gpu_results.json

{
  "paper": "Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solvers",
  "openreview_id": "71069",
  "canonical_openreview_id": "7pQIzVNctu",
  "arxiv_id": "2502.08834",
  "official_code_commit": "e39b57415d5608b18d7c5631595f1d38f06813b8",
  "device": "cuda",
  "gpu": "Tesla T4",
  "torch_version": "2.7.1+cu128",
  "roundtrip": [
    {
      "tableau": "euler",
      "dtype": "float32",
      "dimensions": 1000000,
      "steps_each_direction": 50,
      "linf_error": 3.0040740966796875e-05,
      "relative_l2_error": 2.282993818880641e-06,
      "shadow_linf_error": 2.1219253540039062e-05,
      "nfe": 200,
      "seconds": 0.2792018550007924,
      "input_sha256": "431e0f744b6d70360df741c4ee7ac89af78242d1d938301f4eb3e4741277670e"
    },
    {
      "tableau": "midpoint",
      "dtype": "float32",
      "dimensions": 1000000,
      "steps_each_direction": 50,
      "linf_error": 3.7670135498046875e-05,
      "relative_l2_error": 2.2400461148208706e-06,
      "shadow_linf_error": 2.47955322265625e-05,
      "nfe": 400,
      "seconds": 0.303511379000156,
      "input_sha256": "431e0f744b6d70360df741c4ee7ac89af78242d1d938301f4eb3e4741277670e"
    },
    {
      "tableau": "ssprk3",
      "dtype": "float32",
      "dimensions": 1000000,
      "steps_each_direction": 50,
      "linf_error": 4.4345855712890625e-05,
      "relative_l2_error": 2.2409772100218106e-06,
      "shadow_linf_error": 3.3855438232421875e-05,
      "nfe": 600,
      "seconds": 0.48579267299919593,
      "input_sha256": "431e0f744b6d70360df741c4ee7ac89af78242d1d938301f4eb3e4741277670e"
    },
    {
      "tableau": "rk4",
      "dtype": "float32",
      "dimensions": 1000000,
      "steps_each_direction": 50,
      "linf_error": 4.4345855712890625e-05,
      "relative_l2_error": 2.242354185000295e-06,
      "shadow_linf_error": 3.3855438232421875e-05,
      "nfe": 800,
      "seconds": 0.5671450250001726,
      "input_sha256": "431e0f744b6d70360df741c4ee7ac89af78242d1d938301f4eb3e4741277670e"
    },
    {
      "tableau": "dopri5",
      "dtype": "float32",
      "dimensions": 1000000,
      "steps_each_direction": 50,
      "linf_error": 3.719329833984375e-05,
      "relative_l2_error": 2.2533777155331336e-06,
      "shadow_linf_error": 2.2411346435546875e-05,
      "nfe": 1400,
      "seconds": 1.4179162769996765,
      "input_sha256": "431e0f744b6d70360df741c4ee7ac89af78242d1d938301f4eb3e4741277670e"
    }
  ],
  "convergence": [
    {
      "tableau": "euler",
      "expected_order": 1,
      "fitted_order": 0.9781951526182323,
      "n_steps": [
        16,
        32,
        64,
        128,
        256
      ],
      "absolute_errors": [
        0.01800766438958878,
        0.009363825660256349,
        0.004766146844379052,
        0.002399156395443587,
        0.001199014279126158
      ],
      "exact_endpoint": 0.04462603202968594
    },
    {
      "tableau": "midpoint",
      "expected_order": 2,
      "fitted_order": 2.1181125606161872,
      "n_steps": [
        4,
        8,
        16,
        32,
        64
      ],
      "absolute_errors": [
        0.00987657290366506,
        0.002398576715642406,
        0.0005391167024832652,
        0.00012180123111532604,
        2.842367094964965e-05
      ],
      "exact_endpoint": 0.04462603202968594
    },
    {
      "tableau": "ssprk3",
      "expected_order": 3,
      "fitted_order": 2.861663554369008,
      "n_steps": [
        4,
        8,
        16,
        32,
        64
      ],
      "absolute_errors": [
        0.0021718664985892547,
        0.00034026646956804296,
        4.7048094796671436e-05,
        6.18324143322746e-06,
        7.9414858204091e-07
      ],
      "exact_endpoint": 0.04462603202968594
    },
    {
      "tableau": "rk4",
      "expected_order": 4,
      "fitted_order": 3.6379848453273773,
      "n_steps": [
        2,
        4,
        8,
        16,
        32
      ],
      "absolute_errors": [
        0.0025518916634266683,
        0.00035842265885435015,
        3.064232893397467e-05,
        1.978776357540457e-06,
        1.1485470595429259e-07
      ],
      "exact_endpoint": 0.04462603202968594
    },
    {
      "tableau": "dopri5",
      "expected_order": 5,
      "fitted_order": 4.339572609768267,
      "n_steps": [
        2,
        4,
        8,
        16
      ],
      "absolute_errors": [
        0.00021439312017384332,
        1.811341868888927e-05,
        8.193621397201145e-07,
        2.6601978793394654e-08
      ],
      "exact_endpoint": 0.04462603202968594
    }
  ],
  "stability": [
    {
      "tableau": "euler",
      "negative_real_stability_extent": 1.001,
      "abs_gamma_at_q_minus_0_1": 1.0078999999999998,
      "stability_threshold": 1.999,
      "grid_points": 8000
    },
    {
      "tableau": "midpoint",
      "negative_real_stability_extent": 1.8599999999999999,
      "abs_gamma_at_q_minus_0_1": 0.9978700000000003,
      "stability_threshold": 1.999,
      "grid_points": 8000
    },
    {
      "tableau": "ssprk3",
      "negative_real_stability_extent": 1.597,
      "abs_gamma_at_q_minus_0_1": 0.9979031947398319,
      "stability_threshold": 1.999,
      "grid_points": 8000
    },
    {
      "tableau": "rk4",
      "negative_real_stability_extent": 2.255,
      "abs_gamma_at_q_minus_0_1": 0.9978948155555531,
      "stability_threshold": 1.999,
      "grid_points": 8000
    },
    {
      "tableau": "dopri5",
      "negative_real_stability_extent": 2.626,
      "abs_gamma_at_q_minus_0_1": 0.9978948277682231,
      "stability_threshold": 1.999,
      "grid_points": 8000
    }
  ],
  "gates": {
    "all_roundtrips_below_100eps_relative_l2": true,
    "all_orders_within_0_75": true,
    "all_methods_have_nonzero_stability_interval": true
  },
  "all_gates_pass": true,
  "duration_seconds": 13.349460124969482
}