{
  "seed": 1441,
  "contraction_sweep": [
    {
      "d": 1,
      "factor_min_eigenvalue": 0.0,
      "factor_max_eigenvalue": 0.9999999999999999,
      "global_min_eigenvalue": 0.0,
      "global_max_eigenvalue": 0.9999999999999999,
      "predicted_max_bound": 1.0
    },
    {
      "d": 2,
      "factor_min_eigenvalue": -1.5838531726405977e-16,
      "factor_max_eigenvalue": 1.0000000000000009,
      "global_min_eigenvalue": -5.794910353835645e-16,
      "global_max_eigenvalue": 1.0,
      "predicted_max_bound": 1.0
    },
    {
      "d": 3,
      "factor_min_eigenvalue": -1.5838531726405977e-16,
      "factor_max_eigenvalue": 1.0000000000000009,
      "global_min_eigenvalue": -4.979238160151515e-16,
      "global_max_eigenvalue": 1.000000000000001,
      "predicted_max_bound": 1.0
    },
    {
      "d": 4,
      "factor_min_eigenvalue": -1.5838531726405977e-16,
      "factor_max_eigenvalue": 1.0000000000000009,
      "global_min_eigenvalue": -6.84830158927908e-16,
      "global_max_eigenvalue": 1.000000000000004,
      "predicted_max_bound": 1.0
    }
  ],
  "tensor_identity_sweep": [
    {
      "d": 2,
      "apply_relative_error": 1.7385997772211454e-16,
      "schatten_p0.5_relative_error": 7.681325038113024e-09,
      "schatten_p1.0_relative_error": 1.5987211554602244e-16,
      "schatten_p2.0_relative_error": 0.0
    },
    {
      "d": 3,
      "apply_relative_error": 2.3196642664872965e-16,
      "schatten_p0.5_relative_error": 2.9630520978964855e-08,
      "schatten_p1.0_relative_error": 0.0,
      "schatten_p2.0_relative_error": 1.618553033068464e-16
    },
    {
      "d": 4,
      "apply_relative_error": 4.2063874751920412e-16,
      "schatten_p0.5_relative_error": 3.396583146795002e-08,
      "schatten_p1.0_relative_error": 2.3021584638627215e-16,
      "schatten_p2.0_relative_error": 1.8352666325436245e-16
    }
  ],
  "scaling_sweep": [
    {
      "d": 2,
      "tokens": 64,
      "dense_parameters": 4096,
      "factor_parameters": 128,
      "dense_matvec_ops": 4096,
      "axis_matvec_ops": 1024,
      "predicted_cost_ratio_dense_over_axis": 4.0,
      "median_dense_seconds": 1.1104999430244789e-05,
      "median_axis_seconds": 9.512600081507117e-05,
      "observed_time_ratio_dense_over_axis": 0.11673989587592735
    },
    {
      "d": 3,
      "tokens": 512,
      "dense_parameters": 262144,
      "factor_parameters": 192,
      "dense_matvec_ops": 262144,
      "axis_matvec_ops": 12288,
      "predicted_cost_ratio_dense_over_axis": 21.333333333333332,
      "median_dense_seconds": 5.182300083106384e-05,
      "median_axis_seconds": 0.000183615999048925,
      "observed_time_ratio_dense_over_axis": 0.2822357588635588
    },
    {
      "d": 4,
      "tokens": 4096,
      "dense_parameters": 16777216,
      "factor_parameters": 256,
      "dense_matvec_ops": 16777216,
      "axis_matvec_ops": 131072,
      "predicted_cost_ratio_dense_over_axis": 128.0,
      "median_dense_seconds": 0.007683236999582732,
      "median_axis_seconds": 0.0004948339992552064,
      "observed_time_ratio_dense_over_axis": 15.526897931724712
    }
  ],
  "practical_comparison": {
    "tokens": 144,
    "dense_parameters": 20736,
    "tensor_parameters": 288,
    "dense_apply_seconds": 0.002998898000441841,
    "tensor_apply_seconds": 7.535999975516461e-05,
    "dense_largest_singular_value": 1.000000000000001,
    "tensor_largest_singular_value": 1.0000000000000009
  }
}
 "dense_apply_seconds": 2.2140000510262325e-05,
    "tensor_apply_seconds": 0.0001013409982988378,
    "dense_largest_singular_value": 1.0000000000000009,
    "tensor_largest_singular_value": 1.0000000000000009
  }
}