{
  "predictions": [
    {
      "claim": "adaptive cost approaches C*=L^2/(2N)",
      "observed": [
        {
          "N": 8,
          "uniform_cost": 0.7271701867623693,
          "adaptive_cost": 0.3691377829361041,
          "predicted_lower_bound": 0.34943393360376745,
          "adaptive_over_bound": 1.0563879103815927,
          "uniform_over_adaptive": 1.969915355124292,
          "max_equalized_cost_ratio": 2.028686838560496
        },
        {
          "N": 16,
          "uniform_cost": 0.36358509448295495,
          "adaptive_cost": 0.17738442769116214,
          "predicted_lower_bound": 0.17471696680188373,
          "adaptive_over_bound": 1.015267325996468,
          "uniform_over_adaptive": 2.0497013137815023,
          "max_equalized_cost_ratio": 1.3179127333312886
        },
        {
          "N": 32,
          "uniform_cost": 0.1817925472414657,
          "adaptive_cost": 0.08775244191524562,
          "predicted_lower_bound": 0.08735848340094186,
          "adaptive_over_bound": 1.0045096766675268,
          "uniform_over_adaptive": 2.0716522899390917,
          "max_equalized_cost_ratio": 1.107957314442003
        },
        {
          "N": 64,
          "uniform_cost": 0.09089627362073263,
          "adaptive_cost": 0.04372892214303123,
          "predicted_lower_bound": 0.04367924170047093,
          "adaptive_over_bound": 1.001137392514755,
          "uniform_over_adaptive": 2.0786305531022133,
          "max_equalized_cost_ratio": 1.0329002644698788
        },
        {
          "N": 128,
          "uniform_cost": 0.04544813681036626,
          "adaptive_cost": 0.02184584929866585,
          "predicted_lower_bound": 0.021839620850235466,
          "adaptive_over_bound": 1.0002851903186916,
          "uniform_over_adaptive": 2.0804014615784165,
          "max_equalized_cost_ratio": 1.0082555885953763
        }
      ]
    },
    {
      "claim": "width proportional to a^{-1/2}",
      "observed_log_correlation": 0.9999941127573625,
      "tolerance": "correlation > 0.98 on this smooth density"
    },
    {
      "claim": "a -> c*a leaves grid invariant and scales cost by c",
      "observed": [
        {
          "scale": 0.25,
          "grid_max_difference": 0.0,
          "cost_ratio_to_reference": 0.25,
          "predicted_cost_ratio": 0.25
        },
        {
          "scale": 1.0,
          "grid_max_difference": 0.0,
          "cost_ratio_to_reference": 1.0,
          "predicted_cost_ratio": 1.0
        },
        {
          "scale": 4.0,
          "grid_max_difference": 0.0,
          "cost_ratio_to_reference": 4.0,
          "predicted_cost_ratio": 4.0
        },
        {
          "scale": 16.0,
          "grid_max_difference": 0.0,
          "cost_ratio_to_reference": 16.0,
          "predicted_cost_ratio": 16.0
        }
      ]
    }
  ],
  "pilot_robustness": [
    {
      "relative_noise": 0.0,
      "grid_linf_error": 0.00035867876551431976,
      "cost_ratio_using_true_a": 0.9999436432836555
    },
    {
      "relative_noise": 0.05,
      "grid_linf_error": 0.0013162826737388444,
      "cost_ratio_using_true_a": 1.0001412653274615
    },
    {
      "relative_noise": 0.1,
      "grid_linf_error": 0.004900863792558385,
      "cost_ratio_using_true_a": 1.0009030208470313
    },
    {
      "relative_noise": 0.2,
      "grid_linf_error": 0.012353291078149087,
      "cost_ratio_using_true_a": 1.0034820474265749
    },
    {
      "relative_noise": 0.4,
      "grid_linf_error": 0.008321944801356174,
      "cost_ratio_using_true_a": 1.0116210225456828
    }
  ],
  "ode_mini_experiment": [
    {
      "N": 8,
      "uniform_abs_error": 0.6864483545101536,
      "adaptive_abs_error": 0.03685096351801369,
      "error_ratio_adaptive_over_uniform": 0.053683519344015856
    },
    {
      "N": 16,
      "uniform_abs_error": 0.06977000800414875,
      "adaptive_abs_error": 0.018374636970129636,
      "error_ratio_adaptive_over_uniform": 0.2633601098202113
    },
    {
      "N": 32,
      "uniform_abs_error": 0.034334091052752536,
      "adaptive_abs_error": 0.009468826448912927,
      "error_ratio_adaptive_over_uniform": 0.27578497518296236
    },
    {
      "N": 64,
      "uniform_abs_error": 0.016701189796187614,
      "adaptive_abs_error": 0.004872624944327768,
      "error_ratio_adaptive_over_uniform": 0.2917531627261696
    }
  ],
  "density_summary": {
    "min": 1.0,
    "max": 81.0,
    "peak_u": 0.7000000000000001
  }
}