{
  "family": "root",
  "generator_id": "root-mpmath-o3",
  "generator_version": "1.0.0",
  "seed": "20260909",
  "mpmath_dps": 80,
  "precision_bits": 265,
  "library": "mpmath 1.4.1",
  "notes": "mpmath signed real a**(1/n) at 80 dps, rounded to nearest binary64. Not Node Math.sqrt/cbrt/pow. Even roots of a<0 are outside this table (NOT_REAL). Illegal n is outside this table (INVALID_INDEX).",
  "vectors": [
    {
      "id": "o3-root-42-1",
      "kind": "identity",
      "iut_path": "identity",
      "inputs": {
        "a": 42,
        "n": 1
      },
      "y_f64": 42.0,
      "y_decimal": "42.00000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-100-2",
      "kind": "sqrt-exact",
      "iut_path": "sqrt",
      "inputs": {
        "a": 100,
        "n": 2
      },
      "y_f64": 10.0,
      "y_decimal": "10.00000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-2-2",
      "kind": "sqrt-irrational",
      "iut_path": "sqrt",
      "inputs": {
        "a": 2,
        "n": 2
      },
      "y_f64": 1.4142135623730951,
      "y_decimal": "1.414213562373095048801688724209698078570"
    },
    {
      "id": "o3-root-tiny-2",
      "kind": "sqrt-tiny",
      "iut_path": "sqrt",
      "inputs": {
        "a": 1e-300,
        "n": 2
      },
      "y_f64": 1e-150,
      "y_decimal": "1.000000000000000012529545917604379764353e-150"
    },
    {
      "id": "o3-root-huge-2",
      "kind": "sqrt-huge",
      "iut_path": "sqrt",
      "inputs": {
        "a": 1e+300,
        "n": 2
      },
      "y_f64": 1e+150,
      "y_decimal": "1.000000000000000026252380127602209779759e+150"
    },
    {
      "id": "o3-root-8-3",
      "kind": "cbrt-exact",
      "iut_path": "cbrt",
      "inputs": {
        "a": 8,
        "n": 3
      },
      "y_f64": 2.0,
      "y_decimal": "2.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-27-3",
      "kind": "cbrt-exact",
      "iut_path": "cbrt",
      "inputs": {
        "a": 27,
        "n": 3
      },
      "y_f64": 3.0,
      "y_decimal": "3.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-neg8-3",
      "kind": "cbrt-odd-negative",
      "iut_path": "cbrt",
      "inputs": {
        "a": -8,
        "n": 3
      },
      "y_f64": -2.0,
      "y_decimal": "-2.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-neg27-3",
      "kind": "cbrt-odd-negative",
      "iut_path": "cbrt",
      "inputs": {
        "a": -27,
        "n": 3
      },
      "y_f64": -3.0,
      "y_decimal": "-3.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-tiny-3",
      "kind": "cbrt-tiny",
      "iut_path": "cbrt",
      "inputs": {
        "a": 1e-300,
        "n": 3
      },
      "y_f64": 1e-100,
      "y_decimal": "1.000000000000000008353030611736253158792e-100"
    },
    {
      "id": "o3-root-huge-3",
      "kind": "cbrt-huge",
      "iut_path": "cbrt",
      "inputs": {
        "a": 1e+300,
        "n": 3
      },
      "y_f64": 1e+100,
      "y_decimal": "1.000000000000000017501586751734806443263e+100"
    },
    {
      "id": "o3-root-16-4",
      "kind": "pow-exact",
      "iut_path": "pow",
      "inputs": {
        "a": 16,
        "n": 4
      },
      "y_f64": 2.0,
      "y_decimal": "2.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-32-5",
      "kind": "pow-exact",
      "iut_path": "pow",
      "inputs": {
        "a": 32,
        "n": 5
      },
      "y_f64": 2.0,
      "y_decimal": "2.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-1-7",
      "kind": "pow-exact",
      "iut_path": "pow",
      "inputs": {
        "a": 1,
        "n": 7
      },
      "y_f64": 1.0,
      "y_decimal": "1.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-neg32-5",
      "kind": "pow-odd-negative",
      "iut_path": "pow",
      "inputs": {
        "a": -32,
        "n": 5
      },
      "y_f64": -2.0,
      "y_decimal": "-2.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-root-15-8",
      "kind": "pow-irrational",
      "iut_path": "pow",
      "inputs": {
        "a": 15,
        "n": 8
      },
      "y_f64": 1.402850552006674,
      "y_decimal": "1.402850552006674165866237852751514404831"
    },
    {
      "id": "o3-root-maxsafe-n",
      "kind": "pow-max-safe-index",
      "iut_path": "pow",
      "inputs": {
        "a": 16,
        "n": 9007199254740991
      },
      "y_f64": 1.0000000000000002,
      "y_decimal": "1.000000000000000307819183724664876790745"
    },
    {
      "id": "o3-root-tiny-5",
      "kind": "pow-tiny",
      "iut_path": "pow",
      "inputs": {
        "a": 1e-300,
        "n": 5
      },
      "y_f64": 1e-60,
      "y_decimal": "1.000000000000000005011818367041751886903e-60"
    },
    {
      "id": "o3-root-huge-5",
      "kind": "pow-huge",
      "iut_path": "pow",
      "inputs": {
        "a": 1e+300,
        "n": 5
      },
      "y_f64": 1e+60,
      "y_decimal": "1.000000000000000010500952051040883829201e+60"
    }
  ]
}