{
  "seed": 1303,
  "singular_decay": [
    {
      "h": 4,
      "singular_values": [
        1.0000000000000002,
        0.032471995935982094,
        0.0007112239242100824,
        1.0485620007805735e-05
      ],
      "geometric_bound_check": [
        {
          "N": 0,
          "observed": 1.0000000000000002,
          "predicted_bound": 1.0,
          "satisfies": true
        },
        {
          "N": 1,
          "observed": 0.032471995935982094,
          "predicted_bound": 0.25,
          "satisfies": true
        },
        {
          "N": 2,
          "observed": 0.0007112239242100824,
          "predicted_bound": 0.0625,
          "satisfies": true
        },
        {
          "N": 3,
          "observed": 1.0485620007805735e-05,
          "predicted_bound": 0.015625,
          "satisfies": true
        }
      ],
      "ratios": [
        0.03247199593598209,
        0.021902685797702316,
        0.01474306424583726
      ]
    },
    {
      "h": 8,
      "singular_values": [
        1.0000000000000002,
        0.037517497868420686,
        0.001079614010971153,
        2.7861455019730973e-05,
        6.383014383184403e-07,
        1.250699384949905e-08
      ],
      "geometric_bound_check": [
        {
          "N": 0,
          "observed": 1.0000000000000002,
          "predicted_bound": 1.0,
          "satisfies": true
        },
        {
          "N": 1,
          "observed": 0.037517497868420686,
          "predicted_bound": 0.25,
          "satisfies": true
        },
        {
          "N": 2,
          "observed": 0.001079614010971153,
          "predicted_bound": 0.0625,
          "satisfies": true
        },
        {
          "N": 3,
          "observed": 2.7861455019730973e-05,
          "predicted_bound": 0.015625,
          "satisfies": true
        },
        {
          "N": 4,
          "observed": 6.383014383184403e-07,
          "predicted_bound": 0.00390625,
          "satisfies": true
        }
      ],
      "ratios": [
        0.03751749786842068,
        0.02877627966442528,
        0.02580686684000012,
        0.022909838623517934
      ]
    },
    {
      "h": 16,
      "singular_values": [
        1.0,
        0.040042040676386906,
        0.001269155576889523,
        3.8086545883880336e-05,
        1.1003527416435871e-06,
        3.057672838400633e-08
      ],
      "geometric_bound_check": [
        {
          "N": 0,
          "observed": 1.0,
          "predicted_bound": 1.0,
          "satisfies": true
        },
        {
          "N": 1,
          "observed": 0.040042040676386906,
          "predicted_bound": 0.25,
          "satisfies": true
        },
        {
          "N": 2,
          "observed": 0.001269155576889523,
          "predicted_bound": 0.0625,
          "satisfies": true
        },
        {
          "N": 3,
          "observed": 3.8086545883880336e-05,
          "predicted_bound": 0.015625,
          "satisfies": true
        },
        {
          "N": 4,
          "observed": 1.1003527416435871e-06,
          "predicted_bound": 0.00390625,
          "satisfies": true
        }
      ],
      "ratios": [
        0.040042040676386906,
        0.03169557683502264,
        0.030009359433477618,
        0.028890851509569368
      ]
    },
    {
      "h": 32,
      "singular_values": [
        0.9999999999999999,
        0.04128677317325391,
        0.0013602423417570098,
        4.3008279618050345e-05,
        1.3344305065041076e-06,
        4.0828908628957114e-08
      ],
      "geometric_bound_check": [
        {
          "N": 0,
          "observed": 0.9999999999999999,
          "predicted_bound": 1.0,
          "satisfies": true
        },
        {
          "N": 1,
          "observed": 0.04128677317325391,
          "predicted_bound": 0.25,
          "satisfies": true
        },
        {
          "N": 2,
          "observed": 0.0013602423417570098,
          "predicted_bound": 0.0625,
          "satisfies": true
        },
        {
          "N": 3,
          "observed": 4.3008279618050345e-05,
          "predicted_bound": 0.015625,
          "satisfies": true
        },
        {
          "N": 4,
          "observed": 1.3344305065041076e-06,
          "predicted_bound": 0.00390625,
          "satisfies": true
        }
      ],
      "ratios": [
        0.04128677317325392,
        0.032946201342714566,
        0.03161810090582611,
        0.03102729331084553
      ]
    },
    {
      "h": 64,
      "singular_values": [
        0.9999999999999999,
        0.04190170645943303,
        0.0014039556258478786,
        4.529941550762505e-05,
        1.4412151135005145e-06,
        4.549727726114446e-08
      ],
      "geometric_bound_check": [
        {
          "N": 0,
          "observed": 0.9999999999999999,
          "predicted_bound": 1.0,
          "satisfies": true
        },
        {
          "N": 1,
          "observed": 0.04190170645943303,
          "predicted_bound": 0.25,
          "satisfies": true
        },
        {
          "N": 2,
          "observed": 0.0014039556258478786,
          "predicted_bound": 0.0625,
          "satisfies": true
        },
        {
          "N": 3,
          "observed": 4.529941550762505e-05,
          "predicted_bound": 0.015625,
          "satisfies": true
        },
        {
          "N": 4,
          "observed": 1.4412151135005145e-06,
          "predicted_bound": 0.00390625,
          "satisfies": true
        }
      ],
      "ratios": [
        0.04190170645943304,
        0.0335059295784794,
        0.03226556072971877,
        0.031815313671275096
      ]
    }
  ],
  "rank_scaling": [
    {
      "h": 8,
      "epsilon": 0.01,
      "observed_rank": 2,
      "predicted_rank_bound": 4,
      "bound_holds": true
    },
    {
      "h": 8,
      "epsilon": 0.001,
      "observed_rank": 3,
      "predicted_rank_bound": 5,
      "bound_holds": true
    },
    {
      "h": 8,
      "epsilon": 0.0001,
      "observed_rank": 3,
      "predicted_rank_bound": 7,
      "bound_holds": true
    },
    {
      "h": 16,
      "epsilon": 0.01,
      "observed_rank": 2,
      "predicted_rank_bound": 4,
      "bound_holds": true
    },
    {
      "h": 16,
      "epsilon": 0.001,
      "observed_rank": 3,
      "predicted_rank_bound": 5,
      "bound_holds": true
    },
    {
      "h": 16,
      "epsilon": 0.0001,
      "observed_rank": 3,
      "predicted_rank_bound": 7,
      "bound_holds": true
    },
    {
      "h": 32,
      "epsilon": 0.01,
      "observed_rank": 2,
      "predicted_rank_bound": 4,
      "bound_holds": true
    },
    {
      "h": 32,
      "epsilon": 0.001,
      "observed_rank": 3,
      "predicted_rank_bound": 5,
      "bound_holds": true
    },
    {
      "h": 32,
      "epsilon": 0.0001,
      "observed_rank": 3,
      "predicted_rank_bound": 7,
      "bound_holds": true
    },
    {
      "h": 64,
      "epsilon": 0.01,
      "observed_rank": 2,
      "predicted_rank_bound": 4,
      "bound_holds": true
    },
    {
      "h": 64,
      "epsilon": 0.001,
      "observed_rank": 3,
      "predicted_rank_bound": 5,
      "bound_holds": true
    },
    {
      "h": 64,
      "epsilon": 0.0001,
      "observed_rank": 3,
      "predicted_rank_bound": 7,
      "bound_holds": true
    }
  ],
  "application_scaling": [
    {
      "h": 64,
      "n_left": 256,
      "n_right": 64,
      "rank": 4,
      "relative_output_error": 1.8506525884115408e-06,
      "dense_ms": 0.07653875013602374,
      "factorized_ms": 0.03605612505452882,
      "measured_speedup": 2.1227669368317246,
      "ideal_work_ratio": 12.8
    },
    {
      "h": 128,
      "n_left": 512,
      "n_right": 128,
      "rank": 4,
      "relative_output_error": 1.5201875517994328e-06,
      "dense_ms": 0.09929849989021022,
      "factorized_ms": 0.04479525000533613,
      "measured_speedup": 2.2167194039185296,
      "ideal_work_ratio": 25.6
    },
    {
      "h": 256,
      "n_left": 1024,
      "n_right": 256,
      "rank": 4,
      "relative_output_error": 1.6068503168438619e-06,
      "dense_ms": 0.5982622499232093,
      "factorized_ms": 0.08230074990933645,
      "measured_speedup": 7.269219910903153,
      "ideal_work_ratio": 51.2
    },
    {
      "h": 512,
      "n_left": 2048,
      "n_right": 512,
      "rank": 4,
      "relative_output_error": 9.895432789404913e-07,
      "dense_ms": 1.5680517503824376,
      "factorized_ms": 0.1368737498523842,
      "measured_speedup": 11.456190482642231,
      "ideal_work_ratio": 102.4
    }
  ]
}