{
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  "quadratic_uniform_grids": [
    {
      "subintervals": 2,
      "x": [
        "0",
        "1/2",
        "1"
      ],
      "y": [
        "0",
        "1/4",
        "1"
      ],
      "signed_parts": [
        "1/16",
        "5/16"
      ],
      "exact_trapezoid": "3/8",
      "actual_numpy_trapezoid": 0.375,
      "analytic_integral": "1/3",
      "error_exact": "1/24"
    },
    {
      "subintervals": 4,
      "x": [
        "0",
        "1/4",
        "1/2",
        "3/4",
        "1"
      ],
      "y": [
        "0",
        "1/16",
        "1/4",
        "9/16",
        "1"
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      "signed_parts": [
        "1/128",
        "5/128",
        "13/128",
        "25/128"
      ],
      "exact_trapezoid": "11/32",
      "actual_numpy_trapezoid": 0.34375,
      "analytic_integral": "1/3",
      "error_exact": "1/96"
    }
  ],
  "nonuniform_unsorted_reversed_cases": [
    {
      "x": [
        "0",
        "1/4",
        "1"
      ],
      "y": [
        "0",
        "1/16",
        "1"
      ],
      "parts": [
        "1/128",
        "51/128"
      ],
      "area": "13/32",
      "reversed_pairs_area": "-13/32",
      "line_antiderivative_oracle_equal": true,
      "numpy": 0.40625
    },
    {
      "x": [
        "0",
        "1",
        "1/2"
      ],
      "y": [
        "0",
        "1",
        "1/4"
      ],
      "parts": [
        "1/2",
        "-5/16"
      ],
      "area": "3/16",
      "reversed_pairs_area": "-3/16",
      "line_antiderivative_oracle_equal": true,
      "numpy": 0.1875
    },
    {
      "x": [
        "1",
        "1/2",
        "0"
      ],
      "y": [
        "1",
        "1/4",
        "0"
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      "parts": [
        "-5/16",
        "-1/16"
      ],
      "area": "-3/8",
      "reversed_pairs_area": "3/8",
      "line_antiderivative_oracle_equal": true,
      "numpy": -0.375
    }
  ],
  "order_contract": "paired x/y sequence retained, no hidden sorting; signed integration along path",
  "units": "x units times y units",
  "rejected": [
    [
      "[]",
      "[]"
    ],
    [
      "[0, 1]",
      "[0]"
    ],
    [
      "[0, True]",
      "[0, 1]"
    ],
    [
      "[0, nan]",
      "[0, 1]"
    ]
  ],
  "scope": "piecewise-linear approximation of sampled data, not exact integral of unknown function or ROC curve"
}