1{
  2  "identity_max_abs_error": 1.1857187100668868e-16,
  3  "predictions": [
  4    {
  5      "test": "worst_case_bound",
  6      "K": 1,
  7      "observed": 0.5,
  8      "predicted": 0.5,
  9      "relative_error": 0.0
 10    },
 11    {
 12      "test": "worst_case_bound",
 13      "K": 3,
 14      "observed": 0.25,
 15      "predicted": 0.25,
 16      "relative_error": 0.0
 17    },
 18    {
 19      "test": "worst_case_bound",
 20      "K": 7,
 21      "observed": 0.125,
 22      "predicted": 0.125,
 23      "relative_error": 0.0
 24    },
 25    {
 26      "test": "worst_case_bound",
 27      "K": 15,
 28      "observed": 0.0625,
 29      "predicted": 0.0625,
 30      "relative_error": 0.0
 31    },
 32    {
 33      "test": "worst_case_bound",
 34      "K": 31,
 35      "observed": 0.03125,
 36      "predicted": 0.03125,
 37      "relative_error": 0.0
 38    },
 39    {
 40      "test": "transition_90pct",
 41      "K": 15,
 42      "observed_theta": 0.13997445609697373,
 43      "predicted_theta": 0.13997118937482927,
 44      "observed_Ktheta": 2.099616841454606,
 45      "predicted_Ktheta": 2.099567840622439,
 46      "relative_error": 2.333853244405281e-05
 47    }
 48  ],
 49  "low_frequency": [
 50    {
 51      "K": 3,
 52      "theta": 0.0025,
 53      "observed": 0.0012499947916731762,
 54      "predicted_theta_over_2": 0.00125,
 55      "ratio": 0.9999958333385409
 56    },
 57    {
 58      "K": 7,
 59      "theta": 0.00125,
 60      "observed": 0.0006249973958365881,
 61      "predicted_theta_over_2": 0.000625,
 62      "ratio": 0.9999958333385409
 63    },
 64    {
 65      "K": 15,
 66      "theta": 0.000625,
 67      "observed": 0.00031249869791829404,
 68      "predicted_theta_over_2": 0.0003125,
 69      "ratio": 0.9999958333385409
 70    },
 71    {
 72      "K": 31,
 73      "theta": 0.0003125,
 74      "observed": 0.00015624934895914732,
 75      "predicted_theta_over_2": 0.00015625,
 76      "ratio": 0.9999958333385428
 77    }
 78  ],
 79  "equal_eval_rotation_theta": 0.35,
 80  "comparison": [
 81    {
 82      "evaluations": 3,
 83      "fejer_residual": 0.16105442180942278,
 84      "ppm_residual": 0.16625166276857417,
 85      "ratio_fejer_over_ppm": 0.968738712909079
 86    },
 87    {
 88      "evaluations": 7,
 89      "fejer_residual": 0.12318121624855759,
 90      "ppm_residual": 0.15632504694731683,
 91      "ratio_fejer_over_ppm": 0.7879813161998982
 92    },
 93    {
 94      "evaluations": 15,
 95      "fejer_residual": 0.020936759384744107,
 96      "ppm_residual": 0.13821453218713284,
 97      "ratio_fejer_over_ppm": 0.15148015952763344
 98    },
 99    {
100      "evaluations": 31,
101      "fejer_residual": 0.019727082433510075,
102      "ppm_residual": 0.10804482959003849,
103      "ratio_fejer_over_ppm": 0.18258238277909108
104    }
105  ],
106  "notes": "R is a rotation, hence nonexpansive; J=(I+R)/2 is an exact resolvent of a linear maximal monotone skew operator when -1 is absent."
107}