449113596,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.501029285002005,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.501029285002005,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.7163201021814288,
      "reward": null,
      "residual_heldout": 2.270894287420619,
      "pred_coeffs": {
        "inv_x2": -1.0025533775650946
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.84430132000125,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.84430132000125,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0025533775650946
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=False residual=0.32187672440409504 cons=5.247196916290746 wall_s=15.146 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.32187672440409504,
  "conservation_residual": 5.247196916290746,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.146129056000063,
  "wall_s_per_eq": [
    8.197614128002897,
    6.9485149279971665
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9905130062262749,
      "reward": null,
      "residual_heldout": 0.013105129298170237,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.197614128002897,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.197614128002897,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.00613625982415944,
      "reward": null,
      "residual_heldout": 0.6306483195100199,
      "pred_coeffs": {
        "inv_x2": -0.289429455281964
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 6.9485149279971665,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.9485149279971665,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.289429455281964
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.12452674034264555 cons=0.012763147171740031 wall_s=14.788 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.12452674034264555,
  "conservation_residual": 0.012763147171740031,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.788451284002804,
  "wall_s_per_eq": [
    7.183792407002329,
    7.604658877000475
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9911450960137929,
      "reward": null,
      "residual_heldout": 0.0018751717364168417,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.183792407002329,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.183792407002329,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.290225607860347,
      "reward": null,
      "residual_heldout": 0.24717830894887424,
      "pred_coeffs": {
        "inv_x2": -0.513152251822455
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.604658877000475,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.604658877000475,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.513152251822455
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.049965573584724844 cons=0.0018180134949623815 wall_s=15.036 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.049965573584724844,
  "conservation_residual": 0.0018180134949623815,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.036082080001506,
  "wall_s_per_eq": [
    7.487930596002116,
    7.548151483999391
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9968984163745228,
      "reward": null,
      "residual_heldout": 0.004944396432661608,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.487930596002116,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.487930596002116,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.998423159099243,
      "reward": null,
      "residual_heldout": 0.09498675073678808,
      "pred_coeffs": {
        "inv_x2": -1.005501141384673
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.548151483999391,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.548151483999391,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.005501141384673
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=True accepted=False residual=1.3736779932877141 cons=1.3079089758441198 wall_s=17.088 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 1.3736779932877141,
  "conservation_residual": 1.3079089758441198,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 17.087945052000578,
  "wall_s_per_eq": [
    9.348527756999829,
    7.739417295000749
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9967903471516151,
      "reward": null,
      "residual_heldout": 0.04108299143728922,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.348527756999829,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.348527756999829,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9982943164374013,
      "reward": null,
      "residual_heldout": 2.7062729951381392,
      "pred_coeffs": {
        "inv_x2": -0.9954124980910258
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.739417295000749,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.739417295000749,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9954124980910258
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=False residual=0.21185666880729448 cons=0.6292634480536501 wall_s=14.698 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.21185666880729448,
  "conservation_residual": 0.6292634480536501,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.698162807002518,
  "wall_s_per_eq": [
    7.518505466003262,
    7.179657340999256
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9894182143461592,
      "reward": null,
      "residual_heldout": 0.008683985700494655,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.518505466003262,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.518505466003262,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.3664024567067091,
      "reward": null,
      "residual_heldout": 0.4150293519140943,
      "pred_coeffs": {
        "inv_x2": -0.7152614115791919
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.179657340999256,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.179657340999256,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7152614115791919
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.035068026689229835 cons=0.0034842270266335915 wall_s=17.994 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.035068026689229835,
  "conservation_residual": 0.0034842270266335915,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 17.993933536999975,
  "wall_s_per_eq": [
    7.8333589770008984,
    10.160574559999077
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9945662536040727,
      "reward": null,
      "residual_heldout": 0.004522696142126906,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.8333589770008984,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.8333589770008984,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.929242684793295,
      "reward": null,
      "residual_heldout": 0.06561335723633277,
      "pred_coeffs": {
        "inv_x2": -0.9992794125314269
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.160574559999077,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.160574559999077,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9992794125314269
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=True accepted=False residual=0.21003923818496364 cons=0.7078442259586267 wall_s=15.897 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.21003923818496364,
  "conservation_residual": 0.7078442259586267,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.896830541001691,
  "wall_s_per_eq": [
    8.475728674999118,
    7.421101866002573
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.475728674999118,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.475728674999118,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.7834433749747265,
      "reward": null,
      "residual_heldout": 0.40958493863153184,
      "pred_coeffs": {
        "inv_x2": -0.8398453225400749
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.421101866002573,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.421101866002573,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8398453225400749
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=True accepted=False residual=0.38284961791204064 cons=0.17425371057988298 wall_s=15.461 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.38284961791204064,
  "conservation_residual": 0.17425371057988298,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.461375027000031,
  "wall_s_per_eq": [
    7.767451588999393,
    7.693923438000638
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9947155953086841,
      "reward": null,
      "residual_heldout": 0.013921009830167688,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.767451588999393,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.767451588999393,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.8277496258823506,
      "reward": null,
      "residual_heldout": 0.7517782259939136,
      "pred_coeffs": {
        "inv_x2": -0.9165260580773814
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.693923438000638,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.693923438000638,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9165260580773814
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=17

- recovered=True structure_ok=True accepted=True residual=0.0012043901481501981 cons=0.4282631800108705 wall_s=14.505 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0012043901481501981,
  "conservation_residual": 0.4282631800108705,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.505118138004036,
  "wall_s_per_eq": [
    7.244203877002292,
    7.260914261001744
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9950116035434652,
      "reward": null,
      "residual_heldout": 0.0017065810010881788,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.244203877002292,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.244203877002292,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9591115861493098,
      "reward": null,
      "residual_heldout": 0.0007021992952122175,
      "pred_coeffs": {
        "inv_x2": -0.9891466457285842
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.260914261001744,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.260914261001744,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9891466457285842
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.15281272162050183 cons=0.19034516380741617 wall_s=14.822 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.15281272162050183,
  "conservation_residual": 0.19034516380741617,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 14.822122666002542,
  "wall_s_per_eq": [
    7.410968127001979,
    7.411154539000563
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9937675589766529,
      "reward": null,
      "residual_heldout": 0.008057343875088618,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.410968127001979,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.410968127001979,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.5799552202627132,
      "reward": null,
      "residual_heldout": 0.29756809936591505,
      "pred_coeffs": {
        "inv_x2": -0.6622440804224478
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 7.411154539000563,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.411154539000563,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.6622440804224478
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=True accepted=False residual=1.0269678630944845 cons=0.5789177520311172 wall_s=15.189 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 1.0269678630944845,
  "conservation_residual": 0.5789177520311172,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.188768063999305,
  "wall_s_per_eq": [
    7.6306346470009885,
    7.5581334169983165
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9906071607727022,
      "reward": null,
      "residual_heldout": 0.022698607246391358,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.6306346470009885,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6306346470009885,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.7017417641592283,
      "reward": null,
      "residual_heldout": 2.0312371189425775,
      "pred_coeffs": {
        "inv_x2": -0.8669514416351135
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.5581334169983165,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.5581334169983165,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8669514416351135
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.002336585815410825 cons=2863214942.8852954 wall_s=18.453 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.002336585815410825,
  "conservation_residual": 2863214942.8852954,
  "equations": [
    "v - 0.11094038*(x - (-v + x)*(x - 1*(-0.30629933))) - 1*0.15580317",
    "inv_x2*(x - 1.0663501)"
  ],
  "wall_s_total": 18.45274269500078,
  "wall_s_per_eq": [
    9.542544378000457,
    8.910198317000322
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - 0.11094038*(x - (-v + x)*(x - 1*(-0.30629933))) - 1*0.15580317",
      "r2_train": 0.9947145780498746,
      "reward": null,
      "residual_heldout": 0.003295025978914979,
      "pred_coeffs": {
        "x*v": -0.11094038,
        "x^2": 0.11094038,
        "1": -0.15580317
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 9.542544378000457,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.0663501)",
      "r2_train": 0.9411611056656614,
      "reward": null,
      "residual_heldout": 0.0013781456519066711,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.910198317000322,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.016211464627958083 cons=28654082.061896514 wall_s=17.974 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.016211464627958083,
  "conservation_residual": 28654082.061896514,
  "equations": [
    "-0.047942996*v*x + v - 0.025178922",
    "x*inv_x2*0.39771563 - inv_x2"
  ],
  "wall_s_total": 17.974060286000167,
  "wall_s_per_eq": [
    8.744261503001326,
    9.229798782998841
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "-0.047942996*v*x + v - 0.025178922",
      "r2_train": 0.9956278406404553,
      "reward": null,
      "residual_heldout": 0.0045529654983740035,
      "pred_coeffs": {
        "x*v": -0.047942996,
        "1": -0.025178922
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.744261503001326,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "x*inv_x2*0.39771563 - inv_x2",
      "r2_train": 0.9974141041047282,
      "reward": null,
      "residual_heldout": 0.027869963757542165,
      "pred_coeffs": {
        "x*inv_x2": 0.39771563
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.229798782998841,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.012035779158223014 cons=9678980874.755009 wall_s=18.803 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.012035779158223014,
  "conservation_residual": 9678980874.755009,
  "equations": [
    "v - x*(v - x*(v*0.4720529 + 0.4884472) + 0.4201512) - 0.50840646",
    "inv_x2*(x - 1.0741534)"
  ],
  "wall_s_total": 18.802896838999004,
  "wall_s_per_eq": [
    9.511846129000332,
    9.291050709998672
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v - x*(v - x*(v*0.4720529 + 0.4884472) + 0.4201512) - 0.50840646",
      "r2_train": 0.9961561550626559,
      "reward": null,
      "residual_heldout": 0.003347764088304993,
      "pred_coeffs": {
        "x*v": -1.0,
        "1": -0.50840646
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 9.511846129000332,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.0741534)",
      "r2_train": 0.997690134657629,
      "reward": null,
      "residual_heldout": 0.020723794228141038,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.291050709998672,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.003255593981205517 cons=2241507955806.8804 wall_s=17.031 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003255593981205517,
  "conservation_residual": 2241507955806.8804,
  "equations": [
    "v*(x*v*0.066265635 + 0.049302336) + v",
    "inv_x2*(x - 1.1101946)"
  ],
  "wall_s_total": 17.030948046998674,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "v*(x*v*0.066265635 + 0.049302336) + v",
      "r2_train": 0.9934208904419073,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.049302336
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": true,
      "wall_s": 8.032655773997249,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.1101946)",
      "r2_train": 0.9541809461268589,
      "reward": null,
      "residual_heldout": 0.002455851831850913,
      "pred_coeffs": {
        "x*inv_x2": 1.0
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 8.998292273001425,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.005710305038593925 cons=320864713.1506094 wall_s=17.891 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.005710305038593925,
  "conservation_residual": 320864713.1506094,
  "equations": [
    "v + x*(-0.21142675)*(1.5402932 - (x - (v - 1*0.19126888))) - 1*0.09382643",
    "inv_x2*(x - 1*1.1214021)"
  ],
  "wall_s_total": 17.890968408002664,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "v + x*(-0.21142675)*(1.5402932 - (x - (v - 1*0.19126888))) - 1*0.09382643",
      "r2_train": 0.9952373689703804,
      "reward": null,
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      "structure_ok": false,
      "wall_s": 8.40330714400261,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.1214021)",
      "r2_train": 0.9476161297960018,
      "reward": null,
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      "pred_coeffs": {
        "x*inv_x2": 1.0
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        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 9.487661264000053,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.19401435787632038 cons=2.438781443707633 wall_s=16.770 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.19401435787632038,
  "conservation_residual": 2.438781443707633,
  "equations": [
    "v*x + v + x*(v*(-1.2055962) - 1*x*(-0.3157891) - 0.49277404)",
    "inv_x2*x - inv_x2 + v"
  ],
  "wall_s_total": 16.770240708003257,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v*x + v + x*(v*(-1.2055962) - 1*x*(-0.3157891) - 0.49277404)",
      "r2_train": 0.9970867419736055,
      "reward": null,
      "residual_heldout": 0.008436514295641188,
      "pred_coeffs": {
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        "x^2": 0.3157891
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.152528801001608,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*x - inv_x2 + v",
      "r2_train": 0.9977827604088911,
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      "residual_heldout": 0.37959220145699957,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.617711907001649,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.015899533263186858 cons=724.1578614908793 wall_s=18.123 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
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  "residual": 0.015899533263186858,
  "conservation_residual": 724.1578614908793,
  "equations": [
    "v*x*v*0.30921754 + v - (-0.40327206)*(x - 1.4888114)",
    "inv_x2*x - inv_x2 + v"
  ],
  "wall_s_total": 18.123133214001427,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*x*v*0.30921754 + v - (-0.40327206)*(x - 1.4888114)",
      "r2_train": 0.9965781279100934,
      "reward": null,
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      "structure_ok": false,
      "wall_s": 8.563764369002456,
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      "wall_raw_s": null,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*x - inv_x2 + v",
      "r2_train": 0.9980416951981486,
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        "x*inv_x2": 1.0,
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      "structure_ok": false,
      "wall_s": 9.559368844998971,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=False residual=0.26426002329871084 cons=14864030781531.691 wall_s=17.337 ok=True

```json
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
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  "recovered": false,
  "structure_ok": false,
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  "residual": 0.26426002329871084,
  "conservation_residual": 14864030781531.691,
  "equations": [
    "(v*0.050182696 - 0.52301747)*((-v - x) + 1.6185826)",
    "inv_x2*v*0.22192077"
  ],
  "wall_s_total": 17.33672402200318,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "equation": "(v*0.050182696 - 0.52301747)*((-v - x) + 1.6185826)",
      "r2_train": 0.9947248995722235,
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      "structure_ok": false,
      "wall_s": 8.846684592001111,
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      "free_const_values": null,
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    {
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      "target": "dv/dt",
      "equation": "inv_x2*v*0.22192077",
      "r2_train": 0.9501859303883904,
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      "structure_ok": false,
      "wall_s": 8.49003943000207,
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        "timeout_in_seconds": 100,
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      "free_const_values": null,
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    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.01336570582744639 cons=227987214858706.38 wall_s=17.755 ok=True

```json
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.01336570582744639,
  "conservation_residual": 227987214858706.38,
  "equations": [
    "v - x*(-0.50137246*v*v*x + x*(-0.6643194)) - x",
    "inv_x2*(x - 1*1.0494716)"
  ],
  "wall_s_total": 17.75543118600035,
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  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
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  "tau": 0.2,
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  "eq_results": [
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    {
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      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.0029602125476756607 cons=2598274639.356781 wall_s=17.263 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0029602125476756607,
  "conservation_residual": 2598274639.356781,
  "equations": [
    "v + x*((v + x*(-1.4050134))*(-0.21875235) - 1*0.48624578)",
    "inv_x2*(x - 1.0843985)"
  ],
  "wall_s_total": 17.26309371699972,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "target": "dx/dt",
      "equation": "v + x*((v + x*(-1.4050134))*(-0.21875235) - 1*0.48624578)",
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      "reward": null,
      "residual_heldout": 0.0033341103083522495,
      "pred_coeffs": {
        "x*v": -0.21875235,
        "x^2": 0.30734998303149
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.356628003999504,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.0843985)",
      "r2_train": 0.9530748621456145,
      "reward": null,
      "residual_heldout": 0.002586314786999072,
      "pred_coeffs": {
        "x*inv_x2": 1.0
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      "true_coeffs": {
        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 8.906465713000216,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.05417196367810615 cons=0.9422523001590293 wall_s=18.151 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.05417196367810615,
  "conservation_residual": 0.9422523001590293,
  "equations": [
    "v + x*x*(-(-1)*(-0.07514368)*(v + v - x - x) - 0.22880495) - 0.04558946",
    "inv_x2*(x - 1*1.0261601) + v"
  ],
  "wall_s_total": 18.150559753998095,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "v + x*x*(-(-1)*(-0.07514368)*(v + v - x - x) - 0.22880495) - 0.04558946",
      "r2_train": 0.9963081740427301,
      "reward": null,
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.402636514998449,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.0261601) + v",
      "r2_train": 0.9980049739465131,
      "reward": null,
      "residual_heldout": 0.10078524369062457,
      "pred_coeffs": {
        "x*inv_x2": 1.0,
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.747923238999647,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.1064580708921751 cons=98607978666.53789 wall_s=18.577 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.1064580708921751,
  "conservation_residual": 98607978666.53789,
  "equations": [
    "v + x*(v*0.3263018*v + 0.44154397) - 0.66284156",
    "inv_x2*(x - 1*1.0330384)"
  ],
  "wall_s_total": 18.576981770998827,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
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      "equation": "v + x*(v*0.3263018*v + 0.44154397) - 0.66284156",
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      "pred_coeffs": {
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      "structure_ok": false,
      "wall_s": 9.260064688998682,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
      "zero_eq": false,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.0330384)",
      "r2_train": 0.9974880689540633,
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      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
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      "structure_ok": false,
      "wall_s": 9.316917082000145,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.004651263753229494 cons=4411265369.125279 wall_s=19.290 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004651263753229494,
  "conservation_residual": 4411265369.125279,
  "equations": [
    "v + x*(x*(v*(v*0.31600758 - 0.011361629) - 0.56211466) + x - 0.65867937)",
    "inv_x2*(x - 1*1.0919408)"
  ],
  "wall_s_total": 19.28998059600417,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + x*(x*(v*(v*0.31600758 - 0.011361629) - 0.56211466) + x - 0.65867937)",
      "r2_train": 0.9951041071480919,
      "reward": null,
      "residual_heldout": 0.0026755834080725086,
      "pred_coeffs": {
        "x": -0.65867937
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 9.668126553002367,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.0919408)",
      "r2_train": 0.949150913507988,
      "reward": null,
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      "pred_coeffs": {
        "x*inv_x2": 1.0
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        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 9.621854043001804,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.007010455251471268 cons=6.480818143277581e+39 wall_s=17.471 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007010455251471268,
  "conservation_residual": 6.480818143277581e+39,
  "equations": [
    "v*(-0.09389402) + v + x*(0.35223955 + x*(-0.09777229)) - 0.3276008",
    "inv_x2*(x - 1.063117)"
  ],
  "wall_s_total": 17.471360269002616,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v*(-0.09389402) + v + x*(0.35223955 + x*(-0.09777229)) - 0.3276008",
      "r2_train": 0.9943495448816464,
      "reward": null,
      "residual_heldout": 0.004834216428081454,
      "pred_coeffs": {
        "x^2": -0.09777229,
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      "true_coeffs": {
        "v": 1.0
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      "structure_ok": false,
      "wall_s": 8.552791834001255,
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      "wall_raw_s": null,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
      "zero_eq": false,
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    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.063117)",
      "r2_train": 0.9503875166389073,
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        "x*inv_x2": 1.0
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        "inv_x2": -1.0
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      "structure_ok": false,
      "wall_s": 8.918568435001362,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.003018702444367659 cons=10062986366735.67 wall_s=17.074 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.003018702444367659,
  "conservation_residual": 10062986366735.67,
  "equations": [
    "v + x*(v*0.3134472*v + 0.42776558) - 1*0.644377",
    "inv_x2*(x - 1.087746)"
  ],
  "wall_s_total": 17.07358529299745,
  "wall_s_per_eq": [
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  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
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      "structure_ok": false,
      "wall_s": 8.429090486999485,
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        "wall_cap_s": 120,
        "target_mean_wall_s": 0
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      "free_const_values": null,
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    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.087746)",
      "r2_train": 0.9515670537364712,
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      "structure_ok": false,
      "wall_s": 8.644494805997965,
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      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
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      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.006134333575850539 cons=3.0527516345478126e+21 wall_s=17.598 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006134333575850539,
  "conservation_residual": 3.0527516345478126e+21,
  "equations": [
    "-v*x*x*x*(v*(-0.7524301) + x - 1.6323491) + v",
    "inv_x2*(x - 1.0894898)"
  ],
  "wall_s_total": 17.598240057999647,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0,
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "-v*x*x*x*(v*(-0.7524301) + x - 1.6323491) + v",
      "r2_train": 0.9942576253065759,
      "reward": null,
      "residual_heldout": 0.0026411575135571,
      "pred_coeffs": {
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        "v^2": 1.3666519520003293,
        "x*v": -6.129448978572995,
        "x^2": 9.092835911105956,
        "v^3": 0.11400929231184571,
        "x*v^2": -0.35166438597265104,
        "x^2*v": 1.6166759660989982,
        "x^3": -1.9611959305219218,
        "inv_x2": -0.00021211536145586055
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.276225279001665,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.0894898)",
      "r2_train": 0.9458262327276001,
      "reward": null,
      "residual_heldout": 0.009627509638143978,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.322014778997982,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.010663603555466798 cons=3211089825154.4165 wall_s=17.631 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.010663603555466798,
  "conservation_residual": 3211089825154.4165,
  "equations": [
    "(0.56899494 - 0.05112829*v)*(v + x) - 1*0.9254184",
    "inv_x2*(x - 1.1722842)"
  ],
  "wall_s_total": 17.630963153002085,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
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  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "(0.56899494 - 0.05112829*v)*(v + x) - 1*0.9254184",
      "r2_train": 0.9945638725316716,
      "reward": null,
      "residual_heldout": 0.005039593251816231,
      "pred_coeffs": {
        "v^2": -0.05112829,
        "x*v": -0.05112829,
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.724316847001319,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
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        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.1722842)",
      "r2_train": 0.8671914443781086,
      "reward": null,
      "residual_heldout": 0.016287613859117367,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 8.906646306000766,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.22988787668002508 cons=14832827.228646366 wall_s=18.155 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.22988787668002508,
  "conservation_residual": 14832827.228646366,
  "equations": [
    "v + x*(-v + x)*0.22225255 + x*(-0.3127772) - 0.0790234",
    "inv_x2*(x - 1*1.0175751)"
  ],
  "wall_s_total": 18.15460618600264,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + x*(-v + x)*0.22225255 + x*(-0.3127772) - 0.0790234",
      "r2_train": 0.99644117629936,
      "reward": null,
      "residual_heldout": 0.009999049939792835,
      "pred_coeffs": {
        "x*v": -0.22225255,
        "x^2": 0.22225255,
        "1": -0.0790234
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      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 9.007355298002949,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1*1.0175751)",
      "r2_train": 0.9975899922347498,
      "reward": null,
      "residual_heldout": 0.44977670342025733,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
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        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.14725088799969,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.05839276258717629 cons=4197314.7128875 wall_s=17.596 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.05839276258717629,
  "conservation_residual": 4197314.7128875,
  "equations": [
    "v + x*(-x*(x*0.29881135 + (-v + x*x)*(-0.22829336)) - 0.11973509)",
    "inv_x2*(x - 1.0240898)"
  ],
  "wall_s_total": 17.59605673200349,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v + x*(-x*(x*0.29881135 + (-v + x*x)*(-0.22829336)) - 0.11973509)",
      "r2_train": 0.9968869689794361,
      "reward": null,
      "residual_heldout": 0.004927791924496166,
      "pred_coeffs": {
        "x": -0.11973509
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.277010089001124,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.0240898)",
      "r2_train": 0.9979006769128022,
      "reward": null,
      "residual_heldout": 0.11185773324985641,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
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        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.319046643002366,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `gravity_toy` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.003635467769933831 cons=1977326083311.814 wall_s=18.574 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003635467769933831,
  "conservation_residual": 1977326083311.814,
  "equations": [
    "v*(0.6458929 - 0.0443561*v) + x*0.42833287 - 0.6947083",
    "inv_x2*(x - 1.1004009)"
  ],
  "wall_s_total": 18.57365884200408,
  "wall_s_per_eq": [
    8.638133226002537,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v*(0.6458929 - 0.0443561*v) + x*0.42833287 - 0.6947083",
      "r2_train": 0.9957736168490838,
      "reward": null,
      "residual_heldout": 0.005592022033847101,
      "pred_coeffs": {
        "v^2": -0.0443561,
        "1": -0.6947083,
        "v": 0.6458929,
        "x": 0.42833287
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 8.638133226002537,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "inv_x2*(x - 1.1004009)",
      "r2_train": 0.9542589620020752,
      "reward": null,
      "residual_heldout": 0.0016789135060205607,
      "pred_coeffs": {
        "x*inv_x2": 1.0
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": false,
      "wall_s": 9.935525616001541,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=0

- recovered=True structure_ok=True accepted=True residual=0.005147760009135412 cons=0.2521862134109076 wall_s=17.376 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005147760009135412,
  "conservation_residual": 0.2521862134109076,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 17.37637640200046,
  "wall_s_per_eq": [
    9.435396193999622,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9941420512229222,
      "reward": null,
      "residual_heldout": 0.003573793714028112,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.435396193999622,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.435396193999622,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9126728832978669,
      "reward": null,
      "residual_heldout": 0.0067217263042427125,
      "pred_coeffs": {
        "inv_x2": -0.9203982788638552
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.940980208000838,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.940980208000838,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9203982788638552
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=True accepted=False residual=0.02065647611344638 cons=1.573334455476853 wall_s=15.578 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.02065647611344638,
  "conservation_residual": 1.573334455476853,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.577591825000127,
  "wall_s_per_eq": [
    7.963626708999072,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
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      "r2_train": 0.9953604241491433,
      "reward": null,
      "residual_heldout": 0.004533314576389459,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.963626708999072,
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      "wall_raw_s": 7.963626708999072,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9967517168583977,
      "reward": null,
      "residual_heldout": 0.0367796376505033,
      "pred_coeffs": {
        "inv_x2": -0.9994954792784244
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.613965116001054,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.613965116001054,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9994954792784244
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=True accepted=False residual=0.01756739079254284 cons=1.2007694603657424 wall_s=14.446 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.01756739079254284,
  "conservation_residual": 1.2007694603657424,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.446264681002503,
  "wall_s_per_eq": [
    7.403400987001078,
    7.042863694001426
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.994496448589055,
      "reward": null,
      "residual_heldout": 0.004224895267824491,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.403400987001078,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.403400987001078,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9968597092296246,
      "reward": null,
      "residual_heldout": 0.030909886317261184,
      "pred_coeffs": {
        "inv_x2": -0.9984033168010564
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.042863694001426,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.042863694001426,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9984033168010564
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=0.7656623809781502 cons=0.37757533267502974 wall_s=14.777 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.7656623809781502,
  "conservation_residual": 0.37757533267502974,
  "equations": [
    "2*v",
    "invx2*k"
  ],
  "wall_s_total": 14.776676863999455,
  "wall_s_per_eq": [
    7.34282359899953,
    7.433853264999925
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "2*v",
      "r2_train": -0.9986599111852079,
      "reward": null,
      "residual_heldout": 1.5287934119546154,
      "pred_coeffs": {
        "v": 2.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": false,
      "wall_s": 7.34282359899953,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.34282359899953,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9321384446435693,
      "reward": null,
      "residual_heldout": 0.0025313500016850453,
      "pred_coeffs": {
        "inv_x2": -0.9716171729493768
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.433853264999925,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.433853264999925,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9716171729493768
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=4

- recovered=True structure_ok=True accepted=True residual=0.003512521946370632 cons=0.08592066773876138 wall_s=15.314 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.003512521946370632,
  "conservation_residual": 0.08592066773876138,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.313811790001637,
  "wall_s_per_eq": [
    7.6271689550012525,
    7.686642835000384
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9944107368288346,
      "reward": null,
      "residual_heldout": 0.003881767924021952,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.6271689550012525,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6271689550012525,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9159068763062311,
      "reward": null,
      "residual_heldout": 0.0031432759687193114,
      "pred_coeffs": {
        "inv_x2": -0.9545558658513872
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.686642835000384,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.686642835000384,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9545558658513872
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=True accepted=False residual=0.2675586098488711 cons=0.03830760097838331 wall_s=15.808 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.2675586098488711,
  "conservation_residual": 0.03830760097838331,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.807737178995012,
  "wall_s_per_eq": [
    8.043136404998222,
    7.76460077399679
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9966329160210465,
      "reward": null,
      "residual_heldout": 0.00840981240344551,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 8.043136404998222,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.043136404998222,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9962246696011505,
      "reward": null,
      "residual_heldout": 0.5267074072942967,
      "pred_coeffs": {
        "inv_x2": -0.9989149076227948
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.76460077399679,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.76460077399679,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9989149076227948
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=6

- recovered=True structure_ok=True accepted=True residual=0.021583240550351525 cons=0.026510392467752004 wall_s=15.509 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.021583240550351525,
  "conservation_residual": 0.026510392467752004,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.509463909995247,
  "wall_s_per_eq": [
    7.945630726997479,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9954134468807033,
      "reward": null,
      "residual_heldout": 0.004553467460049293,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.945630726997479,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.945630726997479,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.9964337360507257,
      "reward": null,
      "residual_heldout": 0.038613013640653754,
      "pred_coeffs": {
        "inv_x2": -0.9871317860809664
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.563833182997769,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.563833182997769,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9871317860809664
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=7

- recovered=True structure_ok=True accepted=True residual=0.0020855735175496805 cons=0.002599138055573637 wall_s=15.465 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0020855735175496805,
  "conservation_residual": 0.002599138055573637,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.465310794999823,
  "wall_s_per_eq": [
    7.599901866000437,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
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      "r2_train": 0.9928262384837058,
      "reward": null,
      "residual_heldout": 0.002932425873014328,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.599901866000437,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.599901866000437,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9361074456900383,
      "reward": null,
      "residual_heldout": 0.0012387211620850332,
      "pred_coeffs": {
        "inv_x2": -0.9911455632306481
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.865408928999386,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.865408928999386,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9911455632306481
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=True accepted=False residual=0.015354186517026955 cons=219.30877518569602 wall_s=14.836 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.015354186517026955,
  "conservation_residual": 219.30877518569602,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.835525661001157,
  "wall_s_per_eq": [
    7.404987383000844,
    7.430538278000313
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.404987383000844,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.404987383000844,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9963597414404737,
      "reward": null,
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        "inv_x2": -0.9942412455026326
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.430538278000313,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.430538278000313,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9942412455026326
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=9

- recovered=True structure_ok=True accepted=True residual=0.005854748295642233 cons=0.017167934642013313 wall_s=14.833 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005854748295642233,
  "conservation_residual": 0.017167934642013313,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.833153724997828,
  "wall_s_per_eq": [
    7.425511721998191,
    7.407642002999637
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9941020203938851,
      "reward": null,
      "residual_heldout": 0.003982430668517882,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.425511721998191,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.425511721998191,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.923052343037564,
      "reward": null,
      "residual_heldout": 0.007727065922766584,
      "pred_coeffs": {
        "inv_x2": -0.9254239773688494
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.407642002999637,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.407642002999637,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9254239773688494
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=10

- recovered=True structure_ok=True accepted=True residual=0.1031736983862779 cons=0.14696282313278672 wall_s=14.716 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.1031736983862779,
  "conservation_residual": 0.14696282313278672,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.715908197002136,
  "wall_s_per_eq": [
    7.332023019000189,
    7.383885178001947
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9956489726993054,
      "reward": null,
      "residual_heldout": 0.007249907304460625,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.332023019000189,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.332023019000189,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9968856349269806,
      "reward": null,
      "residual_heldout": 0.1990974894680952,
      "pred_coeffs": {
        "inv_x2": -1.0007229738356216
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.383885178001947,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.383885178001947,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0007229738356216
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=11

- recovered=True structure_ok=True accepted=True residual=0.16141037847103143 cons=0.012135303747878077 wall_s=15.357 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.16141037847103143,
  "conservation_residual": 0.012135303747878077,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.357083058999706,
  "wall_s_per_eq": [
    7.932060562001425,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.995434561174797,
      "reward": null,
      "residual_heldout": 0.00742666828665813,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.932060562001425,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.932060562001425,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9964447298045579,
      "reward": null,
      "residual_heldout": 0.31539408865540475,
      "pred_coeffs": {
        "inv_x2": -0.9991517956377641
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.425022496998281,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.425022496998281,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9991517956377641
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=True accepted=False residual=0.004502452510585174 cons=77.16550056238044 wall_s=15.533 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.004502452510585174,
  "conservation_residual": 77.16550056238044,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.532861338000657,
  "wall_s_per_eq": [
    7.511960525000177,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9934501459146122,
      "reward": null,
      "residual_heldout": 0.0036408670382067107,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.511960525000177,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.511960525000177,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9139713242482899,
      "reward": null,
      "residual_heldout": 0.005364037982963637,
      "pred_coeffs": {
        "inv_x2": -0.9418523615391174
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.02090081300048,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.02090081300048,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9418523615391174
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=True accepted=False residual=0.004103925249420957 cons=1.466351909182224e+26 wall_s=20.323 ok=True

```json
{
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  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.004103925249420957,
  "conservation_residual": 1.466351909182224e+26,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 20.323172609998437,
  "wall_s_per_eq": [
    9.585784704999242,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.993788986227534,
      "reward": null,
      "residual_heldout": 0.003601875421031562,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 9.585784704999242,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.585784704999242,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9127910288177781,
      "reward": null,
      "residual_heldout": 0.004605975077810354,
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        "inv_x2": -0.9447754547655575
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      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 10.737387904999196,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.737387904999196,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9447754547655575
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=14

- recovered=True structure_ok=True accepted=True residual=0.0030627062506512117 cons=0.35132423798841816 wall_s=15.799 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.0030627062506512117,
  "conservation_residual": 0.35132423798841816,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.798738787998445,
  "wall_s_per_eq": [
    7.585413414999493,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "r2_train": 0.9936694071038094,
      "reward": null,
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.585413414999493,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.585413414999493,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9173709041529061,
      "reward": null,
      "residual_heldout": 0.0035102408656926855,
      "pred_coeffs": {
        "inv_x2": -0.9485901754700015
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.213325372998952,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.213325372998952,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9485901754700015
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=True accepted=False residual=0.003817082499891239 cons=18980403.119804494 wall_s=15.860 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.003817082499891239,
  "conservation_residual": 18980403.119804494,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.860017594997771,
  "wall_s_per_eq": [
    7.788574449998123,
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.788574449998123,
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      "wall_raw_s": 7.788574449998123,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9195456329436524,
      "reward": null,
      "residual_heldout": 0.004504039961523977,
      "pred_coeffs": {
        "inv_x2": -0.9453130680037742
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 8.071443144999648,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.071443144999648,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9453130680037742
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=16

- recovered=True structure_ok=True accepted=True residual=0.005254754184382489 cons=0.2823891054485807 wall_s=15.416 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.005254754184382489,
  "conservation_residual": 0.2823891054485807,
  "equations": [
    "v",
    "-invx2*k"
  ],
  "wall_s_total": 15.416043146997254,
  "wall_s_per_eq": [
    7.767703983998217,
    7.6483391629990365
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9932145384319315,
      "reward": null,
      "residual_heldout": 0.0029709645633964324,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.767703983998217,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.767703983998217,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "-invx2*k",
      "r2_train": 0.7800457155816151,
      "reward": null,
      "residual_heldout": 0.007538543805368546,
      "pred_coeffs": {
        "inv_x2": -0.9232162911579106
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.6483391629990365,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6483391629990365,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.9232162911579106
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=True accepted=False residual=0.2770547218169533 cons=0.04185723065137064 wall_s=14.501 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.2770547218169533,
  "conservation_residual": 0.04185723065137064,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.501309717001277,
  "wall_s_per_eq": [
    6.967035700999986,
    7.534274016001291
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9958887457261636,
      "reward": null,
      "residual_heldout": 0.01167157074353886,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 6.967035700999986,
      "wall_pad_s": 0.0,
      "wall_raw_s": 6.967035700999986,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.996854783964132,
      "reward": null,
      "residual_heldout": 0.5424378728903677,
      "pred_coeffs": {
        "inv_x2": -1.0011574715381488
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.534274016001291,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.534274016001291,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0011574715381488
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=18

- recovered=True structure_ok=True accepted=True residual=0.08102652295377077 cons=0.005991311561753235 wall_s=14.951 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": true,
  "structure_ok": true,
  "accepted": true,
  "residual": 0.08102652295377077,
  "conservation_residual": 0.005991311561753235,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 14.950798077999934,
  "wall_s_per_eq": [
    7.4189269810012775,
    7.531871096998657
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9961144464213957,
      "reward": null,
      "residual_heldout": 0.006260438189699401,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.4189269810012775,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.4189269810012775,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9964199635544866,
      "reward": null,
      "residual_heldout": 0.15579260771784215,
      "pred_coeffs": {
        "inv_x2": -1.0075018247911272
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.531871096998657,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.531871096998657,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -1.0075018247911272
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `gravity_toy` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=True accepted=False residual=0.0035291698835967543 cons=0.6724173212625243 wall_s=15.271 ok=True

```json
{
  "law": "gravity_toy",
  "recoverable": true,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": true,
  "accepted": false,
  "residual": 0.0035291698835967543,
  "conservation_residual": 0.6724173212625243,
  "equations": [
    "v",
    "invx2*k"
  ],
  "wall_s_total": 15.270986851999623,
  "wall_s_per_eq": [
    7.607404438997037,
    7.663582413002587
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0,
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dx/dt",
      "equation": "v",
      "r2_train": 0.9945694445504163,
      "reward": null,
      "residual_heldout": 0.003632514810205956,
      "pred_coeffs": {
        "v": 1.0
      },
      "true_coeffs": {
        "v": 1.0
      },
      "structure_ok": true,
      "wall_s": 7.607404438997037,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.607404438997037,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [],
      "zero_eq": false,
      "zero_eq_retries": 0
    },
    {
      "eq_i": 1,
      "target": "dv/dt",
      "equation": "invx2*k",
      "r2_train": 0.9298755259366405,
      "reward": null,
      "residual_heldout": 0.0034258249569875526,
      "pred_coeffs": {
        "inv_x2": -0.9585394756544058
      },
      "true_coeffs": {
        "inv_x2": -1.0
      },
      "structure_ok": true,
      "wall_s": 7.663582413002587,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.663582413002587,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.9585394756544058
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=8.051671848297695e-32 cons=0.0 wall_s=8.480 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.051671848297695e-32,
  "conservation_residual": 0.0,
  "equations": [
    "y*0.1 - 0.8*(y - (t_feat - y))"
  ],
  "wall_s_total": 8.480177113000536,
  "wall_s_per_eq": [
    8.480177113000536
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*0.1 - 0.8*(y - (t_feat - y))",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 8.051671848297695e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.480177113000536,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=6.96667495371878e-17 cons=0.0 wall_s=9.221 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.96667495371878e-17,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.049999993 + (-t_feat + y + y)*(-0.75)"
  ],
  "wall_s_total": 9.220529963000445,
  "wall_s_per_eq": [
    9.220529963000445
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.049999993 + (-t_feat + y + y)*(-0.75)",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 6.96667495371878e-17,
      "pred_coeffs": {
        "t_feat": 0.799999993,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.220529963000445,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=1.786165978634157e-33 cons=0.0 wall_s=8.125 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.786165978634157e-33,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.00462346 + t_feat*0.79537654 + y*(-1.5) - y + y"
  ],
  "wall_s_total": 8.125021339998057,
  "wall_s_per_eq": [
    8.125021339998057
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.00462346 + t_feat*0.79537654 + y*(-1.5) - y + y",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.786165978634157e-33,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.125021339998057,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=4.782790137388547e-15 cons=0.0 wall_s=8.007 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.782790137388547e-15,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + y*1.875)*(-0.79999995)"
  ],
  "wall_s_total": 8.007309136999538,
  "wall_s_per_eq": [
    8.007309136999538
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + y*1.875)*(-0.79999995)",
      "r2_train": 0.9999999999999959,
      "reward": null,
      "residual_heldout": 4.782790137388547e-15,
      "pred_coeffs": {
        "t_feat": 0.79999995,
        "y": -1.49999990625
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.007309136999538,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=8.584074382668473e-16 cons=0.0 wall_s=8.085 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.584074382668473e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + y*0.10834717 + y*1.7666528)*(-0.8)"
  ],
  "wall_s_total": 8.085452578001423,
  "wall_s_per_eq": [
    8.085452578001423
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + y*0.10834717 + y*1.7666528)*(-0.8)",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 8.584074382668473e-16,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.499999976
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.085452578001423,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=1.9388438948557022e-15 cons=0.0 wall_s=8.084 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.9388438948557022e-15,
  "conservation_residual": 0.0,
  "equations": [
    "5.124216e-8 + (y + (t_feat - y)*(-1.1428571) + 3.5130963e-8)*(-0.70000005)"
  ],
  "wall_s_total": 8.08412208700247,
  "wall_s_per_eq": [
    8.08412208700247
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "5.124216e-8 + (y + (t_feat - y)*(-1.1428571) + 3.5130963e-8)*(-0.70000005)",
      "r2_train": 0.9999999999999981,
      "reward": null,
      "residual_heldout": 1.9388438948557022e-15,
      "pred_coeffs": {
        "t_feat": 0.800000027142855,
        "1": 2.6650484143451855e-08,
        "y": -1.500000077142855
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.08412208700247,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=1.646747761718332e-15 cons=0.0 wall_s=7.796 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.646747761718332e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-y + (-t_feat - 0.37499997*y + y)*(-0.8)"
  ],
  "wall_s_total": 7.795759112999804,
  "wall_s_per_eq": [
    7.795759112999804
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-y + (-t_feat - 0.37499997*y + y)*(-0.8)",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 1.646747761718332e-15,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5000000240000002
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.795759112999804,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=8.214331017662124e-16 cons=0.0 wall_s=7.715 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 8.214331017662124e-16,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*(-0.20000002) + t_feat - y + y*(-0.55175877) - (-0.051758815)*y"
  ],
  "wall_s_total": 7.715003844998137,
  "wall_s_per_eq": [
    7.715003844998137
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*(-0.20000002) + t_feat - y + y*(-0.55175877) - (-0.051758815)*y",
      "r2_train": 0.9999999999999991,
      "reward": null,
      "residual_heldout": 8.214331017662124e-16,
      "pred_coeffs": {
        "t_feat": 0.7999999799999999,
        "y": -1.499999955
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.715003844998137,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=4.8522107425989234e-15 cons=0.0 wall_s=8.899 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.8522107425989234e-15,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8 + y*(-1.1438144) + y*(-0.35618553)"
  ],
  "wall_s_total": 8.898568160999275,
  "wall_s_per_eq": [
    8.898568160999275
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8 + y*(-1.1438144) + y*(-0.35618553)",
      "r2_train": 0.9999999999999928,
      "reward": null,
      "residual_heldout": 4.8522107425989234e-15,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.49999993
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.898568160999275,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=2.126820976820074e-15 cons=0.0 wall_s=8.746 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.126820976820074e-15,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.44627172) + (t_feat + y*(-1.3171604))*0.8"
  ],
  "wall_s_total": 8.746321381000598,
  "wall_s_per_eq": [
    8.746321381000598
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.44627172) + (t_feat + y*(-1.3171604))*0.8",
      "r2_train": 0.999999999999998,
      "reward": null,
      "residual_heldout": 2.126820976820074e-15,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.50000004
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.746321381000598,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=2.0671349959447438e-15 cons=0.0 wall_s=8.580 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.0671349959447438e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-(4.9195258e-8 - 0.05000003*t_feat) + (t_feat - y - y - 1*2.4597629e-8)*0.74999994"
  ],
  "wall_s_total": 8.580414184998517,
  "wall_s_per_eq": [
    8.580414184998517
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(4.9195258e-8 - 0.05000003*t_feat) + (t_feat - y - y - 1*2.4597629e-8)*0.74999994",
      "r2_train": 0.999999999999997,
      "reward": null,
      "residual_heldout": 2.0671349959447438e-15,
      "pred_coeffs": {
        "t_feat": 0.79999997,
        "1": -6.764347827414226e-08,
        "y": -1.49999988
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.580414184998517,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=3.423942859036238e-14 cons=0.0 wall_s=8.098 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.423942859036238e-14,
  "conservation_residual": 0.0,
  "equations": [
    "(-1*t_feat*(-0.79999995) - 1*y*1.5 + 1.1673438e-8) + 8.78174e-8"
  ],
  "wall_s_total": 8.097788977000164,
  "wall_s_per_eq": [
    8.097788977000164
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-1*t_feat*(-0.79999995) - 1*y*1.5 + 1.1673438e-8) + 8.78174e-8",
      "r2_train": 0.9999999999999957,
      "reward": null,
      "residual_heldout": 3.423942859036238e-14,
      "pred_coeffs": {
        "t_feat": 0.79999995,
        "1": 9.949083800000001e-08,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.097788977000164,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=2.4065573310883708e-15 cons=0.0 wall_s=8.121 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.4065573310883708e-15,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.020372977 - 0.779627*(-t_feat + y*1.9239969)"
  ],
  "wall_s_total": 8.12076275399886,
  "wall_s_per_eq": [
    8.12076275399886
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.020372977 - 0.779627*(-t_feat + y*1.9239969)",
      "r2_train": 0.9999999999999976,
      "reward": null,
      "residual_heldout": 2.4065573310883708e-15,
      "pred_coeffs": {
        "t_feat": 0.7999999769999999,
        "y": -1.4999999311563
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.12076275399886,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=1.0012867007995558e-15 cons=0.0 wall_s=8.116 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.0012867007995558e-15,
  "conservation_residual": 0.0,
  "equations": [
    "(-0.9833646*y + (t_feat - y)*1.1238452)*0.7118418"
  ],
  "wall_s_total": 8.115680502000032,
  "wall_s_per_eq": [
    8.115680502000032
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-0.9833646*y + (t_feat - y)*1.1238452)*0.7118418",
      "r2_train": 0.9999999999999987,
      "reward": null,
      "residual_heldout": 1.0012867007995558e-15,
      "pred_coeffs": {
        "t_feat": 0.7999999900893601,
        "y": -1.50000001700964
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.115680502000032,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=3.644978179378122e-16 cons=0.0 wall_s=8.295 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.644978179378122e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(y*1.4134319 - (t_feat - 0.46156812*y))*(-0.8)"
  ],
  "wall_s_total": 8.295076714999595,
  "wall_s_per_eq": [
    8.295076714999595
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*1.4134319 - (t_feat - 0.46156812*y))*(-0.8)",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 3.644978179378122e-16,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.500000016
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.295076714999595,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=1.3817612189525755e-15 cons=0.0 wall_s=8.338 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.3817612189525755e-15,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat*(-0.53333336) + y)*(-1.5) - 7.2327914e-8"
  ],
  "wall_s_total": 8.337908022000192,
  "wall_s_per_eq": [
    8.337908022000192
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat*(-0.53333336) + y)*(-1.5) - 7.2327914e-8",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 1.3817612189525755e-15,
      "pred_coeffs": {
        "t_feat": 0.80000004,
        "1": -7.2327914e-08,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.337908022000192,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=1.9378629137439901e-31 cons=0.0 wall_s=8.036 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.9378629137439901e-31,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - 1.875*y)*0.8"
  ],
  "wall_s_total": 8.036051985000086,
  "wall_s_per_eq": [
    8.036051985000086
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - 1.875*y)*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.9378629137439901e-31,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.036051985000086,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=1.608436129360479e-15 cons=0.0 wall_s=8.084 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.608436129360479e-15,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-1.5) + (t_feat - 1*(-1.7822675e-8))*0.8"
  ],
  "wall_s_total": 8.083702479998465,
  "wall_s_per_eq": [
    8.083702479998465
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-1.5) + (t_feat - 1*(-1.7822675e-8))*0.8",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 1.608436129360479e-15,
      "pred_coeffs": {
        "t_feat": 0.8,
        "1": 1.425814e-08,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.083702479998465,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=1.809115005219123e-15 cons=0.0 wall_s=8.328 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.809115005219123e-15,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.70000005) + (t_feat - y - 1*(-1.8891134e-8))*0.8"
  ],
  "wall_s_total": 8.327816154000175,
  "wall_s_per_eq": [
    8.327816154000175
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.70000005) + (t_feat - y - 1*(-1.8891134e-8))*0.8",
      "r2_train": 0.9999999999999986,
      "reward": null,
      "residual_heldout": 1.809115005219123e-15,
      "pred_coeffs": {
        "t_feat": 0.8,
        "1": 1.51129072e-08,
        "y": -1.5000000500000001
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.327816154000175,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=3.0757844018114886e-15 cons=0.0 wall_s=8.596 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.0757844018114886e-15,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.79999995)*t_feat - y + y*(-0.49999994)"
  ],
  "wall_s_total": 8.595887719999155,
  "wall_s_per_eq": [
    8.595887719999155
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(-0.79999995)*t_feat - y + y*(-0.49999994)",
      "r2_train": 0.999999999999997,
      "reward": null,
      "residual_heldout": 3.0757844018114886e-15,
      "pred_coeffs": {
        "t_feat": 0.79999995,
        "y": -1.49999994
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.595887719999155,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.09306876920784933 cons=0.0 wall_s=8.172 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.09306876920784933,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 8.17154849399958,
  "wall_s_per_eq": [
    8.17154849399958
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9999999999997715,
      "reward": null,
      "residual_heldout": 0.09306876920784933,
      "pred_coeffs": {
        "t_feat": 0.7499997824046202,
        "y": -1.5999998568837084
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.17154849399958,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.17154849399958,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999999284418542,
        -0.7499997824046202
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=False residual=0.3861888061986566 cons=0.0 wall_s=7.709 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.3861888061986566,
  "conservation_residual": 0.0,
  "equations": [
    "k*y*(k*tfeat - 1)"
  ],
  "wall_s_total": 7.708547412999906,
  "wall_s_per_eq": [
    7.708547412999906
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y*(k*tfeat - 1)",
      "r2_train": 0.6787987491498095,
      "reward": null,
      "residual_heldout": 0.3861888061986566,
      "pred_coeffs": {
        "y*tfeat": 1.0
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.708547412999906,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.708547412999906,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0,
        0.7435118408692293
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=False residual=8.585625252582943 cons=0.0 wall_s=8.446 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 8.585625252582943,
  "conservation_residual": 0.0,
  "equations": [
    "2*alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 8.446124406000308,
  "wall_s_per_eq": [
    8.446124406000308
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*alpha*tfeat - 2*k*y",
      "r2_train": 0.9999999999840503,
      "reward": null,
      "residual_heldout": 8.585625252582943,
      "pred_coeffs": {
        "t_feat": 1.4999943342986921,
        "y": -0.7999977542294963
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.446124406000308,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.446124406000308,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.39999887711474813,
        0.7499971671493461
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=5.349403120322202 cons=0.0 wall_s=8.426 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 5.349403120322202,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 8.425848290000431,
  "wall_s_per_eq": [
    8.425848290000431
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 4*k*y",
      "r2_train": 0.9999999999933158,
      "reward": null,
      "residual_heldout": 5.349403120322202,
      "pred_coeffs": {
        "t_feat": 0.3749993797260935,
        "y": -3.199991145337757
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      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.425848290000431,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.425848290000431,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7999977863344393,
        0.3749993797260935
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=False residual=4.889671676782513 cons=0.0 wall_s=9.542 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 4.889671676782513,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - k*y"
  ],
  "wall_s_total": 9.541609563002567,
  "wall_s_per_eq": [
    9.541609563002567
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - k*y",
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      "reward": null,
      "residual_heldout": 4.889671676782513,
      "pred_coeffs": {
        "t_feat": 1.5000002908017211,
        "y": -0.8000001691168737
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.541609563002567,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.541609563002567,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8000001691168737,
        1.5000002908017211
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=False residual=81.11744328591165 cons=0.0 wall_s=8.384 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
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  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 81.11744328591165,
  "conservation_residual": 0.0,
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    "-4*alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.383730771998671,
  "wall_s_per_eq": [
    8.383730771998671
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-4*alpha*tfeat + k*y",
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      "reward": null,
      "residual_heldout": 81.11744328591165,
      "pred_coeffs": {
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        "y": -0.20000000228693726
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.383730771998671,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.383730771998671,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.20000000228693726,
        -1.4999999998981866
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.11280818370638439 cons=0.0 wall_s=8.253 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.11280818370638439,
  "conservation_residual": 0.0,
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    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 8.253146363000269,
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    8.253146363000269
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
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      "residual_heldout": 0.11280818370638439,
      "pred_coeffs": {
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        "y": -1.5999934869080479
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.253146363000269,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.253146363000269,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999967434540239,
        -0.7499974148012103
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=False residual=7.446070208448437 cons=0.0 wall_s=8.043 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
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  "seed": 7,
  "recovered": false,
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  "residual": 7.446070208448437,
  "conservation_residual": 0.0,
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  ],
  "wall_s_total": 8.042869646000327,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
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      "r2_train": 0.9999999995718354,
      "reward": null,
      "residual_heldout": 7.446070208448437,
      "pred_coeffs": {
        "t_feat": 1.5000043368408935,
        "y": -0.8000109762570585
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.042869646000327,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.042869646000327,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8000109762570585,
        1.5000043368408935
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=False residual=5.986300205987326 cons=0.0 wall_s=7.683 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
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  "residual": 5.986300205987326,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.682629396000266,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
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      "residual_heldout": 5.986300205987326,
      "pred_coeffs": {
        "t_feat": -1.500028914987662,
        "y": 0.8000185346745308
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.682629396000266,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.682629396000266,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8000185346745308,
        1.500028914987662
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.046396288051188596 cons=0.0 wall_s=7.868 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
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  "residual": 0.046396288051188596,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 7.8681694570004765,
  "wall_s_per_eq": [
    7.8681694570004765
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 2*k*y",
      "r2_train": 0.9999999999999926,
      "reward": null,
      "residual_heldout": 0.046396288051188596,
      "pred_coeffs": {
        "t_feat": 0.7499999999999999,
        "y": -1.6000000000000008
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.8681694570004765,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.8681694570004765,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8000000000000004,
        0.7499999999999999
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=False residual=27.308942269031164 cons=0.0 wall_s=7.775 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
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  "residual": 27.308942269031164,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 7.775012591999257,
  "wall_s_per_eq": [
    7.775012591999257
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 4*k*y",
      "r2_train": 0.9999999999946191,
      "reward": null,
      "residual_heldout": 27.308942269031164,
      "pred_coeffs": {
        "t_feat": 0.3749994199470233,
        "y": -3.1999924455312523
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.775012591999257,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.775012591999257,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7999981113828131,
        0.3749994199470233
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=False residual=1570.1276075958078 cons=0.0 wall_s=7.841 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
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  "residual": 1570.1276075958078,
  "conservation_residual": 0.0,
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    "-2*alpha*tfeat + k*y"
  ],
  "wall_s_total": 7.8412911250015895,
  "wall_s_per_eq": [
    7.8412911250015895
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
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      "r2_train": 0.9999999999992485,
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      "residual_heldout": 1570.1276075958078,
      "pred_coeffs": {
        "t_feat": 2.999999515129724,
        "y": -0.40000013936648127
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.8412911250015895,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.8412911250015895,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.40000013936648127,
        -1.499999757564862
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=False residual=6.263206144000305 cons=0.0 wall_s=8.690 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.263206144000305,
  "conservation_residual": 0.0,
  "equations": [
    "k*y*(k*tfeat + 1)"
  ],
  "wall_s_total": 8.689821201001905,
  "wall_s_per_eq": [
    8.689821201001905
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y*(k*tfeat + 1)",
      "r2_train": 0.6801157790978225,
      "reward": null,
      "residual_heldout": 6.263206144000305,
      "pred_coeffs": {
        "y*tfeat": 1.0
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.689821201001905,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.689821201001905,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0,
        -0.6898898048372502
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=False residual=6.707851106624654 cons=0.0 wall_s=7.687 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.707851106624654,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.686689026999375,
  "wall_s_per_eq": [
    7.686689026999375
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.999999999999873,
      "reward": null,
      "residual_heldout": 6.707851106624654,
      "pred_coeffs": {
        "t_feat": -1.4999996098806248,
        "y": 0.7999997336909286
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.686689026999375,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.686689026999375,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999997336909286,
        1.4999996098806248
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=False residual=83.22999769425286 cons=0.0 wall_s=8.178 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 83.22999769425286,
  "conservation_residual": 0.0,
  "equations": [
    "3*alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.178340724000009,
  "wall_s_per_eq": [
    8.178340724000009
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "3*alpha*tfeat - k*y",
      "r2_train": 0.9999999999989323,
      "reward": null,
      "residual_heldout": 83.22999769425286,
      "pred_coeffs": {
        "t_feat": 4.50000409228356,
        "y": -0.26666693884918363
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.178340724000009,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.178340724000009,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.26666693884918363,
        1.50000136409452
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=False residual=2.4298526763698343 cons=0.0 wall_s=7.859 ok=True

```json
{
  "law": "dim_violating",
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  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 2.4298526763698343,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 7.858709339998313,
  "wall_s_per_eq": [
    7.858709339998313
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.9999999999987577,
      "reward": null,
      "residual_heldout": 2.4298526763698343,
      "pred_coeffs": {
        "t_feat": 1.4999985083249594,
        "y": -0.799999161602345
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.858709339998313,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.858709339998313,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.799999161602345,
        -1.4999985083249594
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.238663136347181 cons=0.0 wall_s=8.436 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.238663136347181,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 8.43625578299907,
  "wall_s_per_eq": [
    8.43625578299907
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9999999999999893,
      "reward": null,
      "residual_heldout": 0.238663136347181,
      "pred_coeffs": {
        "t_feat": 0.7499999999833302,
        "y": -1.5999999999877412
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.43625578299907,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.43625578299907,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999999999938706,
        -0.7499999999833302
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=False residual=39.21553263121472 cons=0.0 wall_s=9.836 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 39.21553263121472,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 9.836468229001184,
  "wall_s_per_eq": [
    9.836468229001184
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9999999999997042,
      "reward": null,
      "residual_heldout": 39.21553263121472,
      "pred_coeffs": {
        "t_feat": -1.5000007312323986,
        "y": 0.8000004894027378
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.836468229001184,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.836468229001184,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8000004894027378,
        1.5000007312323986
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=False residual=31.604706850614043 cons=0.0 wall_s=9.435 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 31.604706850614043,
  "conservation_residual": 0.0,
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    "k*tfeat*(alpha*tfeat - k*y)"
  ],
  "wall_s_total": 9.435359463997884,
  "wall_s_per_eq": [
    9.435359463997884
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*tfeat*(alpha*tfeat - k*y)",
      "r2_train": 0.3028294714414713,
      "reward": null,
      "residual_heldout": 31.604706850614043,
      "pred_coeffs": {
        "tfeat^2": 1.380011158387837,
        "y*tfeat": -0.610861347632955
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.435359463997884,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.435359463997884,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7815761943873131,
        1.7656770616838504
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.031350714345021805 cons=0.0 wall_s=7.910 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.031350714345021805,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 7.909699114999967,
  "wall_s_per_eq": [
    7.909699114999967
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 2*k*y",
      "r2_train": 0.9999999999999916,
      "reward": null,
      "residual_heldout": 0.031350714345021805,
      "pred_coeffs": {
        "t_feat": 0.75,
        "y": -1.6000000000000005
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.909699114999967,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.909699114999967,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8000000000000003,
        0.75
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=5.729299357905698e-16 cons=0.0 wall_s=8.649 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.729299357905698e-16,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.17536777) - 0.8*(y - (t_feat + y*(-0.65579027)))"
  ],
  "wall_s_total": 8.64936623199901,
  "wall_s_per_eq": [
    8.64936623199901
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.17536777) - 0.8*(y - (t_feat + y*(-0.65579027)))",
      "r2_train": 0.9999999999999997,
      "reward": null,
      "residual_heldout": 5.729299357905698e-16,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.4999999860000002
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.64936623199901,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=3.9056808862763195e-33 cons=0.0 wall_s=8.155 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.9056808862763195e-33,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*(-0.2) + t_feat - 1.5*y"
  ],
  "wall_s_total": 8.154861405000702,
  "wall_s_per_eq": [
    8.154861405000702
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*(-0.2) + t_feat - 1.5*y",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.9056808862763195e-33,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.154861405000702,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=6.197701939810675e-32 cons=0.0 wall_s=8.195 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.197701939810675e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(-0.5161854*t_feat + y)*(-0.5) - (-0.5419073*t_feat + y)"
  ],
  "wall_s_total": 8.194921461999911,
  "wall_s_per_eq": [
    8.194921461999911
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-0.5161854*t_feat + y)*(-0.5) - (-0.5419073*t_feat + y)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 6.197701939810675e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.194921461999911,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=2.4093995202939968e-17 cons=0.0 wall_s=8.652 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.4093995202939968e-17,
  "conservation_residual": 0.0,
  "equations": [
    "-(-5.1906635e-8)*t_feat + (t_feat*0.5333333 - y)*1.5"
  ],
  "wall_s_total": 8.651699620997533,
  "wall_s_per_eq": [
    8.651699620997533
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(-5.1906635e-8)*t_feat + (t_feat*0.5333333 - y)*1.5",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.4093995202939968e-17,
      "pred_coeffs": {
        "t_feat": 0.800000001906635,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.651699620997533,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=4.469571747128197e-32 cons=0.0 wall_s=7.830 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.469571747128197e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.875))*0.8"
  ],
  "wall_s_total": 7.8299764709990995,
  "wall_s_per_eq": [
    7.8299764709990995
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 4.469571747128197e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.8299764709990995,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=1.0306297210027226e-16 cons=0.0 wall_s=8.633 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.0306297210027226e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(-y + y*0.12500001 - (-t_feat + y))*0.8"
  ],
  "wall_s_total": 8.633380596998904,
  "wall_s_per_eq": [
    8.633380596998904
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-y + y*0.12500001 - (-t_feat + y))*0.8",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.0306297210027226e-16,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.4999999920000002
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.633380596998904,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=1.7406411148973403e-32 cons=0.0 wall_s=8.520 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.7406411148973403e-32,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.8)*t_feat - y + y*(-0.5)"
  ],
  "wall_s_total": 8.520163443001366,
  "wall_s_per_eq": [
    8.520163443001366
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(-0.8)*t_feat - y + y*(-0.5)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.7406411148973403e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.520163443001366,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=1.2534959903482817e-16 cons=0.0 wall_s=8.157 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.2534959903482817e-16,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*(-0.18537791) + t_feat + y*(-1.5) + (t_feat + t_feat)*(-0.007311042)"
  ],
  "wall_s_total": 8.157010251998145,
  "wall_s_per_eq": [
    8.157010251998145
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*(-0.18537791) + t_feat + y*(-1.5) + (t_feat + t_feat)*(-0.007311042)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.2534959903482817e-16,
      "pred_coeffs": {
        "t_feat": 0.800000006,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.157010251998145,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=5.086222729348752e-15 cons=0.0 wall_s=8.590 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.086222729348752e-15,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.875) + 8.9705196e-8)*0.8"
  ],
  "wall_s_total": 8.589851062999514,
  "wall_s_per_eq": [
    8.589851062999514
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.875) + 8.9705196e-8)*0.8",
      "r2_train": 0.9999999999999942,
      "reward": null,
      "residual_heldout": 5.086222729348752e-15,
      "pred_coeffs": {
        "t_feat": 0.8,
        "1": 7.17641568e-08,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.589851062999514,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=2.4507076726715848e-32 cons=0.0 wall_s=7.788 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.4507076726715848e-32,
  "conservation_residual": 0.0,
  "equations": [
    "-0.2*t_feat + t_feat - 1.5*y"
  ],
  "wall_s_total": 7.787634357999195,
  "wall_s_per_eq": [
    7.787634357999195
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-0.2*t_feat + t_feat - 1.5*y",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.4507076726715848e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.787634357999195,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=5.566096055295562e-16 cons=0.0 wall_s=8.385 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.566096055295562e-16,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.09230916 + t_feat*0.70769083 - y + y*(-0.5)"
  ],
  "wall_s_total": 8.38478190800015,
  "wall_s_per_eq": [
    8.38478190800015
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.09230916 + t_feat*0.70769083 - y + y*(-0.5)",
      "r2_train": 0.9999999999999998,
      "reward": null,
      "residual_heldout": 5.566096055295562e-16,
      "pred_coeffs": {
        "t_feat": 0.79999999,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.38478190800015,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=3.8710954988369065e-32 cons=0.0 wall_s=7.763 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.8710954988369065e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - y - 0.875*y)*0.8"
  ],
  "wall_s_total": 7.763403900000412,
  "wall_s_per_eq": [
    7.763403900000412
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - y - 0.875*y)*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.8710954988369065e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.763403900000412,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.0 cons=0.0 wall_s=8.839 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8 - 1.5*y"
  ],
  "wall_s_total": 8.839339658999961,
  "wall_s_per_eq": [
    8.839339658999961
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8 - 1.5*y",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 0.0,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.839339658999961,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=6.446389353163259e-16 cons=0.0 wall_s=8.282 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.446389353163259e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + y*(-0.12500003) + y + y)*(-0.8)"
  ],
  "wall_s_total": 8.281725458000437,
  "wall_s_per_eq": [
    8.281725458000437
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + y*(-0.12500003) + y + y)*(-0.8)",
      "r2_train": 0.9999999999999992,
      "reward": null,
      "residual_heldout": 6.446389353163259e-16,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.499999976
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.281725458000437,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=3.93086828073229e-32 cons=0.0 wall_s=8.719 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.93086828073229e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + t_feat + y*(-3.75))*0.4"
  ],
  "wall_s_total": 8.719264688999829,
  "wall_s_per_eq": [
    8.719264688999829
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + t_feat + y*(-3.75))*0.4",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.93086828073229e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.719264688999829,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=4.226069599949119e-15 cons=0.0 wall_s=8.393 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.226069599949119e-15,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8 - y - 0.50000006*y"
  ],
  "wall_s_total": 8.392712289998599,
  "wall_s_per_eq": [
    8.392712289998599
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8 - y - 0.50000006*y",
      "r2_train": 0.9999999999999952,
      "reward": null,
      "residual_heldout": 4.226069599949119e-15,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.50000006
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.392712289998599,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=6.32599286457106e-16 cons=0.0 wall_s=9.088 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 6.32599286457106e-16,
  "conservation_residual": 0.0,
  "equations": [
    "-0.30260134*y + (t_feat + y*(-1.4967483))*0.8"
  ],
  "wall_s_total": 9.08812044500155,
  "wall_s_per_eq": [
    9.08812044500155
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-0.30260134*y + (t_feat + y*(-1.4967483))*0.8",
      "r2_train": 0.9999999999999996,
      "reward": null,
      "residual_heldout": 6.32599286457106e-16,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.4999999800000001
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.08812044500155,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=7.406617265237659e-16 cons=0.0 wall_s=8.097 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 7.406617265237659e-16,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8 + y*(-1.3432201) - 0.15677992*y"
  ],
  "wall_s_total": 8.097119481000846,
  "wall_s_per_eq": [
    8.097119481000846
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8 + y*(-1.3432201) - 0.15677992*y",
      "r2_train": 0.9999999999999994,
      "reward": null,
      "residual_heldout": 7.406617265237659e-16,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5000000199999999
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.097119481000846,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=1.033881733501484e-16 cons=0.0 wall_s=9.125 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.033881733501484e-16,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + t_feat*(-0.06666666) + y + y)*(-0.75)"
  ],
  "wall_s_total": 9.12537648900252,
  "wall_s_per_eq": [
    9.12537648900252
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + t_feat*(-0.06666666) + y + y)*(-0.75)",
      "r2_train": 0.9999999999999999,
      "reward": null,
      "residual_heldout": 1.033881733501484e-16,
      "pred_coeffs": {
        "t_feat": 0.7999999950000001,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.12537648900252,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=5.206380761862231e-32 cons=0.0 wall_s=8.605 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 5.206380761862231e-32,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*(-0.11006748) + t_feat*(-0.08993252) + t_feat - y + y*(-0.29114404) + y*(-0.20885596)"
  ],
  "wall_s_total": 8.60546736300239,
  "wall_s_per_eq": [
    8.60546736300239
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*(-0.11006748) + t_feat*(-0.08993252) + t_feat - y + y*(-0.29114404) + y*(-0.20885596)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 5.206380761862231e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.60546736300239,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.10225355324736414 cons=0.0 wall_s=8.641 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.10225355324736414,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 8.641131731001224,
  "wall_s_per_eq": [
    8.641131731001224
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9999999999999883,
      "reward": null,
      "residual_heldout": 0.10225355324736414,
      "pred_coeffs": {
        "t_feat": 0.7499999996976938,
        "y": -1.5999999997853247
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.641131731001224,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.641131731001224,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999999998926624,
        -0.7499999996976938
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=False residual=6.179931055853738 cons=0.0 wall_s=8.033 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.179931055853738,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.033345238996844,
  "wall_s_per_eq": [
    8.033345238996844
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat + k*y",
      "r2_train": 0.9999999999676863,
      "reward": null,
      "residual_heldout": 6.179931055853738,
      "pred_coeffs": {
        "t_feat": -1.500007649262519,
        "y": 0.800002430982386
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.033345238996844,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.033345238996844,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.800002430982386,
        -1.500007649262519
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=False residual=9.546871298574457 cons=0.0 wall_s=8.236 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 9.546871298574457,
  "conservation_residual": 0.0,
  "equations": [
    "2*alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 8.23638286699861,
  "wall_s_per_eq": [
    8.23638286699861
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*alpha*tfeat - 2*k*y",
      "r2_train": 0.9999999997118578,
      "reward": null,
      "residual_heldout": 9.546871298574457,
      "pred_coeffs": {
        "t_feat": 1.5000036751041317,
        "y": -0.7999919109799155
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.23638286699861,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.23638286699861,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.39999595548995776,
        0.7500018375520658
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=13.133151904326535 cons=0.0 wall_s=8.051 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 13.133151904326535,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.051099640000757,
  "wall_s_per_eq": [
    8.051099640000757
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  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat + k*y",
      "r2_train": 0.9999999999996866,
      "reward": null,
      "residual_heldout": 13.133151904326535,
      "pred_coeffs": {
        "t_feat": -1.5000007287614627,
        "y": 0.8000002150064355
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      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.051099640000757,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.051099640000757,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8000002150064355,
        -1.5000007287614627
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=False residual=7.805603676069572 cons=0.0 wall_s=7.688 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 7.805603676069572,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - 3*k*y"
  ],
  "wall_s_total": 7.687583060000179,
  "wall_s_per_eq": [
    7.687583060000179
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - 3*k*y",
      "r2_train": 0.9999999999994922,
      "reward": null,
      "residual_heldout": 7.805603676069572,
      "pred_coeffs": {
        "t_feat": -0.5000003825791886,
        "y": 2.4000015150981096
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.687583060000179,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.687583060000179,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8000005050327031,
        0.5000003825791886
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=False residual=169.27571221851818 cons=0.0 wall_s=7.974 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
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  "seed": 5,
  "recovered": false,
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  "accepted": false,
  "residual": 169.27571221851818,
  "conservation_residual": 0.0,
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    "-4*alpha*tfeat + k*y"
  ],
  "wall_s_total": 7.973563518997253,
  "wall_s_per_eq": [
    7.973563518997253
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-4*alpha*tfeat + k*y",
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      "reward": null,
      "residual_heldout": 169.27571221851818,
      "pred_coeffs": {
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        "y": -0.20000018290216662
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.973563518997253,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.973563518997253,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.20000018290216662,
        -1.4999998416945715
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.031193220307908085 cons=0.0 wall_s=8.131 ok=True

```json
{
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  "residual": 0.031193220307908085,
  "conservation_residual": 0.0,
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    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 8.130787386999145,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "pred_coeffs": {
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        "y": -1.6000001537286823
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      "true_coeffs": {
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        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.130787386999145,
      "wall_pad_s": 0.0,
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      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8000000768643412,
        -0.7500000309658167
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=False residual=7.690622875414186 cons=0.0 wall_s=7.832 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
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  "residual": 7.690622875414186,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.831614333998004,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "reward": null,
      "residual_heldout": 7.690622875414186,
      "pred_coeffs": {
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        "y": 0.7999996213606688
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.831614333998004,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.831614333998004,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999996213606688,
        1.4999994608556462
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=False residual=8.037546545638651 cons=0.0 wall_s=7.851 ok=True

```json
{
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  "noise": 0.0,
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  "residual": 8.037546545638651,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.851103590997809,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 8.037546545638651,
      "pred_coeffs": {
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        "y": 0.7999994401356222
      },
      "true_coeffs": {
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        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.851103590997809,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.851103590997809,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999994401356222,
        1.4999992545085752
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.035295058030307296 cons=0.0 wall_s=7.703 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
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  "recovered": false,
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  "residual": 0.035295058030307296,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 7.702913297001942,
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  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 0.035295058030307296,
      "pred_coeffs": {
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        "y": -1.6000000000000008
      },
      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 7.702913297001942,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.702913297001942,
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8000000000000004,
        0.7500000000000001
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=False residual=9.240564415739428 cons=0.0 wall_s=7.956 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
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  "residual": 9.240564415739428,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 7.955918720999762,
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    7.955918720999762
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
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      "residual_heldout": 9.240564415739428,
      "pred_coeffs": {
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        "y": -3.199995289966132
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      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.955918720999762,
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      "wall_raw_s": 7.955918720999762,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.799998822491533,
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=False residual=29.65584710201926 cons=0.0 wall_s=7.973 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
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  "residual": 29.65584710201926,
  "conservation_residual": 0.0,
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    "-2*alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.973323620000883,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "pred_coeffs": {
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        "y": 0.40000004402059763
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 7.973323620000883,
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [
        -0.40000004402059763,
        1.5000001586035268
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=False residual=1.864447934236952 cons=0.0 wall_s=8.697 ok=True

```json
{
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  "arm": "A4_physo",
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  "residual": 1.864447934236952,
  "conservation_residual": 0.0,
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    "k*(alpha*tfeat**2 + y)"
  ],
  "wall_s_total": 8.697184329001175,
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    8.697184329001175
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
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  "eq_results": [
    {
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      "residual_heldout": 1.864447934236952,
      "pred_coeffs": {
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      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.697184329001175,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
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      "free_const_values": [
        -0.23490612424908494,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=False residual=6.506731681095207 cons=0.0 wall_s=7.845 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.506731681095207,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.844592777997605,
  "wall_s_per_eq": [
    7.844592777997605
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9999999999997498,
      "reward": null,
      "residual_heldout": 6.506731681095207,
      "pred_coeffs": {
        "t_feat": -1.4999994559606264,
        "y": 0.7999996177138223
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.844592777997605,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.844592777997605,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999996177138223,
        1.4999994559606264
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=False residual=3.650705345159443 cons=0.0 wall_s=7.648 ok=True

```json
{
  "law": "dim_violating",
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.650705345159443,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.6477478810011235,
  "wall_s_per_eq": [
    7.6477478810011235
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - k*y",
      "r2_train": 0.9999999999989108,
      "reward": null,
      "residual_heldout": 3.650705345159443,
      "pred_coeffs": {
        "t_feat": 1.500000268932058,
        "y": -0.7999995204405468
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.6477478810011235,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6477478810011235,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7999995204405468,
        1.500000268932058
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=False residual=3.3032300068392177 cons=0.0 wall_s=7.759 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.3032300068392177,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 7.759236096000677,
  "wall_s_per_eq": [
    7.759236096000677
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.9999999999993562,
      "reward": null,
      "residual_heldout": 3.3032300068392177,
      "pred_coeffs": {
        "t_feat": 1.500000378172557,
        "y": -0.8000005518959522
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.759236096000677,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.759236096000677,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8000005518959522,
        -1.500000378172557
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.05129948555463813 cons=0.0 wall_s=8.793 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.05129948555463813,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 8.792504824999924,
  "wall_s_per_eq": [
    8.792504824999924
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9999999999999407,
      "reward": null,
      "residual_heldout": 0.05129948555463813,
      "pred_coeffs": {
        "t_feat": 0.749999884981833,
        "y": -1.5999999332571215
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.792504824999924,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.792504824999924,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999999666285608,
        -0.749999884981833
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=False residual=7.898650749803092 cons=0.0 wall_s=8.167 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 7.898650749803092,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.166946118999476,
  "wall_s_per_eq": [
    8.166946118999476
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.9999999999947615,
      "reward": null,
      "residual_heldout": 7.898650749803092,
      "pred_coeffs": {
        "t_feat": 1.5000013065160014,
        "y": -0.8000015980107772
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.166946118999476,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.166946118999476,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8000015980107772,
        -1.5000013065160014
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=False residual=15.967596632190345 cons=0.0 wall_s=7.997 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 15.967596632190345,
  "conservation_residual": 0.0,
  "equations": [
    "k*tfeat*(alpha*tfeat - k*y)"
  ],
  "wall_s_total": 7.997274727000331,
  "wall_s_per_eq": [
    7.997274727000331
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*tfeat*(alpha*tfeat - k*y)",
      "r2_train": 0.3632755453425054,
      "reward": null,
      "residual_heldout": 15.967596632190345,
      "pred_coeffs": {
        "tfeat^2": 1.1396727746489688,
        "y*tfeat": -0.5106076980234844
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.997274727000331,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.997274727000331,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7145681899045635,
        1.5949111515881802
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=False residual=87.4307886730565 cons=0.0 wall_s=7.675 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 87.4307886730565,
  "conservation_residual": 0.0,
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    "3*alpha*tfeat + k*y"
  ],
  "wall_s_total": 7.67493653999918,
  "wall_s_per_eq": [
    7.67493653999918
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "3*alpha*tfeat + k*y",
      "r2_train": 0.9999999998906334,
      "reward": null,
      "residual_heldout": 87.4307886730565,
      "pred_coeffs": {
        "t_feat": -4.500037665887345,
        "y": 0.26666950431166225
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.67493653999918,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.67493653999918,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.26666950431166225,
        -1.5000125552957817
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=3.049150299495437e-32 cons=0.0 wall_s=9.116 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.049150299495437e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat - (-0.875)*y + y)*(-0.8)"
  ],
  "wall_s_total": 9.116311492998648,
  "wall_s_per_eq": [
    9.116311492998648
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat - (-0.875)*y + y)*(-0.8)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.049150299495437e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.116311492998648,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=True residual=2.4946958328927076e-32 cons=0.0 wall_s=8.589 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.4946958328927076e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + y*0.875 + y)*(-0.8)"
  ],
  "wall_s_total": 8.589449031002005,
  "wall_s_per_eq": [
    8.589449031002005
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + y*0.875 + y)*(-0.8)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.4946958328927076e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.589449031002005,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=True residual=2.359515649946723e-32 cons=0.0 wall_s=9.190 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.359515649946723e-32,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*(-0.2) + t_feat - y - 0.5*y"
  ],
  "wall_s_total": 9.190090738997242,
  "wall_s_per_eq": [
    9.190090738997242
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*(-0.2) + t_feat - y - 0.5*y",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.359515649946723e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.190090738997242,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=True residual=3.7233040237829184e-32 cons=0.0 wall_s=9.021 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.7233040237829184e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - y + y*(-0.875))*0.8"
  ],
  "wall_s_total": 9.020982168000046,
  "wall_s_per_eq": [
    9.020982168000046
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - y + y*(-0.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.7233040237829184e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.020982168000046,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=True residual=2.4890561796851046e-32 cons=0.0 wall_s=9.158 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.4890561796851046e-32,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.7) + (t_feat - y)*0.8"
  ],
  "wall_s_total": 9.158384137997928,
  "wall_s_per_eq": [
    9.158384137997928
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.7) + (t_feat - y)*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.4890561796851046e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.158384137997928,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=True residual=3.2437331075785796e-32 cons=0.0 wall_s=9.103 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.2437331075785796e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - y - 0.875*y)*0.8"
  ],
  "wall_s_total": 9.102875012998993,
  "wall_s_per_eq": [
    9.102875012998993
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - y - 0.875*y)*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.2437331075785796e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.102875012998993,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=2.241613080199627e-32 cons=0.0 wall_s=9.698 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.241613080199627e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - y + y*(-0.875))*0.8"
  ],
  "wall_s_total": 9.698243405997346,
  "wall_s_per_eq": [
    9.698243405997346
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - y + y*(-0.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.241613080199627e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.698243405997346,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=True residual=2.6902748504380117e-32 cons=0.0 wall_s=9.229 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.6902748504380117e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(y - (t_feat + y*(-0.875)))*(-0.8)"
  ],
  "wall_s_total": 9.22946599900024,
  "wall_s_per_eq": [
    9.22946599900024
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y - (t_feat + y*(-0.875)))*(-0.8)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.6902748504380117e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.22946599900024,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=True residual=2.266584654416045e-32 cons=0.0 wall_s=9.167 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.266584654416045e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + 0.875*y + y)*(-0.8)"
  ],
  "wall_s_total": 9.166634801000328,
  "wall_s_per_eq": [
    9.166634801000328
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + 0.875*y + y)*(-0.8)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.266584654416045e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.166634801000328,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=3.0772947885496636e-32 cons=0.0 wall_s=9.130 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.0772947885496636e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - y + y*(-0.875))*0.8"
  ],
  "wall_s_total": 9.129577267998684,
  "wall_s_per_eq": [
    9.129577267998684
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - y + y*(-0.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.0772947885496636e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.129577267998684,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=True residual=2.8423511003153183e-32 cons=0.0 wall_s=9.030 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.8423511003153183e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(y*(-0.875) - (-t_feat + y))*0.8"
  ],
  "wall_s_total": 9.030123326996545,
  "wall_s_per_eq": [
    9.030123326996545
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*(-0.875) - (-t_feat + y))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.8423511003153183e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.030123326996545,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=True residual=3.183005251635065e-32 cons=0.0 wall_s=8.963 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.183005251635065e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - y + y*(-0.875))*0.8"
  ],
  "wall_s_total": 8.963422381002601,
  "wall_s_per_eq": [
    8.963422381002601
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - y + y*(-0.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.183005251635065e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.963422381002601,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=True residual=4.181040997984179e-32 cons=0.0 wall_s=9.040 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 4.181040997984179e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.875))*0.8"
  ],
  "wall_s_total": 9.039601992000826,
  "wall_s_per_eq": [
    9.039601992000826
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 4.181040997984179e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.039601992000826,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=True residual=2.4587268663052505e-32 cons=0.0 wall_s=8.631 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.4587268663052505e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(y - (t_feat - 0.875*y))*(-0.8)"
  ],
  "wall_s_total": 8.630799778002256,
  "wall_s_per_eq": [
    8.630799778002256
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y - (t_feat - 0.875*y))*(-0.8)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.4587268663052505e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.630799778002256,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=True residual=1.3594128003131773e-32 cons=0.0 wall_s=8.913 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 1.3594128003131773e-32,
  "conservation_residual": 0.0,
  "equations": [
    "y*(-0.5) - (t_feat*(-0.8) + y)"
  ],
  "wall_s_total": 8.913008883002476,
  "wall_s_per_eq": [
    8.913008883002476
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "y*(-0.5) - (t_feat*(-0.8) + y)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 1.3594128003131773e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.913008883002476,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=True residual=3.2781553241148793e-32 cons=0.0 wall_s=9.314 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.2781553241148793e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - y + y*(-0.875))*0.8"
  ],
  "wall_s_total": 9.313529220999044,
  "wall_s_per_eq": [
    9.313529220999044
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - y + y*(-0.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.2781553241148793e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.313529220999044,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=2.7576997732863016e-32 cons=0.0 wall_s=9.077 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.7576997732863016e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + y*0.875 + y)*(-0.8)"
  ],
  "wall_s_total": 9.076687235003192,
  "wall_s_per_eq": [
    9.076687235003192
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + y*0.875 + y)*(-0.8)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.7576997732863016e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.076687235003192,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=True residual=3.0423996164714697e-32 cons=0.0 wall_s=9.150 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.0423996164714697e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat - y + y*(-0.875))*0.8"
  ],
  "wall_s_total": 9.150370327002747,
  "wall_s_per_eq": [
    9.150370327002747
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat - y + y*(-0.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.0423996164714697e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.150370327002747,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=True residual=3.30769109932015e-32 cons=0.0 wall_s=9.217 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 3.30769109932015e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.875))*0.8"
  ],
  "wall_s_total": 9.216832979000174,
  "wall_s_per_eq": [
    9.216832979000174
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.875))*0.8",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 3.30769109932015e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.216832979000174,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=2.9071249348626747e-32 cons=0.0 wall_s=8.574 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 2.9071249348626747e-32,
  "conservation_residual": 0.0,
  "equations": [
    "(y*0.875 - (t_feat - y))*(-0.8)"
  ],
  "wall_s_total": 8.573546102001274,
  "wall_s_per_eq": [
    8.573546102001274
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(y*0.875 - (t_feat - y))*(-0.8)",
      "r2_train": 1.0,
      "reward": null,
      "residual_heldout": 2.9071249348626747e-32,
      "pred_coeffs": {
        "t_feat": 0.8,
        "y": -1.5
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.573546102001274,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.03780627576693241 cons=0.0 wall_s=7.992 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.03780627576693241,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 7.9921516659997,
  "wall_s_per_eq": [
    7.9921516659997
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9999999999999902,
      "reward": null,
      "residual_heldout": 0.03780627576693241,
      "pred_coeffs": {
        "t_feat": 0.7499999999981544,
        "y": -1.5999999999989543
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.9921516659997,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.9921516659997,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999999999994771,
        -0.7499999999981544
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=1

- recovered=False structure_ok=False accepted=False residual=0.7847102040946651 cons=0.0 wall_s=7.954 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.7847102040946651,
  "conservation_residual": 0.0,
  "equations": [
    "k*y*(k*tfeat - 1)"
  ],
  "wall_s_total": 7.953596945000754,
  "wall_s_per_eq": [
    7.953596945000754
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y*(k*tfeat - 1)",
      "r2_train": 0.6672203083712602,
      "reward": null,
      "residual_heldout": 0.7847102040946651,
      "pred_coeffs": {
        "y*tfeat": 1.0
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.953596945000754,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.953596945000754,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0,
        0.7198802958297844
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=2

- recovered=False structure_ok=False accepted=False residual=3.3427127801808525 cons=0.0 wall_s=8.087 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.3427127801808525,
  "conservation_residual": 0.0,
  "equations": [
    "2*alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 8.086973403998854,
  "wall_s_per_eq": [
    8.086973403998854
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*alpha*tfeat - 2*k*y",
      "r2_train": 0.9999999999831131,
      "reward": null,
      "residual_heldout": 3.3427127801808525,
      "pred_coeffs": {
        "t_feat": 1.4999940270334258,
        "y": -0.7999976596258718
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.086973403998854,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.086973403998854,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3999988298129359,
        0.7499970135167129
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=3

- recovered=False structure_ok=False accepted=False residual=7.13544299837265 cons=0.0 wall_s=7.681 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 7.13544299837265,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 7.681308896997507,
  "wall_s_per_eq": [
    7.681308896997507
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 4*k*y",
      "r2_train": 0.9999999999950938,
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      "residual_heldout": 7.13544299837265,
      "pred_coeffs": {
        "t_feat": 0.37499948205438177,
        "y": -3.1999926383814308
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      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.681308896997507,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.681308896997507,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7999981595953577,
        0.37499948205438177
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=4

- recovered=False structure_ok=False accepted=False residual=39.17137194037425 cons=0.0 wall_s=8.067 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 39.17137194037425,
  "conservation_residual": 0.0,
  "equations": [
    "2*alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.067211063000286,
  "wall_s_per_eq": [
    8.067211063000286
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*alpha*tfeat + k*y",
      "r2_train": 0.9999999999969355,
      "reward": null,
      "residual_heldout": 39.17137194037425,
      "pred_coeffs": {
        "t_feat": -3.000003627643728,
        "y": 0.40000076103815985
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.067211063000286,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.067211063000286,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.40000076103815985,
        -1.500001813821864
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=5

- recovered=False structure_ok=False accepted=False residual=13.97790851948213 cons=0.0 wall_s=8.135 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
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  "residual": 13.97790851948213,
  "conservation_residual": 0.0,
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    "alpha*tfeat + 4*k*y"
  ],
  "wall_s_total": 8.13518072900115,
  "wall_s_per_eq": [
    8.13518072900115
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
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      "residual_heldout": 13.97790851948213,
      "pred_coeffs": {
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        "y": 3.2000000079882622
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.13518072900115,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.13518072900115,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8000000019970656,
        -0.37500001620797396
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.037320992177586984 cons=0.0 wall_s=7.570 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
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  "residual": 0.037320992177586984,
  "conservation_residual": 0.0,
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    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 7.569879924998531,
  "wall_s_per_eq": [
    7.569879924998531
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
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      "residual_heldout": 0.037320992177586984,
      "pred_coeffs": {
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        "y": -1.5999999968789622
      },
      "true_coeffs": {
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        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.569879924998531,
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      "wall_raw_s": 7.569879924998531,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999999984394811,
        -0.7499999947913336
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=7

- recovered=False structure_ok=False accepted=False residual=8.182082159552754 cons=0.0 wall_s=8.645 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
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  "residual": 8.182082159552754,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.644637633999082,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9999999999998732,
      "reward": null,
      "residual_heldout": 8.182082159552754,
      "pred_coeffs": {
        "t_feat": -1.499999609617846,
        "y": 0.7999997336916539
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.644637633999082,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.644637633999082,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999997336916539,
        1.499999609617846
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=8

- recovered=False structure_ok=False accepted=False residual=7.081170040040838 cons=0.0 wall_s=8.001 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
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  "residual": 7.081170040040838,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.000946533000388,
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    8.000946533000388
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 7.081170040040838,
      "pred_coeffs": {
        "t_feat": -1.500002060864252,
        "y": 0.800001364257575
      },
      "true_coeffs": {
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        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.000946533000388,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.000946533000388,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.800001364257575,
        1.500002060864252
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.038407994954577085 cons=0.0 wall_s=8.011 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
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  "residual": 0.038407994954577085,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 8.011350618999131,
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    8.011350618999131
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
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      "r2_train": 0.9999999999999903,
      "reward": null,
      "residual_heldout": 0.038407994954577085,
      "pred_coeffs": {
        "t_feat": 0.75,
        "y": -1.6
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.011350618999131,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.011350618999131,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8,
        0.75
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=10

- recovered=False structure_ok=False accepted=False residual=7.041932845363358 cons=0.0 wall_s=7.760 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
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  "residual": 7.041932845363358,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 7.759660681000241,
  "wall_s_per_eq": [
    7.759660681000241
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 4*k*y",
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      "residual_heldout": 7.041932845363358,
      "pred_coeffs": {
        "t_feat": 0.37499950312005836,
        "y": -3.1999929295313265
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.759660681000241,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.759660681000241,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7999982323828316,
        0.37499950312005836
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      "zero_eq": false,
      "zero_eq_retries": 0
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  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=11

- recovered=False structure_ok=False accepted=False residual=4.921822976554505 cons=0.0 wall_s=7.947 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
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  "residual": 4.921822976554505,
  "conservation_residual": 0.0,
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    "alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.946682166999381,
  "wall_s_per_eq": [
    7.946682166999381
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "alpha*tfeat - k*y",
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      "reward": null,
      "residual_heldout": 4.921822976554505,
      "pred_coeffs": {
        "t_feat": 1.500001674552212,
        "y": -0.800001264471537
      },
      "true_coeffs": {
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        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.946682166999381,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.946682166999381,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.800001264471537,
        1.500001674552212
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=12

- recovered=False structure_ok=False accepted=False residual=10.6040334113971 cons=0.0 wall_s=7.905 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
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  "accepted": false,
  "residual": 10.6040334113971,
  "conservation_residual": 0.0,
  "equations": [
    "k*y*(k*tfeat + 1)"
  ],
  "wall_s_total": 7.904943320998427,
  "wall_s_per_eq": [
    7.904943320998427
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y*(k*tfeat + 1)",
      "r2_train": 0.6748803623065143,
      "reward": null,
      "residual_heldout": 10.6040334113971,
      "pred_coeffs": {
        "y*tfeat": 1.0
      },
      "true_coeffs": {
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        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.904943320998427,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.904943320998427,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0,
        -0.7355398302185764
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=13

- recovered=False structure_ok=False accepted=False residual=9.07320988273341 cons=0.0 wall_s=7.798 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 9.07320988273341,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.798374802998296,
  "wall_s_per_eq": [
    7.798374802998296
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9999999999997606,
      "reward": null,
      "residual_heldout": 9.07320988273341,
      "pred_coeffs": {
        "t_feat": -1.4999994421629368,
        "y": 0.7999996070758646
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.798374802998296,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.798374802998296,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999996070758646,
        1.4999994421629368
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=14

- recovered=False structure_ok=False accepted=False residual=22.098449326536194 cons=0.0 wall_s=8.309 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 22.098449326536194,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - 6*k*y"
  ],
  "wall_s_total": 8.308546767002554,
  "wall_s_per_eq": [
    8.308546767002554
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 6*k*y",
      "r2_train": 0.999999999994909,
      "reward": null,
      "residual_heldout": 22.098449326536194,
      "pred_coeffs": {
        "t_feat": 0.24999969057037835,
        "y": -4.7999890937995895
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.308546767002554,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.308546767002554,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7999981822999316,
        0.24999969057037835
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=15

- recovered=False structure_ok=False accepted=False residual=4.31597759018717 cons=0.0 wall_s=8.750 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 4.31597759018717,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.750331383998855,
  "wall_s_per_eq": [
    8.750331383998855
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.999999999827477,
      "reward": null,
      "residual_heldout": 4.31597759018717,
      "pred_coeffs": {
        "t_feat": 1.5000149353898158,
        "y": -0.8000112938573657
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.750331383998855,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.750331383998855,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8000112938573657,
        -1.5000149353898158
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.0433163344657796 cons=0.0 wall_s=8.408 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0433163344657796,
  "conservation_residual": 0.0,
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    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 8.407532088000153,
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    8.407532088000153
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
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      "reward": null,
      "residual_heldout": 0.0433163344657796,
      "pred_coeffs": {
        "t_feat": 0.7499999988913018,
        "y": -1.599999999476656
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.407532088000153,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.407532088000153,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.799999999738328,
        -0.7499999988913018
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=17

- recovered=False structure_ok=False accepted=False residual=7.967300556518193 cons=0.0 wall_s=8.132 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
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  "accepted": false,
  "residual": 7.967300556518193,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.131770282998332,
  "wall_s_per_eq": [
    8.131770282998332
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9999999999999655,
      "reward": null,
      "residual_heldout": 7.967300556518193,
      "pred_coeffs": {
        "t_feat": -1.500000212717882,
        "y": 0.800000145400369
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.131770282998332,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.131770282998332,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.800000145400369,
        1.500000212717882
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=18

- recovered=False structure_ok=False accepted=False residual=23.80679472972992 cons=0.0 wall_s=9.225 ok=True

```json
{
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  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
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  "residual": 23.80679472972992,
  "conservation_residual": 0.0,
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    "k*tfeat*(alpha*tfeat - k*y)"
  ],
  "wall_s_total": 9.22541335400092,
  "wall_s_per_eq": [
    9.22541335400092
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*tfeat*(alpha*tfeat - k*y)",
      "r2_train": 0.43248893373144304,
      "reward": null,
      "residual_heldout": 23.80679472972992,
      "pred_coeffs": {
        "tfeat^2": 1.2585088780045104,
        "y*tfeat": -0.5612220752063724
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.22541335400092,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.22541335400092,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7491475657081003,
        1.6799212005914452
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.0 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.03205368085727263 cons=0.0 wall_s=7.870 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.0,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.03205368085727263,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 7.870231559001695,
  "wall_s_per_eq": [
    7.870231559001695
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 2*k*y",
      "r2_train": 0.9999999999999895,
      "reward": null,
      "residual_heldout": 0.03205368085727263,
      "pred_coeffs": {
        "t_feat": 0.7500000000000006,
        "y": -1.6000000000000014
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.870231559001695,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.870231559001695,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8000000000000007,
        0.7500000000000006
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.007448207637014903 cons=0.0 wall_s=8.346 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007448207637014903,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7856704 + y*(-1.4817456)"
  ],
  "wall_s_total": 8.345550025002012,
  "wall_s_per_eq": [
    8.345550025002012
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7856704 + y*(-1.4817456)",
      "r2_train": 0.9931493923123911,
      "reward": null,
      "residual_heldout": 0.007448207637014903,
      "pred_coeffs": {
        "t_feat": 0.7856704,
        "y": -1.4817456
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.345550025002012,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.007502764978024419 cons=0.0 wall_s=8.285 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.007502764978024419,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7987656 - 1.4957484*y"
  ],
  "wall_s_total": 8.28542123599982,
  "wall_s_per_eq": [
    8.28542123599982
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7987656 - 1.4957484*y",
      "r2_train": 0.9944821342088745,
      "reward": null,
      "residual_heldout": 0.007502764978024419,
      "pred_coeffs": {
        "t_feat": 0.7987656,
        "y": -1.4957484
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.28542123599982,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.01130102484933538 cons=0.0 wall_s=8.086 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.01130102484933538,
  "conservation_residual": 0.0,
  "equations": [
    "(1.0218565 + t_feat*(-0.1396794))*(t_feat + y*(-1.2949661)) - 0.34067136"
  ],
  "wall_s_total": 8.086147567999433,
  "wall_s_per_eq": [
    8.086147567999433
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(1.0218565 + t_feat*(-0.1396794))*(t_feat + y*(-1.2949661)) - 0.34067136",
      "r2_train": 0.994944271903445,
      "reward": null,
      "residual_heldout": 0.01130102484933538,
      "pred_coeffs": {
        "t_feat^2": -0.1396794,
        "y*t_feat": 0.18088008786834,
        "1": -0.34067136
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.086147567999433,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.014661587585521385 cons=0.0 wall_s=7.749 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.014661587585521385,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8061217 + y*(-1.5257083)"
  ],
  "wall_s_total": 7.748559832001774,
  "wall_s_per_eq": [
    7.748559832001774
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8061217 + y*(-1.5257083)",
      "r2_train": 0.9958315545102867,
      "reward": null,
      "residual_heldout": 0.014661587585521385,
      "pred_coeffs": {
        "t_feat": 0.8061217,
        "y": -1.5257083
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.748559832001774,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.006285683961405253 cons=0.0 wall_s=8.682 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006285683961405253,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*(0.6352932 - (t_feat*y*(-0.24435934) - (-0.0297689)*t_feat*t_feat*t_feat)) - 1.4952892*y"
  ],
  "wall_s_total": 8.682445713999186,
  "wall_s_per_eq": [
    8.682445713999186
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*(0.6352932 - (t_feat*y*(-0.24435934) - (-0.0297689)*t_feat*t_feat*t_feat)) - 1.4952892*y",
      "r2_train": 0.9977800237694895,
      "reward": null,
      "residual_heldout": 0.006285683961405253,
      "pred_coeffs": {
        "t_feat": 0.6352932
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.682445713999186,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.0013959002051589058 cons=0.0 wall_s=8.978 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0013959002051589058,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7930371 + y*(-1.4905591)"
  ],
  "wall_s_total": 8.978408803999628,
  "wall_s_per_eq": [
    8.978408803999628
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7930371 + y*(-1.4905591)",
      "r2_train": 0.9955592099084023,
      "reward": null,
      "residual_heldout": 0.0013959002051589058,
      "pred_coeffs": {
        "t_feat": 0.7930371,
        "y": -1.4905591
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.978408803999628,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.005077920663073851 cons=0.0 wall_s=8.696 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005077920663073851,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.7965281)*t_feat + y*(-1.5137042)"
  ],
  "wall_s_total": 8.696097872998507,
  "wall_s_per_eq": [
    8.696097872998507
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(-0.7965281)*t_feat + y*(-1.5137042)",
      "r2_train": 0.9965296675486017,
      "reward": null,
      "residual_heldout": 0.005077920663073851,
      "pred_coeffs": {
        "t_feat": 0.7965281,
        "y": -1.5137042
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.696097872998507,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.0034435005723147897 cons=0.0 wall_s=8.788 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0034435005723147897,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.80556154 + y*(-1.5115428)"
  ],
  "wall_s_total": 8.78757853299976,
  "wall_s_per_eq": [
    8.78757853299976
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.80556154 + y*(-1.5115428)",
      "r2_train": 0.9967544724112225,
      "reward": null,
      "residual_heldout": 0.0034435005723147897,
      "pred_coeffs": {
        "t_feat": 0.80556154,
        "y": -1.5115428
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.78757853299976,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.005696745753358724 cons=0.0 wall_s=8.820 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005696745753358724,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7999583 + y*(-1.4907162)"
  ],
  "wall_s_total": 8.820153459997528,
  "wall_s_per_eq": [
    8.820153459997528
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7999583 + y*(-1.4907162)",
      "r2_train": 0.9967662013151026,
      "reward": null,
      "residual_heldout": 0.005696745753358724,
      "pred_coeffs": {
        "t_feat": 0.7999583,
        "y": -1.4907162
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.820153459997528,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.004003707895219023 cons=0.0 wall_s=8.417 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004003707895219023,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat*(-0.5289008) + y)*(-1.4751688)"
  ],
  "wall_s_total": 8.41698095099855,
  "wall_s_per_eq": [
    8.41698095099855
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat*(-0.5289008) + y)*(-1.4751688)",
      "r2_train": 0.9957972734478451,
      "reward": null,
      "residual_heldout": 0.004003707895219023,
      "pred_coeffs": {
        "t_feat": 0.7802179584550399,
        "y": -1.4751688
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.41698095099855,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.0032925600915676536 cons=0.0 wall_s=8.948 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0032925600915676536,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.78999525)*t_feat + y*(-1.4863188)"
  ],
  "wall_s_total": 8.947664432998863,
  "wall_s_per_eq": [
    8.947664432998863
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(-0.78999525)*t_feat + y*(-1.4863188)",
      "r2_train": 0.9945138035757406,
      "reward": null,
      "residual_heldout": 0.0032925600915676536,
      "pred_coeffs": {
        "t_feat": 0.78999525,
        "y": -1.4863188
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.947664432998863,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.005635825133189003 cons=0.0 wall_s=7.918 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005635825133189003,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7815029 + y*(-1.4617288)"
  ],
  "wall_s_total": 7.91783117399973,
  "wall_s_per_eq": [
    7.91783117399973
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7815029 + y*(-1.4617288)",
      "r2_train": 0.9950540916439221,
      "reward": null,
      "residual_heldout": 0.005635825133189003,
      "pred_coeffs": {
        "t_feat": 0.7815029,
        "y": -1.4617288
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.91783117399973,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.002673770372476858 cons=0.0 wall_s=8.499 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.002673770372476858,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7975635 - 1.4990102*y"
  ],
  "wall_s_total": 8.499419215000671,
  "wall_s_per_eq": [
    8.499419215000671
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7975635 - 1.4990102*y",
      "r2_train": 0.9963885944653921,
      "reward": null,
      "residual_heldout": 0.002673770372476858,
      "pred_coeffs": {
        "t_feat": 0.7975635,
        "y": -1.4990102
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.499419215000671,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.0035815750715059926 cons=0.0 wall_s=8.108 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0035815750715059926,
  "conservation_residual": 0.0,
  "equations": [
    "(-0.53720415*t_feat + y)*(-1.5117755)"
  ],
  "wall_s_total": 8.10771736300012,
  "wall_s_per_eq": [
    8.10771736300012
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-0.53720415*t_feat + y)*(-1.5117755)",
      "r2_train": 0.9965786765814143,
      "reward": null,
      "residual_heldout": 0.0035815750715059926,
      "pred_coeffs": {
        "t_feat": 0.812132072468325,
        "y": -1.5117755
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.10771736300012,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.006859973415867842 cons=0.0 wall_s=8.754 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006859973415867842,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7892115 + y*(-1.5073408)"
  ],
  "wall_s_total": 8.753922750001948,
  "wall_s_per_eq": [
    8.753922750001948
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7892115 + y*(-1.5073408)",
      "r2_train": 0.996973981926759,
      "reward": null,
      "residual_heldout": 0.006859973415867842,
      "pred_coeffs": {
        "t_feat": 0.7892115,
        "y": -1.5073408
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.753922750001948,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.002544180731554368 cons=0.0 wall_s=9.421 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.002544180731554368,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.80112743 - 1.4923885*y"
  ],
  "wall_s_total": 9.420550997001556,
  "wall_s_per_eq": [
    9.420550997001556
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.80112743 - 1.4923885*y",
      "r2_train": 0.9908048937153073,
      "reward": null,
      "residual_heldout": 0.002544180731554368,
      "pred_coeffs": {
        "t_feat": 0.80112743,
        "y": -1.4923885
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.420550997001556,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.013866167153848186 cons=0.0 wall_s=8.120 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.013866167153848186,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.774915 + y*(-1.4629666)"
  ],
  "wall_s_total": 8.119698263999453,
  "wall_s_per_eq": [
    8.119698263999453
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.774915 + y*(-1.4629666)",
      "r2_train": 0.9944918227973676,
      "reward": null,
      "residual_heldout": 0.013866167153848186,
      "pred_coeffs": {
        "t_feat": 0.774915,
        "y": -1.4629666
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.119698263999453,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.00658406700246173 cons=0.0 wall_s=8.022 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00658406700246173,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.79329085 + y*(-1.4831365)"
  ],
  "wall_s_total": 8.02157814200109,
  "wall_s_per_eq": [
    8.02157814200109
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.79329085 + y*(-1.4831365)",
      "r2_train": 0.9960856015994742,
      "reward": null,
      "residual_heldout": 0.00658406700246173,
      "pred_coeffs": {
        "t_feat": 0.79329085,
        "y": -1.4831365
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.02157814200109,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.004031193942551311 cons=0.0 wall_s=8.269 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004031193942551311,
  "conservation_residual": 0.0,
  "equations": [
    "(-0.5334713*t_feat + y)*(-1.474521)"
  ],
  "wall_s_total": 8.268946735999634,
  "wall_s_per_eq": [
    8.268946735999634
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-0.5334713*t_feat + y)*(-1.474521)",
      "r2_train": 0.9971005245606291,
      "reward": null,
      "residual_heldout": 0.004031193942551311,
      "pred_coeffs": {
        "t_feat": 0.7866146347473,
        "y": -1.474521
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.268946735999634,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=50 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.004213971664392892 cons=0.0 wall_s=7.797 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004213971664392892,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8177175 + y*(-1.5346549)"
  ],
  "wall_s_total": 7.79727019100028,
  "wall_s_per_eq": [
    7.79727019100028
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8177175 + y*(-1.5346549)",
      "r2_train": 0.9866829034266563,
      "reward": null,
      "residual_heldout": 0.004213971664392892,
      "pred_coeffs": {
        "t_feat": 0.8177175,
        "y": -1.5346549
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.79727019100028,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.06245150025898686 cons=0.0 wall_s=7.902 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.06245150025898686,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 7.902105631997983,
  "wall_s_per_eq": [
    7.902105631997983
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9931493906359362,
      "reward": null,
      "residual_heldout": 0.06245150025898686,
      "pred_coeffs": {
        "t_feat": 0.7408753106498298,
        "y": -1.57134597580961
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.902105631997983,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.902105631997983,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.785672987904805,
        -0.7408753106498298
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=False residual=1.0296230725789923 cons=0.0 wall_s=7.808 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 1.0296230725789923,
  "conservation_residual": 0.0,
  "equations": [
    "k*y*(k*tfeat - 1)"
  ],
  "wall_s_total": 7.807681084002979,
  "wall_s_per_eq": [
    7.807681084002979
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y*(k*tfeat - 1)",
      "r2_train": 0.6287891669969163,
      "reward": null,
      "residual_heldout": 1.0296230725789923,
      "pred_coeffs": {
        "y*tfeat": 1.0
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.807681084002979,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.807681084002979,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0,
        0.7129102709132749
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=False residual=17.611718240939744 cons=0.0 wall_s=8.075 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 17.611718240939744,
  "conservation_residual": 0.0,
  "equations": [
    "2*alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 8.074614213001041,
  "wall_s_per_eq": [
    8.074614213001041
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*alpha*tfeat - 2*k*y",
      "r2_train": 0.9939886848897324,
      "reward": null,
      "residual_heldout": 17.611718240939744,
      "pred_coeffs": {
        "t_feat": 1.4865510662594958,
        "y": -0.7873183166777711
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.074614213001041,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.074614213001041,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.39365915833888554,
        0.7432755331297479
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=8.034757314450419 cons=0.0 wall_s=7.839 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 8.034757314450419,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 7.839397727002506,
  "wall_s_per_eq": [
    7.839397727002506
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 4*k*y",
      "r2_train": 0.9958315544426541,
      "reward": null,
      "residual_heldout": 8.034757314450419,
      "pred_coeffs": {
        "t_feat": 0.3814286186705732,
        "y": -3.224497305750916
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.839397727002506,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.839397727002506,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.806124326437729,
        0.3814286186705732
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=False residual=19.14436545022465 cons=0.0 wall_s=8.256 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 19.14436545022465,
  "conservation_residual": 0.0,
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    "alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.256042097000318,
  "wall_s_per_eq": [
    8.256042097000318
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - k*y",
      "r2_train": 0.9964904711308088,
      "reward": null,
      "residual_heldout": 19.14436545022465,
      "pred_coeffs": {
        "t_feat": 1.5059705901934635,
        "y": -0.7989016059423604
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.256042097000318,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.256042097000318,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7989016059423604,
        1.5059705901934635
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=False residual=76.26636915110764 cons=0.0 wall_s=8.193 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
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  "residual": 76.26636915110764,
  "conservation_residual": 0.0,
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    "-4*alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.192788738997479,
  "wall_s_per_eq": [
    8.192788738997479
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-4*alpha*tfeat + k*y",
      "r2_train": 0.9955592087786783,
      "reward": null,
      "residual_heldout": 76.26636915110764,
      "pred_coeffs": {
        "t_feat": 5.962241249546259,
        "y": -0.19825973814778858
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.192788738997479,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.192788738997479,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.19825973814778858,
        -1.4905603123865647
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.036978716058458 cons=0.0 wall_s=7.853 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.036978716058458,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 7.853068273001554,
  "wall_s_per_eq": [
    7.853068273001554
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9965296700001215,
      "reward": null,
      "residual_heldout": 0.036978716058458,
      "pred_coeffs": {
        "t_feat": 0.7568539978686286,
        "y": -1.5930560429151157
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.853068273001554,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.853068273001554,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7965280214575579,
        -0.7568539978686286
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=False residual=6.476715116036421 cons=0.0 wall_s=8.134 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.476715116036421,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.134013137001602,
  "wall_s_per_eq": [
    8.134013137001602
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9967544729125623,
      "reward": null,
      "residual_heldout": 6.476715116036421,
      "pred_coeffs": {
        "t_feat": -1.5115517602047632,
        "y": 0.8055675344079823
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.134013137001602,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.134013137001602,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8055675344079823,
        1.5115517602047632
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=False residual=5.902791583193941 cons=0.0 wall_s=7.601 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 5.902791583193941,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.600794921996567,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.996766201726093,
      "reward": null,
      "residual_heldout": 5.902791583193941,
      "pred_coeffs": {
        "t_feat": -1.4907157507631073,
        "y": 0.7999580941481347
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.600794921996567,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.600794921996567,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7999580941481347,
        1.4907157507631073
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.02317771040312273 cons=0.0 wall_s=9.438 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.02317771040312273,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 9.437855487001798,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 2*k*y",
      "r2_train": 0.9957972750168664,
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      "residual_heldout": 0.02317771040312273,
      "pred_coeffs": {
        "t_feat": 0.7375848295816995,
        "y": -1.560436302057381
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.437855487001798,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.437855487001798,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        0.7802181510286905,
        0.7375848295816995
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=False residual=4.054436680870078 cons=0.0 wall_s=7.664 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
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  "residual": 4.054436680870078,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 7.663510389000294,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "alpha*tfeat - 4*k*y",
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      "residual_heldout": 4.054436680870078,
      "pred_coeffs": {
        "t_feat": 0.37157933700418455,
        "y": -3.159974152826281
      },
      "true_coeffs": {
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        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.663510389000294,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.663510389000294,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      "free_const_values": [
        0.7899935382065703,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=False residual=21.443235892248047 cons=0.0 wall_s=7.786 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
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  "residual": 21.443235892248047,
  "conservation_residual": 0.0,
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    "-2*alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.786087116000999,
  "wall_s_per_eq": [
    7.786087116000999
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-2*alpha*tfeat - k*y",
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      "residual_heldout": 21.443235892248047,
      "pred_coeffs": {
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        "y": 0.3907514207931752
      },
      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 7.786087116000999,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.786087116000999,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
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        "device": "cpu",
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      "free_const_values": [
        -0.3907514207931752,
        1.4617279904729792
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=False residual=1.0614609342556607 cons=0.0 wall_s=7.931 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
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  "residual": 1.0614609342556607,
  "conservation_residual": 0.0,
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    "k*(alpha*tfeat**2 + y)"
  ],
  "wall_s_total": 7.931209430000308,
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    7.931209430000308
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "k*(alpha*tfeat**2 + y)",
      "r2_train": 0.9072446738846562,
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      "residual_heldout": 1.0614609342556607,
      "pred_coeffs": {
        "tfeat^2": 0.28455450483724537,
        "y": -0.2278379550261572
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      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.931209430000308,
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      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.2278379550261572,
        -1.248933720479438
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=False residual=5.306290672843422 cons=0.0 wall_s=7.514 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 5.306290672843422,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.514283885000623,
  "wall_s_per_eq": [
    7.514283885000623
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9965786769371404,
      "reward": null,
      "residual_heldout": 5.306290672843422,
      "pred_coeffs": {
        "t_feat": -1.511777776070265,
        "y": 0.8121304595844487
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.514283885000623,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.514283885000623,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8121304595844487,
        1.511777776070265
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=False residual=8.3237196821412 cons=0.0 wall_s=7.971 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 8.3237196821412,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 7.970702292001079,
  "wall_s_per_eq": [
    7.970702292001079
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.9969739815148952,
      "reward": null,
      "residual_heldout": 8.3237196821412,
      "pred_coeffs": {
        "t_feat": 1.507340416168848,
        "y": -0.7892112354318956
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.970702292001079,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.970702292001079,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7892112354318956,
        -1.507340416168848
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=False residual=2.950847391106793 cons=0.0 wall_s=7.774 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 2.950847391106793,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 7.774439753000479,
  "wall_s_per_eq": [
    7.774439753000479
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.9908048939134507,
      "reward": null,
      "residual_heldout": 2.950847391106793,
      "pred_coeffs": {
        "t_feat": 1.4923938312466074,
        "y": -0.8011319887870101
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.774439753000479,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.774439753000479,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8011319887870101,
        -1.4923938312466074
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.09469581203650608 cons=0.0 wall_s=8.655 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.09469581203650608,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 8.655011651000677,
  "wall_s_per_eq": [
    8.655011651000677
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9944918271653942,
      "reward": null,
      "residual_heldout": 0.09469581203650608,
      "pred_coeffs": {
        "t_feat": 0.7314832510566366,
        "y": -1.5498299333259578
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.655011651000677,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.655011651000677,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7749149666629789,
        -0.7314832510566366
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=False residual=8.349200333504573 cons=0.0 wall_s=8.618 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 8.349200333504573,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.61792444800085,
  "wall_s_per_eq": [
    8.61792444800085
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9960856001507189,
      "reward": null,
      "residual_heldout": 8.349200333504573,
      "pred_coeffs": {
        "t_feat": -1.483136791998944,
        "y": 0.7932909879489536
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.61792444800085,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.61792444800085,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7932909879489536,
        1.483136791998944
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=False residual=35.895611372172496 cons=0.0 wall_s=8.618 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 35.895611372172496,
  "conservation_residual": 0.0,
  "equations": [
    "k*tfeat*(alpha*tfeat - k*y)"
  ],
  "wall_s_total": 8.618323185000918,
  "wall_s_per_eq": [
    8.618323185000918
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*tfeat*(alpha*tfeat - k*y)",
      "r2_train": 0.2707283917031177,
      "reward": null,
      "residual_heldout": 35.895611372172496,
      "pred_coeffs": {
        "tfeat^2": 1.1540589473884655,
        "y*tfeat": -0.5111260507622575
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.618323185000918,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.618323185000918,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7149308013802856,
        1.6142246846273434
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=50 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=False residual=3.213241321225366 cons=0.0 wall_s=7.782 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 50,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.213241321225366,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.782199393997871,
  "wall_s_per_eq": [
    7.782199393997871
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - k*y",
      "r2_train": 0.9866829060567622,
      "reward": null,
      "residual_heldout": 3.213241321225366,
      "pred_coeffs": {
        "t_feat": 1.5346860951676804,
        "y": -0.8177312134487289
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.782199393997871,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.782199393997871,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8177312134487289,
        1.5346860951676804
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.003921582405937155 cons=0.0 wall_s=8.603 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003921582405937155,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.45113555 + t_feat - ((t_feat - y)*t_feat*0.32288855 + y) - 0.935057"
  ],
  "wall_s_total": 8.603069109001808,
  "wall_s_per_eq": [
    8.603069109001808
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.45113555 + t_feat - ((t_feat - y)*t_feat*0.32288855 + y) - 0.935057",
      "r2_train": 0.9947081040755114,
      "reward": null,
      "residual_heldout": 0.003921582405937155,
      "pred_coeffs": {
        "t_feat^2": -0.32288855,
        "y*t_feat": 0.32288855,
        "1": -0.935057
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.603069109001808,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.0033650171929120406 cons=0.0 wall_s=8.416 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0033650171929120406,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.8661158))*0.7923275"
  ],
  "wall_s_total": 8.415949316000479,
  "wall_s_per_eq": [
    8.415949316000479
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.8661158))*0.7923275",
      "r2_train": 0.9933043989278821,
      "reward": null,
      "residual_heldout": 0.0033650171929120406,
      "pred_coeffs": {
        "t_feat": 0.7923275,
        "y": -1.4785748665245
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.415949316000479,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.004099033521257711 cons=0.0 wall_s=8.132 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004099033521257711,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.79896283 + y*(-1.4979981)"
  ],
  "wall_s_total": 8.132014908998826,
  "wall_s_per_eq": [
    8.132014908998826
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.79896283 + y*(-1.4979981)",
      "r2_train": 0.9964436489311546,
      "reward": null,
      "residual_heldout": 0.004099033521257711,
      "pred_coeffs": {
        "t_feat": 0.79896283,
        "y": -1.4979981
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.132014908998826,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.008631669984836842 cons=0.0 wall_s=8.472 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008631669984836842,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + y*1.8718021)*(-0.7974333)"
  ],
  "wall_s_total": 8.472171098997933,
  "wall_s_per_eq": [
    8.472171098997933
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + y*1.8718021)*(-0.7974333)",
      "r2_train": 0.995815837780628,
      "reward": null,
      "residual_heldout": 0.008631669984836842,
      "pred_coeffs": {
        "t_feat": 0.7974333,
        "y": -1.4926373255499301
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.472171098997933,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.008339828669663978 cons=0.0 wall_s=8.888 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008339828669663978,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7963255 - 1.4873637*y"
  ],
  "wall_s_total": 8.887988459999178,
  "wall_s_per_eq": [
    8.887988459999178
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7963255 - 1.4873637*y",
      "r2_train": 0.9963837145708179,
      "reward": null,
      "residual_heldout": 0.008339828669663978,
      "pred_coeffs": {
        "t_feat": 0.7963255,
        "y": -1.4873637
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.887988459999178,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.00815275335460336 cons=0.0 wall_s=9.864 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00815275335460336,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.8725871))*0.79560107"
  ],
  "wall_s_total": 9.863628134000464,
  "wall_s_per_eq": [
    9.863628134000464
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.8725871))*0.79560107",
      "r2_train": 0.9970946075741866,
      "reward": null,
      "residual_heldout": 0.00815275335460336,
      "pred_coeffs": {
        "t_feat": 0.79560107,
        "y": -1.489832300428197
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.863628134000464,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.002810541623924151 cons=0.0 wall_s=8.649 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.002810541623924151,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.79710966 + y*(-1.4833509)"
  ],
  "wall_s_total": 8.648912664997624,
  "wall_s_per_eq": [
    8.648912664997624
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.79710966 + y*(-1.4833509)",
      "r2_train": 0.9941079706132967,
      "reward": null,
      "residual_heldout": 0.002810541623924151,
      "pred_coeffs": {
        "t_feat": 0.79710966,
        "y": -1.4833509
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.648912664997624,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.004194208172711005 cons=0.0 wall_s=8.448 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004194208172711005,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.80363494 + y*(-1.4939206)"
  ],
  "wall_s_total": 8.447571855002025,
  "wall_s_per_eq": [
    8.447571855002025
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.80363494 + y*(-1.4939206)",
      "r2_train": 0.9959026285579852,
      "reward": null,
      "residual_heldout": 0.004194208172711005,
      "pred_coeffs": {
        "t_feat": 0.80363494,
        "y": -1.4939206
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.447571855002025,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.0035672477748932125 cons=0.0 wall_s=8.475 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0035672477748932125,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7920086 + y*(-1.4980927)"
  ],
  "wall_s_total": 8.474527139998827,
  "wall_s_per_eq": [
    8.474527139998827
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7920086 + y*(-1.4980927)",
      "r2_train": 0.9966368606362737,
      "reward": null,
      "residual_heldout": 0.0035672477748932125,
      "pred_coeffs": {
        "t_feat": 0.7920086,
        "y": -1.4980927
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.474527139998827,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.00705008603836102 cons=0.0 wall_s=7.995 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00705008603836102,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7933735 + y*(-1.4973015)"
  ],
  "wall_s_total": 7.995330687001115,
  "wall_s_per_eq": [
    7.995330687001115
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7933735 + y*(-1.4973015)",
      "r2_train": 0.9945105908021866,
      "reward": null,
      "residual_heldout": 0.00705008603836102,
      "pred_coeffs": {
        "t_feat": 0.7933735,
        "y": -1.4973015
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.995330687001115,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.010305820453535277 cons=0.0 wall_s=8.414 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.010305820453535277,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7929401 + y*(-1.4987731)"
  ],
  "wall_s_total": 8.414217186000315,
  "wall_s_per_eq": [
    8.414217186000315
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7929401 + y*(-1.4987731)",
      "r2_train": 0.9948884692830173,
      "reward": null,
      "residual_heldout": 0.010305820453535277,
      "pred_coeffs": {
        "t_feat": 0.7929401,
        "y": -1.4987731
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.414217186000315,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.0038452096269341986 cons=0.0 wall_s=8.726 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0038452096269341986,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.79708105 - 1.490709*y"
  ],
  "wall_s_total": 8.725823610999214,
  "wall_s_per_eq": [
    8.725823610999214
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.79708105 - 1.490709*y",
      "r2_train": 0.9959895446014171,
      "reward": null,
      "residual_heldout": 0.0038452096269341986,
      "pred_coeffs": {
        "t_feat": 0.79708105,
        "y": -1.490709
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.725823610999214,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.006043733277215992 cons=0.0 wall_s=8.945 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006043733277215992,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.7928921)*t_feat + y*(-1.4968605)"
  ],
  "wall_s_total": 8.94510999600243,
  "wall_s_per_eq": [
    8.94510999600243
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(-0.7928921)*t_feat + y*(-1.4968605)",
      "r2_train": 0.9963856390464286,
      "reward": null,
      "residual_heldout": 0.006043733277215992,
      "pred_coeffs": {
        "t_feat": 0.7928921,
        "y": -1.4968605
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.94510999600243,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.004862668270092343 cons=0.0 wall_s=8.448 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004862668270092343,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.80277824 - 1.5054743*y"
  ],
  "wall_s_total": 8.447788788002072,
  "wall_s_per_eq": [
    8.447788788002072
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.80277824 - 1.5054743*y",
      "r2_train": 0.9951436106548119,
      "reward": null,
      "residual_heldout": 0.004862668270092343,
      "pred_coeffs": {
        "t_feat": 0.80277824,
        "y": -1.5054743
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.447788788002072,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.009022462473934324 cons=0.0 wall_s=9.006 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.009022462473934324,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7941323 + y*(-1.4918703)"
  ],
  "wall_s_total": 9.005763206001575,
  "wall_s_per_eq": [
    9.005763206001575
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7941323 + y*(-1.4918703)",
      "r2_train": 0.9951958066500798,
      "reward": null,
      "residual_heldout": 0.009022462473934324,
      "pred_coeffs": {
        "t_feat": 0.7941323,
        "y": -1.4918703
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.005763206001575,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.0030914641256729303 cons=0.0 wall_s=8.477 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0030914641256729303,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.8769695))*0.7858862"
  ],
  "wall_s_total": 8.477299761001632,
  "wall_s_per_eq": [
    8.477299761001632
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.8769695))*0.7858862",
      "r2_train": 0.9952765183586025,
      "reward": null,
      "residual_heldout": 0.0030914641256729303,
      "pred_coeffs": {
        "t_feat": 0.7858862,
        "y": -1.4750844278708999
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.477299761001632,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.006935701614491579 cons=0.0 wall_s=8.196 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.006935701614491579,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8034585 - 1.5079694*y"
  ],
  "wall_s_total": 8.195819681997818,
  "wall_s_per_eq": [
    8.195819681997818
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8034585 - 1.5079694*y",
      "r2_train": 0.9961214095172422,
      "reward": null,
      "residual_heldout": 0.006935701614491579,
      "pred_coeffs": {
        "t_feat": 0.8034585,
        "y": -1.5079694
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.195819681997818,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.0032704085191774222 cons=0.0 wall_s=8.356 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0032704085191774222,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8053578 + y*(-1.5018963)"
  ],
  "wall_s_total": 8.356129671999952,
  "wall_s_per_eq": [
    8.356129671999952
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8053578 + y*(-1.5018963)",
      "r2_train": 0.9937182696187077,
      "reward": null,
      "residual_heldout": 0.0032704085191774222,
      "pred_coeffs": {
        "t_feat": 0.8053578,
        "y": -1.5018963
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.356129671999952,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.004702322163822812 cons=0.0 wall_s=8.505 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004702322163822812,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.79481 + y*(-1.4926382)"
  ],
  "wall_s_total": 8.505040061998443,
  "wall_s_per_eq": [
    8.505040061998443
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.79481 + y*(-1.4926382)",
      "r2_train": 0.9957076019016847,
      "reward": null,
      "residual_heldout": 0.004702322163822812,
      "pred_coeffs": {
        "t_feat": 0.79481,
        "y": -1.4926382
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.505040061998443,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.008631632277866277 cons=0.0 wall_s=8.334 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.008631632277866277,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.8770425))*0.80196124"
  ],
  "wall_s_total": 8.333656071001315,
  "wall_s_per_eq": [
    8.333656071001315
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.8770425))*0.80196124",
      "r2_train": 0.9959865467957464,
      "reward": null,
      "residual_heldout": 0.008631632277866277,
      "pred_coeffs": {
        "t_feat": 0.80196124,
        "y": -1.5053153308327
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.333656071001315,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.038155000888557986 cons=0.0 wall_s=13.615 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.038155000888557986,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 13.61487921799926,
  "wall_s_per_eq": [
    13.61487921799926
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9922071001511849,
      "reward": null,
      "residual_heldout": 0.038155000888557986,
      "pred_coeffs": {
        "t_feat": 0.7569438907018147,
        "y": -1.6248768717457138
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 13.61487921799926,
      "wall_pad_s": 0.0,
      "wall_raw_s": 13.61487921799926,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8124384358728569,
        -0.7569438907018147
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=False residual=7.162724752372576 cons=0.0 wall_s=14.508 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 7.162724752372576,
  "conservation_residual": 0.0,
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    "alpha*tfeat + k*y"
  ],
  "wall_s_total": 14.50833018299818,
  "wall_s_per_eq": [
    14.50833018299818
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat + k*y",
      "r2_train": 0.9933043966139928,
      "reward": null,
      "residual_heldout": 7.162724752372576,
      "pred_coeffs": {
        "t_feat": -1.478583949095418,
        "y": 0.7923303980859911
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 14.50833018299818,
      "wall_pad_s": 0.0,
      "wall_raw_s": 14.50833018299818,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7923303980859911,
        -1.478583949095418
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=False residual=3.517421613902536 cons=0.0 wall_s=10.298 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.517421613902536,
  "conservation_residual": 0.0,
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    "2*alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 10.298045406998426,
  "wall_s_per_eq": [
    10.298045406998426
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "2*alpha*tfeat - 2*k*y",
      "r2_train": 0.9964436475081384,
      "reward": null,
      "residual_heldout": 3.517421613902536,
      "pred_coeffs": {
        "t_feat": 1.4980016672568752,
        "y": -0.7989539354188987
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.298045406998426,
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      "wall_raw_s": 10.298045406998426,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.39947696770944935,
        0.7490008336284376
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=11.561377817257776 cons=0.0 wall_s=10.368 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 11.561377817257776,
  "conservation_residual": 0.0,
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    "alpha*tfeat + k*y"
  ],
  "wall_s_total": 10.367735664000065,
  "wall_s_per_eq": [
    10.367735664000065
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat + k*y",
      "r2_train": 0.9958158363403571,
      "reward": null,
      "residual_heldout": 11.561377817257776,
      "pred_coeffs": {
        "t_feat": -1.4926387836073902,
        "y": 0.7974326913541858
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.367735664000065,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.367735664000065,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7974326913541858,
        -1.4926387836073902
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=False residual=6.154528306004354 cons=0.0 wall_s=8.807 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.154528306004354,
  "conservation_residual": 0.0,
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    "alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.806844672002626,
  "wall_s_per_eq": [
    8.806844672002626
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - k*y",
      "r2_train": 0.9963837138625127,
      "reward": null,
      "residual_heldout": 6.154528306004354,
      "pred_coeffs": {
        "t_feat": 1.48736201679978,
        "y": -0.7963242866397446
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.806844672002626,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.806844672002626,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7963242866397446,
        1.48736201679978
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=False residual=186.08470105945406 cons=0.0 wall_s=8.251 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 5,
  "recovered": false,
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  "accepted": false,
  "residual": 186.08470105945406,
  "conservation_residual": 0.0,
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    "-4*alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.250950518999161,
  "wall_s_per_eq": [
    8.250950518999161
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-4*alpha*tfeat + k*y",
      "r2_train": 0.9970946081029439,
      "reward": null,
      "residual_heldout": 186.08470105945406,
      "pred_coeffs": {
        "t_feat": 5.959330764995699,
        "y": -0.1989000018479076
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.250950518999161,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.250950518999161,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.1989000018479076,
        -1.4898326912489248
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.02873048184505306 cons=0.0 wall_s=7.669 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 6,
  "recovered": false,
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  "residual": 0.02873048184505306,
  "conservation_residual": 0.0,
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    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 7.6686624879985175,
  "wall_s_per_eq": [
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9941079691275543,
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      "residual_heldout": 0.02873048184505306,
      "pred_coeffs": {
        "t_feat": 0.7416775452457137,
        "y": -1.5942225169456339
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.6686624879985175,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.6686624879985175,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7971112584728169,
        -0.7416775452457137
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=False residual=7.486292492134076 cons=0.0 wall_s=8.192 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
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  "residual": 7.486292492134076,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.191891419999592,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9959026286113037,
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      "residual_heldout": 7.486292492134076,
      "pred_coeffs": {
        "t_feat": -1.493924283871515,
        "y": 0.8036374482576225
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.191891419999592,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.191891419999592,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8036374482576225,
        1.493924283871515
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=False residual=7.402436239898728 cons=0.0 wall_s=9.801 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 8,
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  "residual": 7.402436239898728,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 9.800704039000266,
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  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9966368600714827,
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      "residual_heldout": 7.402436239898728,
      "pred_coeffs": {
        "t_feat": -1.4980923059988538,
        "y": 0.7920039803228766
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.800704039000266,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.800704039000266,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7920039803228766,
        1.4980923059988538
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.05429597965449576 cons=0.0 wall_s=9.928 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
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  "residual": 0.05429597965449576,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 9.927720425999723,
  "wall_s_per_eq": [
    9.927720425999723
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "alpha*tfeat - 2*k*y",
      "r2_train": 0.9945105934730285,
      "reward": null,
      "residual_heldout": 0.05429597965449576,
      "pred_coeffs": {
        "t_feat": 0.7486532887060676,
        "y": -1.5867499825535125
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.927720425999723,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.927720425999723,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7933749912767563,
        0.7486532887060676
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=False residual=8.243207828443213 cons=0.0 wall_s=9.161 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 10,
  "recovered": false,
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  "residual": 8.243207828443213,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 9.160959608998382,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "alpha*tfeat - 4*k*y",
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      "residual_heldout": 8.243207828443213,
      "pred_coeffs": {
        "t_feat": 0.37469312762409496,
        "y": -3.171757081516287
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      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 9.160959608998382,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.160959608998382,
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      "timed_out": false,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7929392703790717,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=False residual=32.084515639529776 cons=0.0 wall_s=7.682 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 11,
  "recovered": false,
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  "residual": 32.084515639529776,
  "conservation_residual": 0.0,
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    "-2*alpha*tfeat - k*y"
  ],
  "wall_s_total": 7.681513880001148,
  "wall_s_per_eq": [
    7.681513880001148
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-2*alpha*tfeat - k*y",
      "r2_train": 0.9959895461390463,
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      "residual_heldout": 32.084515639529776,
      "pred_coeffs": {
        "t_feat": -2.9814296813313805,
        "y": 0.39854219897136456
      },
      "true_coeffs": {
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      },
      "structure_ok": false,
      "wall_s": 7.681513880001148,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.681513880001148,
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      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      },
      "free_const_values": [
        -0.39854219897136456,
        1.4907148406656903
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=False residual=11.134504710229837 cons=0.0 wall_s=7.916 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
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  "accepted": false,
  "residual": 11.134504710229837,
  "conservation_residual": 0.0,
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    "k*y*(k*tfeat + 1)"
  ],
  "wall_s_total": 7.916218223999749,
  "wall_s_per_eq": [
    7.916218223999749
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y*(k*tfeat + 1)",
      "r2_train": 0.677054341868724,
      "reward": null,
      "residual_heldout": 11.134504710229837,
      "pred_coeffs": {
        "y*tfeat": 1.0
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.916218223999749,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.916218223999749,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0,
        -0.7675403105888777
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=False residual=8.544722100195898 cons=0.0 wall_s=8.207 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 8.544722100195898,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.207294992000243,
  "wall_s_per_eq": [
    8.207294992000243
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat + k*y",
      "r2_train": 0.9951436132422984,
      "reward": null,
      "residual_heldout": 8.544722100195898,
      "pred_coeffs": {
        "t_feat": -1.505474729250839,
        "y": 0.802778002575858
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.207294992000243,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.207294992000243,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.802778002575858,
        -1.505474729250839
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=False residual=4.7944379817435125 cons=0.0 wall_s=8.814 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 4.7944379817435125,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.813899873999617,
  "wall_s_per_eq": [
    8.813899873999617
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.9951958078972412,
      "reward": null,
      "residual_heldout": 4.7944379817435125,
      "pred_coeffs": {
        "t_feat": 1.4918713584269552,
        "y": -0.7941336667977938
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.813899873999617,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.813899873999617,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7941336667977938,
        -1.4918713584269552
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=False residual=79.04113319242522 cons=0.0 wall_s=8.419 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 79.04113319242522,
  "conservation_residual": 0.0,
  "equations": [
    "3*alpha*tfeat + k*y"
  ],
  "wall_s_total": 8.419390410999767,
  "wall_s_per_eq": [
    8.419390410999767
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "3*alpha*tfeat + k*y",
      "r2_train": 0.9952765193520998,
      "reward": null,
      "residual_heldout": 79.04113319242522,
      "pred_coeffs": {
        "t_feat": -4.425260368378711,
        "y": 0.2619628805376465
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.419390410999767,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.419390410999767,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.2619628805376465,
        -1.4750867894595705
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.05374598749839147 cons=0.0 wall_s=9.224 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.05374598749839147,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 9.223807643000328,
  "wall_s_per_eq": [
    9.223807643000328
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9961214106586755,
      "reward": null,
      "residual_heldout": 0.05374598749839147,
      "pred_coeffs": {
        "t_feat": 0.7539819965645262,
        "y": -1.6069098986326844
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.223807643000328,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.223807643000328,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8034549493163422,
        -0.7539819965645262
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=False residual=7.385314158273758 cons=0.0 wall_s=8.801 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 7.385314158273758,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.801053522001894,
  "wall_s_per_eq": [
    8.801053522001894
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9937182689504304,
      "reward": null,
      "residual_heldout": 7.385314158273758,
      "pred_coeffs": {
        "t_feat": -1.5019007299259652,
        "y": 0.805360708083048
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.801053522001894,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.801053522001894,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.805360708083048,
        1.5019007299259652
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=False residual=26.36767188020303 cons=0.0 wall_s=7.791 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 26.36767188020303,
  "conservation_residual": 0.0,
  "equations": [
    "k*tfeat*(alpha*tfeat - k*y)"
  ],
  "wall_s_total": 7.7908566480000445,
  "wall_s_per_eq": [
    7.7908566480000445
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*tfeat*(alpha*tfeat - k*y)",
      "r2_train": 0.5063272514753525,
      "reward": null,
      "residual_heldout": 26.36767188020303,
      "pred_coeffs": {
        "tfeat^2": 1.350081743428877,
        "y*tfeat": -0.5934721819349068
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 7.7908566480000445,
      "wall_pad_s": 0.0,
      "wall_raw_s": 7.7908566480000445,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7703714571133246,
        1.7525074831923255
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=100 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.07646626373096152 cons=0.0 wall_s=8.615 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 100,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.07646626373096152,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 8.61494992200096,
  "wall_s_per_eq": [
    8.61494992200096
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 2*k*y",
      "r2_train": 0.9959865489931324,
      "reward": null,
      "residual_heldout": 0.07646626373096152,
      "pred_coeffs": {
        "t_feat": 0.7526581160497636,
        "y": -1.603925794363059
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.61494992200096,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.61494992200096,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8019628971815295,
        0.7526581160497636
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.0038986755736339068 cons=0.0 wall_s=10.804 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0038986755736339068,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + y*1.8764864)*(-0.7948253)"
  ],
  "wall_s_total": 10.804005193000194,
  "wall_s_per_eq": [
    10.804005193000194
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + y*1.8764864)*(-0.7948253)",
      "r2_train": 0.9947849326649435,
      "reward": null,
      "residual_heldout": 0.0038986755736339068,
      "pred_coeffs": {
        "t_feat": 0.7948253,
        "y": -1.49147886582592
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.804005193000194,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=True residual=0.004218967581635673 cons=0.0 wall_s=9.192 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004218967581635673,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7994888 + y*(-1.4996346)"
  ],
  "wall_s_total": 9.19204662500124,
  "wall_s_per_eq": [
    9.19204662500124
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7994888 + y*(-1.4996346)",
      "r2_train": 0.9955953313955441,
      "reward": null,
      "residual_heldout": 0.004218967581635673,
      "pred_coeffs": {
        "t_feat": 0.7994888,
        "y": -1.4996346
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.19204662500124,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=True residual=0.005039099182473945 cons=0.0 wall_s=9.113 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005039099182473945,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.79754424 + y*(-1.4972036)"
  ],
  "wall_s_total": 9.113168845000473,
  "wall_s_per_eq": [
    9.113168845000473
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.79754424 + y*(-1.4972036)",
      "r2_train": 0.9954713067617013,
      "reward": null,
      "residual_heldout": 0.005039099182473945,
      "pred_coeffs": {
        "t_feat": 0.79754424,
        "y": -1.4972036
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.113168845000473,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=True residual=0.003733180431629344 cons=0.0 wall_s=8.901 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003733180431629344,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.79498875 + y*(-1.493168)"
  ],
  "wall_s_total": 8.901442769998539,
  "wall_s_per_eq": [
    8.901442769998539
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.79498875 + y*(-1.493168)",
      "r2_train": 0.9954309022085759,
      "reward": null,
      "residual_heldout": 0.003733180431629344,
      "pred_coeffs": {
        "t_feat": 0.79498875,
        "y": -1.493168
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.901442769998539,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=True residual=0.005882038006407087 cons=0.0 wall_s=9.311 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 4,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005882038006407087,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.79904133 + y*(-1.49519)"
  ],
  "wall_s_total": 9.310998597000435,
  "wall_s_per_eq": [
    9.310998597000435
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.79904133 + y*(-1.49519)",
      "r2_train": 0.9960314825971138,
      "reward": null,
      "residual_heldout": 0.005882038006407087,
      "pred_coeffs": {
        "t_feat": 0.79904133,
        "y": -1.49519
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.310998597000435,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=True residual=0.00474233582704827 cons=0.0 wall_s=9.209 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 5,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00474233582704827,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat + y*(-1.8736818))*0.7971702"
  ],
  "wall_s_total": 9.20854934900126,
  "wall_s_per_eq": [
    9.20854934900126
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat + y*(-1.8736818))*0.7971702",
      "r2_train": 0.9966002930348379,
      "reward": null,
      "residual_heldout": 0.00474233582704827,
      "pred_coeffs": {
        "t_feat": 0.7971702,
        "y": -1.49364329524236
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.20854934900126,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.004787376387278802 cons=0.0 wall_s=8.865 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 6,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004787376387278802,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat*(-0.534563) + y)*(-1.500609)"
  ],
  "wall_s_total": 8.865107600999181,
  "wall_s_per_eq": [
    8.865107600999181
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat*(-0.534563) + y)*(-1.500609)",
      "r2_train": 0.9953781227192595,
      "reward": null,
      "residual_heldout": 0.004787376387278802,
      "pred_coeffs": {
        "t_feat": 0.802170048867,
        "y": -1.500609
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.865107600999181,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=True residual=0.005490701558510139 cons=0.0 wall_s=8.912 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 7,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005490701558510139,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7980896 + y*(-1.4938594)"
  ],
  "wall_s_total": 8.911928931000148,
  "wall_s_per_eq": [
    8.911928931000148
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7980896 + y*(-1.4938594)",
      "r2_train": 0.9957791021691865,
      "reward": null,
      "residual_heldout": 0.005490701558510139,
      "pred_coeffs": {
        "t_feat": 0.7980896,
        "y": -1.4938594
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.911928931000148,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=True residual=0.0056979056764105505 cons=0.0 wall_s=9.298 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 8,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0056979056764105505,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8009454 + y*(-1.5056851)"
  ],
  "wall_s_total": 9.297626559000491,
  "wall_s_per_eq": [
    9.297626559000491
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8009454 + y*(-1.5056851)",
      "r2_train": 0.9962068697687959,
      "reward": null,
      "residual_heldout": 0.0056979056764105505,
      "pred_coeffs": {
        "t_feat": 0.8009454,
        "y": -1.5056851
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.297626559000491,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.003662798233882803 cons=0.0 wall_s=9.146 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 9,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003662798233882803,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat*(-0.5328446) + y)*(-1.4875976)"
  ],
  "wall_s_total": 9.14585778699984,
  "wall_s_per_eq": [
    9.14585778699984
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat*(-0.5328446) + y)*(-1.4875976)",
      "r2_train": 0.9953736344834934,
      "reward": null,
      "residual_heldout": 0.003662798233882803,
      "pred_coeffs": {
        "t_feat": 0.79265834813296,
        "y": -1.4875976
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.14585778699984,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=True residual=0.0050138665406749775 cons=0.0 wall_s=9.089 ok=True

```json
{
  "law": "dim_violating",
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 10,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0050138665406749775,
  "conservation_residual": 0.0,
  "equations": [
    "(-t_feat + y*1.8762978)*(-0.8009382)"
  ],
  "wall_s_total": 9.08863470399956,
  "wall_s_per_eq": [
    9.08863470399956
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-t_feat + y*1.8762978)*(-0.8009382)",
      "r2_train": 0.9944985108643696,
      "reward": null,
      "residual_heldout": 0.0050138665406749775,
      "pred_coeffs": {
        "t_feat": 0.8009382,
        "y": -1.50279858259596
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.08863470399956,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
        "populations": 15,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=True residual=0.00647402074103401 cons=0.0 wall_s=9.171 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 11,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.00647402074103401,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.7994086 + y*(-1.4978459)"
  ],
  "wall_s_total": 9.171125995999319,
  "wall_s_per_eq": [
    9.171125995999319
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.7994086 + y*(-1.4978459)",
      "r2_train": 0.995892711292002,
      "reward": null,
      "residual_heldout": 0.00647402074103401,
      "pred_coeffs": {
        "t_feat": 0.7994086,
        "y": -1.4978459
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.171125995999319,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
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      "budget": {
        "niterations": 55,
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        "population_size": 40,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
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      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=True residual=0.0051862984184832366 cons=0.0 wall_s=9.050 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 12,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0051862984184832366,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.79656345)*t_feat + y*(-1.4945157)"
  ],
  "wall_s_total": 9.050468690002162,
  "wall_s_per_eq": [
    9.050468690002162
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(-0.79656345)*t_feat + y*(-1.4945157)",
      "r2_train": 0.9957627637291406,
      "reward": null,
      "residual_heldout": 0.0051862984184832366,
      "pred_coeffs": {
        "t_feat": 0.79656345,
        "y": -1.4945157
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.050468690002162,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=True residual=0.0033326351068991133 cons=0.0 wall_s=8.817 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0033326351068991133,
  "conservation_residual": 0.0,
  "equations": [
    "(-0.5340852*t_feat + y)*(-1.494834)"
  ],
  "wall_s_total": 8.817285569002706,
  "wall_s_per_eq": [
    8.817285569002706
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(-0.5340852*t_feat + y)*(-1.494834)",
      "r2_train": 0.9942955890348693,
      "reward": null,
      "residual_heldout": 0.0033326351068991133,
      "pred_coeffs": {
        "t_feat": 0.7983687158568,
        "y": -1.494834
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.817285569002706,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=True residual=0.004251502233229538 cons=0.0 wall_s=8.943 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004251502233229538,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8042103 - 1.5048217*y"
  ],
  "wall_s_total": 8.943155545999616,
  "wall_s_per_eq": [
    8.943155545999616
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8042103 - 1.5048217*y",
      "r2_train": 0.9962136095254224,
      "reward": null,
      "residual_heldout": 0.004251502233229538,
      "pred_coeffs": {
        "t_feat": 0.8042103,
        "y": -1.5048217
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.943155545999616,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
        "maxsize": 22,
        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=True residual=0.004605104974784606 cons=0.0 wall_s=8.983 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.004605104974784606,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8002844 + y*(-1.5001727)"
  ],
  "wall_s_total": 8.982914650998282,
  "wall_s_per_eq": [
    8.982914650998282
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8002844 + y*(-1.5001727)",
      "r2_train": 0.9950506470891907,
      "reward": null,
      "residual_heldout": 0.004605104974784606,
      "pred_coeffs": {
        "t_feat": 0.8002844,
        "y": -1.5001727
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.982914650998282,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=True residual=0.003795490857786603 cons=0.0 wall_s=8.996 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.003795490857786603,
  "conservation_residual": 0.0,
  "equations": [
    "(t_feat*(-0.5329883) + y)*(-1.4970002)"
  ],
  "wall_s_total": 8.996462243001588,
  "wall_s_per_eq": [
    8.996462243001588
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "(t_feat*(-0.5329883) + y)*(-1.4970002)",
      "r2_train": 0.9952819197610597,
      "reward": null,
      "residual_heldout": 0.003795490857786603,
      "pred_coeffs": {
        "t_feat": 0.79788359169766,
        "y": -1.4970002
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.996462243001588,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=True residual=0.0039014301528747385 cons=0.0 wall_s=11.319 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0039014301528747385,
  "conservation_residual": 0.0,
  "equations": [
    "-(-0.79856205)*t_feat + y*(-1.4923973)"
  ],
  "wall_s_total": 11.319394920999912,
  "wall_s_per_eq": [
    11.319394920999912
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-(-0.79856205)*t_feat + y*(-1.4923973)",
      "r2_train": 0.9950638411978852,
      "reward": null,
      "residual_heldout": 0.0039014301528747385,
      "pred_coeffs": {
        "t_feat": 0.79856205,
        "y": -1.4923973
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 11.319394920999912,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=True residual=0.0039792235626809795 cons=0.0 wall_s=9.036 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.0039792235626809795,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.8014264 + y*(-1.500824)"
  ],
  "wall_s_total": 9.0355573429988,
  "wall_s_per_eq": [
    9.0355573429988
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.8014264 + y*(-1.500824)",
      "r2_train": 0.99511713289173,
      "reward": null,
      "residual_heldout": 0.0039792235626809795,
      "pred_coeffs": {
        "t_feat": 0.8014264,
        "y": -1.500824
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.0355573429988,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A0_pysr` / `dim_violating` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=True residual=0.005063186913579496 cons=0.0 wall_s=9.300 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A0_pysr",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.005063186913579496,
  "conservation_residual": 0.0,
  "equations": [
    "t_feat*0.80201954 - 1.5014697*y"
  ],
  "wall_s_total": 9.300067791999027,
  "wall_s_per_eq": [
    9.300067791999027
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "t_feat*0.80201954 - 1.5014697*y",
      "r2_train": 0.9957450646556728,
      "reward": null,
      "residual_heldout": 0.005063186913579496,
      "pred_coeffs": {
        "t_feat": 0.80201954,
        "y": -1.5014697
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.300067791999027,
      "wall_pad_s": 0.0,
      "wall_raw_s": null,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "niterations": 55,
        "populations": 15,
        "population_size": 40,
        "tournament_selection_n": 10,
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        "timeout_in_seconds": 100,
        "wall_cap_s": 120,
        "target_mean_wall_s": 0
      },
      "free_const_values": null,
      "zero_eq": false,
      "zero_eq_retries": null
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=0

- recovered=False structure_ok=False accepted=True residual=0.05305977687132338 cons=0.0 wall_s=9.871 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 0,
  "recovered": false,
  "structure_ok": false,
  "accepted": true,
  "residual": 0.05305977687132338,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 9.871455622000212,
  "wall_s_per_eq": [
    9.871455622000212
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.994784933176373,
      "reward": null,
      "residual_heldout": 0.05305977687132338,
      "pred_coeffs": {
        "t_feat": 0.745739144484208,
        "y": -1.589646371673591
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.871455622000212,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.871455622000212,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7948231858367955,
        -0.745739144484208
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=1

- recovered=False structure_ok=False accepted=False residual=0.8334298304484866 cons=0.0 wall_s=9.982 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 1,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 0.8334298304484866,
  "conservation_residual": 0.0,
  "equations": [
    "k*y*(k*tfeat - 1)"
  ],
  "wall_s_total": 9.981900227998267,
  "wall_s_per_eq": [
    9.981900227998267
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y*(k*tfeat - 1)",
      "r2_train": 0.6679911492354933,
      "reward": null,
      "residual_heldout": 0.8334298304484866,
      "pred_coeffs": {
        "y*tfeat": 1.0
      },
      "true_coeffs": {
        "y": -1.5,
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      },
      "structure_ok": false,
      "wall_s": 9.981900227998267,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.981900227998267,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0,
        0.7238201350519471
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=2

- recovered=False structure_ok=False accepted=False residual=4.781581884348143 cons=0.0 wall_s=10.307 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 2,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 4.781581884348143,
  "conservation_residual": 0.0,
  "equations": [
    "2*alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 10.307251423997513,
  "wall_s_per_eq": [
    10.307251423997513
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "2*alpha*tfeat - 2*k*y",
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      "reward": null,
      "residual_heldout": 4.781581884348143,
      "pred_coeffs": {
        "t_feat": 1.4971956283537475,
        "y": -0.797539798387262
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      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.307251423997513,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.307251423997513,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.398769899193631,
        0.7485978141768738
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=3

- recovered=False structure_ok=False accepted=False residual=6.48428306077037 cons=0.0 wall_s=8.483 ok=True

```json
{
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  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 3,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 6.48428306077037,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 8.483191973999055,
  "wall_s_per_eq": [
    8.483191973999055
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - 4*k*y",
      "r2_train": 0.9954309027411764,
      "reward": null,
      "residual_heldout": 6.48428306077037,
      "pred_coeffs": {
        "t_feat": 0.37329129557494267,
        "y": -3.179946923545193
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.483191973999055,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.483191973999055,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7949867308862982,
        0.37329129557494267
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=4

- recovered=False structure_ok=False accepted=False residual=38.80847443742996 cons=0.0 wall_s=9.688 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
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  "residual": 38.80847443742996,
  "conservation_residual": 0.0,
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    "2*alpha*tfeat + k*y"
  ],
  "wall_s_total": 9.68829447400276,
  "wall_s_per_eq": [
    9.68829447400276
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "2*alpha*tfeat + k*y",
      "r2_train": 0.9960314826059256,
      "reward": null,
      "residual_heldout": 38.80847443742996,
      "pred_coeffs": {
        "t_feat": -2.9903705995849714,
        "y": 0.3995197668998709
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.68829447400276,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.68829447400276,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.3995197668998709,
        -1.4951852997924857
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=5

- recovered=False structure_ok=False accepted=False residual=14.696367905471623 cons=0.0 wall_s=9.701 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
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  "residual": 14.696367905471623,
  "conservation_residual": 0.0,
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    "alpha*tfeat + 4*k*y"
  ],
  "wall_s_total": 9.701298910000332,
  "wall_s_per_eq": [
    9.701298910000332
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "alpha*tfeat + 4*k*y",
      "r2_train": 0.9966002934422232,
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      "residual_heldout": 14.696367905471623,
      "pred_coeffs": {
        "t_feat": -0.37341109256986615,
        "y": 3.1886831659815136
      },
      "true_coeffs": {
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        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.701298910000332,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.701298910000332,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7971707914953784,
        -0.37341109256986615
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=6

- recovered=False structure_ok=False accepted=True residual=0.049202576247544434 cons=0.0 wall_s=10.326 ok=True

```json
{
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  "noise": 0.05,
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  "residual": 0.049202576247544434,
  "conservation_residual": 0.0,
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    "-alpha*tfeat + 2*k*y"
  ],
  "wall_s_total": 10.326161071003298,
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    10.326161071003298
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-alpha*tfeat + 2*k*y",
      "r2_train": 0.9953781220207412,
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      "residual_heldout": 0.049202576247544434,
      "pred_coeffs": {
        "t_feat": 0.7503028515946348,
        "y": -1.6043352670240063
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.326161071003298,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.326161071003298,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8021676335120032,
        -0.7503028515946348
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=7

- recovered=False structure_ok=False accepted=False residual=10.887809416894715 cons=0.0 wall_s=10.007 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 7,
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  "residual": 10.887809416894715,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
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  "wall_s_total": 10.007178176998423,
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    10.007178176998423
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9957791029494213,
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      "residual_heldout": 10.887809416894715,
      "pred_coeffs": {
        "t_feat": -1.4938567715045306,
        "y": 0.7980883026886063
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.007178176998423,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.007178176998423,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7980883026886063,
        1.4938567715045306
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=8

- recovered=False structure_ok=False accepted=False residual=9.911483388667582 cons=0.0 wall_s=12.516 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
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  "residual": 9.911483388667582,
  "conservation_residual": 0.0,
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    "-alpha*tfeat - k*y"
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  "wall_s_total": 12.516396274000726,
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  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.9962068691054295,
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      "residual_heldout": 9.911483388667582,
      "pred_coeffs": {
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        "y": 0.8009466274764562
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 12.516396274000726,
      "wall_pad_s": 0.0,
      "wall_raw_s": 12.516396274000726,
      "wall_cap_s": 120,
      "timed_out": false,
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      "budget": {
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        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
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      "free_const_values": [
        -0.8009466274764562,
        1.5056879366513312
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=9

- recovered=False structure_ok=False accepted=True residual=0.033406313824387995 cons=0.0 wall_s=10.726 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 9,
  "recovered": false,
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  "residual": 0.033406313824387995,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 2*k*y"
  ],
  "wall_s_total": 10.725720749000175,
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  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "target": "dy/dt",
      "equation": "alpha*tfeat - 2*k*y",
      "r2_train": 0.9953736328826281,
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      "residual_heldout": 0.033406313824387995,
      "pred_coeffs": {
        "t_feat": 0.7438000998127683,
        "y": -1.5853165237204832
      },
      "true_coeffs": {
        "y": -1.5,
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      "structure_ok": false,
      "wall_s": 10.725720749000175,
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      "wall_raw_s": 10.725720749000175,
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      "budget": {
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        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
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      "free_const_values": [
        0.7926582618602416,
        0.7438000998127683
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=10

- recovered=False structure_ok=False accepted=False residual=6.116116801635366 cons=0.0 wall_s=8.743 ok=True

```json
{
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  "n_samples": 400,
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  "residual": 6.116116801635366,
  "conservation_residual": 0.0,
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    "alpha*tfeat - 4*k*y"
  ],
  "wall_s_total": 8.743401972002175,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "residual_heldout": 6.116116801635366,
      "pred_coeffs": {
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        "y": -3.2037443475796294
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      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.743401972002175,
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      "wall_raw_s": 8.743401972002175,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "device": "cpu",
        "wall_cap_s": 120,
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      "free_const_values": [
        0.8009360868949074,
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=11

- recovered=False structure_ok=False accepted=False residual=8.858090637906589 cons=0.0 wall_s=8.490 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
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  "seed": 11,
  "recovered": false,
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  "residual": 8.858090637906589,
  "conservation_residual": 0.0,
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  ],
  "wall_s_total": 8.490182240999275,
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  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
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      "equation": "alpha*tfeat + k*y",
      "r2_train": 0.995892709977696,
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      "pred_coeffs": {
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        "y": 0.7994085018268539
      },
      "true_coeffs": {
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      "structure_ok": false,
      "wall_s": 8.490182240999275,
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      "wall_raw_s": 8.490182240999275,
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      "budget": {
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        "max_n_evaluations": 2500,
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        "device": "cpu",
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      "free_const_values": [
        0.7994085018268539,
        -1.4978455173460723
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      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=12

- recovered=False structure_ok=False accepted=False residual=11.437106476120762 cons=0.0 wall_s=8.902 ok=True

```json
{
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  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 12,
  "recovered": false,
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  "residual": 11.437106476120762,
  "conservation_residual": 0.0,
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    "k*y*(k*tfeat + 1)"
  ],
  "wall_s_total": 8.902087841001048,
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    8.902087841001048
  ],
  "wall_pad_s_total": 0.0,
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    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*y*(k*tfeat + 1)",
      "r2_train": 0.662538790971325,
      "reward": null,
      "residual_heldout": 11.437106476120762,
      "pred_coeffs": {
        "y*tfeat": 1.0
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.902087841001048,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.902087841001048,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        1.0,
        -0.7298612805879179
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=13

- recovered=False structure_ok=False accepted=False residual=7.450747208165156 cons=0.0 wall_s=8.416 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 13,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 7.450747208165156,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat - k*y"
  ],
  "wall_s_total": 8.416473217999737,
  "wall_s_per_eq": [
    8.416473217999737
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat - k*y",
      "r2_train": 0.994295589695995,
      "reward": null,
      "residual_heldout": 7.450747208165156,
      "pred_coeffs": {
        "t_feat": -1.4948341685186026,
        "y": 0.7983679001286217
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.416473217999737,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.416473217999737,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7983679001286217,
        1.4948341685186026
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=14

- recovered=False structure_ok=False accepted=False residual=4.079614247874473 cons=0.0 wall_s=10.939 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 14,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 4.079614247874473,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 10.939075925001816,
  "wall_s_per_eq": [
    10.939075925001816
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.9962136098419625,
      "reward": null,
      "residual_heldout": 4.079614247874473,
      "pred_coeffs": {
        "t_feat": 1.5048223442177124,
        "y": -0.8042109628919983
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.939075925001816,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.939075925001816,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.8042109628919983,
        -1.5048223442177124
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=15

- recovered=False structure_ok=False accepted=False residual=67.64977350272713 cons=0.0 wall_s=9.973 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 15,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 67.64977350272713,
  "conservation_residual": 0.0,
  "equations": [
    "3*alpha*tfeat + k*y"
  ],
  "wall_s_total": 9.97274980399743,
  "wall_s_per_eq": [
    9.97274980399743
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "3*alpha*tfeat + k*y",
      "r2_train": 0.9950506473002019,
      "reward": null,
      "residual_heldout": 67.64977350272713,
      "pred_coeffs": {
        "t_feat": -4.500592621265146,
        "y": 0.2667672328669724
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.97274980399743,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.97274980399743,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.2667672328669724,
        -1.5001975404217154
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=16

- recovered=False structure_ok=False accepted=False residual=3.2605829907902057 cons=0.0 wall_s=10.049 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 16,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.2605829907902057,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - k*y"
  ],
  "wall_s_total": 10.048825906997081,
  "wall_s_per_eq": [
    10.048825906997081
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - k*y",
      "r2_train": 0.9952819210373599,
      "reward": null,
      "residual_heldout": 3.2605829907902057,
      "pred_coeffs": {
        "t_feat": 1.4970000459110713,
        "y": -0.7978838591917997
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.048825906997081,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.048825906997081,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7978838591917997,
        1.4970000459110713
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=17

- recovered=False structure_ok=False accepted=False residual=3.9573062247164166 cons=0.0 wall_s=10.730 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 17,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.9573062247164166,
  "conservation_residual": 0.0,
  "equations": [
    "-alpha*tfeat + k*y"
  ],
  "wall_s_total": 10.729810572000133,
  "wall_s_per_eq": [
    10.729810572000133
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "-alpha*tfeat + k*y",
      "r2_train": 0.995063840885224,
      "reward": null,
      "residual_heldout": 3.9573062247164166,
      "pred_coeffs": {
        "t_feat": 1.4924008813636105,
        "y": -0.7985661428945896
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 10.729810572000133,
      "wall_pad_s": 0.0,
      "wall_raw_s": 10.729810572000133,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        -0.7985661428945896,
        -1.4924008813636105
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=18

- recovered=False structure_ok=False accepted=False residual=15.387553268015598 cons=0.0 wall_s=8.732 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 18,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 15.387553268015598,
  "conservation_residual": 0.0,
  "equations": [
    "k*tfeat*(alpha*tfeat - k*y)"
  ],
  "wall_s_total": 8.73160512100003,
  "wall_s_per_eq": [
    8.73160512100003
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "k*tfeat*(alpha*tfeat - k*y)",
      "r2_train": 0.462711813183602,
      "reward": null,
      "residual_heldout": 15.387553268015598,
      "pred_coeffs": {
        "tfeat^2": 1.2090773671387656,
        "y*tfeat": -0.5373717643194984
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 8.73160512100003,
      "wall_pad_s": 0.0,
      "wall_raw_s": 8.73160512100003,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.7330564537056463,
        1.6493646035401555
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

### `A4_physo` / `dim_violating` / N=400 / σ=0.05 / seed=19

- recovered=False structure_ok=False accepted=False residual=3.5166234758888524 cons=0.0 wall_s=9.094 ok=True

```json
{
  "law": "dim_violating",
  "recoverable": false,
  "noise": 0.05,
  "n_samples": 400,
  "arm": "A4_physo",
  "seed": 19,
  "recovered": false,
  "structure_ok": false,
  "accepted": false,
  "residual": 3.5166234758888524,
  "conservation_residual": 0.0,
  "equations": [
    "alpha*tfeat - k*y"
  ],
  "wall_s_total": 9.094011162000243,
  "wall_s_per_eq": [
    9.094011162000243
  ],
  "wall_pad_s_total": 0.0,
  "wall_pad_s_per_eq": [
    0.0
  ],
  "zero_eq_count": 0,
  "blockers": [],
  "ok": true,
  "tau": 0.2,
  "R_star": 0.25,
  "C_star": 0.5,
  "eq_results": [
    {
      "eq_i": 0,
      "target": "dy/dt",
      "equation": "alpha*tfeat - k*y",
      "r2_train": 0.9957450648970645,
      "reward": null,
      "residual_heldout": 3.5166234758888524,
      "pred_coeffs": {
        "t_feat": 1.5014699556623614,
        "y": -0.8020195214424667
      },
      "true_coeffs": {
        "y": -1.5,
        "t_feat": 0.8
      },
      "structure_ok": false,
      "wall_s": 9.094011162000243,
      "wall_pad_s": 0.0,
      "wall_raw_s": 9.094011162000243,
      "wall_cap_s": 120,
      "timed_out": false,
      "blocker": null,
      "budget": {
        "epochs": 8,
        "stop_after_n_epochs": 8,
        "max_n_evaluations": 2500,
        "batch_size": 32,
        "parallel_mode": false,
        "device": "cpu",
        "wall_cap_s": 120,
        "zero_eq_retry": 2
      },
      "free_const_values": [
        0.8020195214424667,
        1.5014699556623614
      ],
      "zero_eq": false,
      "zero_eq_retries": 0
    }
  ]
}
```

## Honest status

- Cells completed: 1920
- matched wall arm_means_within_band: True
- A4 zero-eq cells: 0
- prop01_support_claim: **false** (§5 not claimed on this live artifact)
- Do not equate these rates with STLS-proxy tables.

## Full E1 command (when ready)

```bash
cd /workspace/lumen-axiom/sims/sr-ladder
/workspace/lumen-axiom/sims/.venv/bin/python run_prop01_live_e1.py --mode full \
  2>&1 | tee results/prop01_live_e1_full_run.log
```