1{
  2  "predictions": [
  3    {
  4      "claim": "adaptive cost approaches C*=L^2/(2N)",
  5      "observed": [
  6        {
  7          "N": 8,
  8          "uniform_cost": 0.7271701867623693,
  9          "adaptive_cost": 0.3691377829361041,
 10          "predicted_lower_bound": 0.34943393360376745,
 11          "adaptive_over_bound": 1.0563879103815927,
 12          "uniform_over_adaptive": 1.969915355124292,
 13          "max_equalized_cost_ratio": 2.028686838560496
 14        },
 15        {
 16          "N": 16,
 17          "uniform_cost": 0.36358509448295495,
 18          "adaptive_cost": 0.17738442769116214,
 19          "predicted_lower_bound": 0.17471696680188373,
 20          "adaptive_over_bound": 1.015267325996468,
 21          "uniform_over_adaptive": 2.0497013137815023,
 22          "max_equalized_cost_ratio": 1.3179127333312886
 23        },
 24        {
 25          "N": 32,
 26          "uniform_cost": 0.1817925472414657,
 27          "adaptive_cost": 0.08775244191524562,
 28          "predicted_lower_bound": 0.08735848340094186,
 29          "adaptive_over_bound": 1.0045096766675268,
 30          "uniform_over_adaptive": 2.0716522899390917,
 31          "max_equalized_cost_ratio": 1.107957314442003
 32        },
 33        {
 34          "N": 64,
 35          "uniform_cost": 0.09089627362073263,
 36          "adaptive_cost": 0.04372892214303123,
 37          "predicted_lower_bound": 0.04367924170047093,
 38          "adaptive_over_bound": 1.001137392514755,
 39          "uniform_over_adaptive": 2.0786305531022133,
 40          "max_equalized_cost_ratio": 1.0329002644698788
 41        },
 42        {
 43          "N": 128,
 44          "uniform_cost": 0.04544813681036626,
 45          "adaptive_cost": 0.02184584929866585,
 46          "predicted_lower_bound": 0.021839620850235466,
 47          "adaptive_over_bound": 1.0002851903186916,
 48          "uniform_over_adaptive": 2.0804014615784165,
 49          "max_equalized_cost_ratio": 1.0082555885953763
 50        }
 51      ]
 52    },
 53    {
 54      "claim": "width proportional to a^{-1/2}",
 55      "observed_log_correlation": 0.9999941127573625,
 56      "tolerance": "correlation > 0.98 on this smooth density"
 57    },
 58    {
 59      "claim": "a -> c*a leaves grid invariant and scales cost by c",
 60      "observed": [
 61        {
 62          "scale": 0.25,
 63          "grid_max_difference": 0.0,
 64          "cost_ratio_to_reference": 0.25,
 65          "predicted_cost_ratio": 0.25
 66        },
 67        {
 68          "scale": 1.0,
 69          "grid_max_difference": 0.0,
 70          "cost_ratio_to_reference": 1.0,
 71          "predicted_cost_ratio": 1.0
 72        },
 73        {
 74          "scale": 4.0,
 75          "grid_max_difference": 0.0,
 76          "cost_ratio_to_reference": 4.0,
 77          "predicted_cost_ratio": 4.0
 78        },
 79        {
 80          "scale": 16.0,
 81          "grid_max_difference": 0.0,
 82          "cost_ratio_to_reference": 16.0,
 83          "predicted_cost_ratio": 16.0
 84        }
 85      ]
 86    }
 87  ],
 88  "pilot_robustness": [
 89    {
 90      "relative_noise": 0.0,
 91      "grid_linf_error": 0.00035867876551431976,
 92      "cost_ratio_using_true_a": 0.9999436432836555
 93    },
 94    {
 95      "relative_noise": 0.05,
 96      "grid_linf_error": 0.0013162826737388444,
 97      "cost_ratio_using_true_a": 1.0001412653274615
 98    },
 99    {
100      "relative_noise": 0.1,
101      "grid_linf_error": 0.004900863792558385,
102      "cost_ratio_using_true_a": 1.0009030208470313
103    },
104    {
105      "relative_noise": 0.2,
106      "grid_linf_error": 0.012353291078149087,
107      "cost_ratio_using_true_a": 1.0034820474265749
108    },
109    {
110      "relative_noise": 0.4,
111      "grid_linf_error": 0.008321944801356174,
112      "cost_ratio_using_true_a": 1.0116210225456828
113    }
114  ],
115  "ode_mini_experiment": [
116    {
117      "N": 8,
118      "uniform_abs_error": 0.6864483545101536,
119      "adaptive_abs_error": 0.03685096351801369,
120      "error_ratio_adaptive_over_uniform": 0.053683519344015856
121    },
122    {
123      "N": 16,
124      "uniform_abs_error": 0.06977000800414875,
125      "adaptive_abs_error": 0.018374636970129636,
126      "error_ratio_adaptive_over_uniform": 0.2633601098202113
127    },
128    {
129      "N": 32,
130      "uniform_abs_error": 0.034334091052752536,
131      "adaptive_abs_error": 0.009468826448912927,
132      "error_ratio_adaptive_over_uniform": 0.27578497518296236
133    },
134    {
135      "N": 64,
136      "uniform_abs_error": 0.016701189796187614,
137      "adaptive_abs_error": 0.004872624944327768,
138      "error_ratio_adaptive_over_uniform": 0.2917531627261696
139    }
140  ],
141  "density_summary": {
142    "min": 1.0,
143    "max": 81.0,
144    "peak_u": 0.7000000000000001
145  }
146}