{
  "family": "overhang_span_deflection",
  "generator_id": "overhang-span-deflection-mpmath-o3",
  "generator_version": "1.0.0",
  "seed": "20260927.overhang-span-deflection-o3",
  "mpmath_dps": 80,
  "precision_bits": 265,
  "library": "mpmath 1.4.1",
  "notes": "overhang-end load span midspan \u03b4 = \u2212P a L\u00b2/(16 E I); + O3 mpmath tabulated \u03b4.",
  "vectors": [
    {
      "id": "o3-check",
      "kind": "check",
      "inputs": {
        "P": "16",
        "a": "1",
        "L": "2",
        "E": "1",
        "I": "1"
      },
      "delta_f64": -4.0,
      "delta_decimal": "-4.000000000000000000000000000000000000000",
      "P_f64": 16.0,
      "P_decimal": "16.00000000000000000000000000000000000000",
      "L_f64": 2.0,
      "L_decimal": "2.000000000000000000000000000000000000000",
      "E_f64": 1.0,
      "E_decimal": "1.000000000000000000000000000000000000000",
      "I_f64": 1.0,
      "I_decimal": "1.000000000000000000000000000000000000000",
      "a_f64": 1.0,
      "a_decimal": "1.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-SI",
      "kind": "SI",
      "inputs": {
        "P": "1000",
        "a": "1",
        "L": "2",
        "E": "200e9",
        "I": "1e-5"
      },
      "delta_f64": -0.000125,
      "delta_decimal": "-0.0001250000000000000000000000000000000000000",
      "P_f64": 1000.0,
      "P_decimal": "1000.000000000000000000000000000000000000",
      "L_f64": 2.0,
      "L_decimal": "2.000000000000000000000000000000000000000",
      "E_f64": 200000000000.0,
      "E_decimal": "200000000000.0000000000000000000000000000",
      "I_f64": 1e-05,
      "I_decimal": "0.00001000000000000000000000000000000000000000",
      "a_f64": 1.0,
      "a_decimal": "1.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-alias",
      "kind": "alias",
      "inputs": {
        "load": "32",
        "span": "2",
        "modulus": "1",
        "Ix": "1",
        "a": "1"
      },
      "delta_f64": -8.0,
      "delta_decimal": "-8.000000000000000000000000000000000000000",
      "P_f64": 32.0,
      "P_decimal": "32.00000000000000000000000000000000000000",
      "L_f64": 2.0,
      "L_decimal": "2.000000000000000000000000000000000000000",
      "E_f64": 1.0,
      "E_decimal": "1.000000000000000000000000000000000000000",
      "I_f64": 1.0,
      "I_decimal": "1.000000000000000000000000000000000000000",
      "a_f64": 1.0,
      "a_decimal": "1.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-awkward",
      "kind": "awkward",
      "inputs": {
        "P": "13.7",
        "a": "1.2",
        "L": "3.5",
        "E": "210000",
        "I": "0.83"
      },
      "delta_f64": -7.221385542168674e-05,
      "delta_decimal": "-0.00007221385542168674698795180722891566265060",
      "P_f64": 13.7,
      "P_decimal": "13.70000000000000000000000000000000000000",
      "L_f64": 3.5,
      "L_decimal": "3.500000000000000000000000000000000000000",
      "E_f64": 210000.0,
      "E_decimal": "210000.0000000000000000000000000000000000",
      "I_f64": 0.83,
      "I_decimal": "0.8300000000000000000000000000000000000000",
      "a_f64": 1.2,
      "a_decimal": "1.200000000000000000000000000000000000000"
    },
    {
      "id": "o3-neg",
      "kind": "signed",
      "inputs": {
        "P": "-16",
        "a": "1",
        "L": "2",
        "E": "1",
        "I": "1"
      },
      "delta_f64": 4.0,
      "delta_decimal": "4.000000000000000000000000000000000000000",
      "P_f64": -16.0,
      "P_decimal": "-16.00000000000000000000000000000000000000",
      "L_f64": 2.0,
      "L_decimal": "2.000000000000000000000000000000000000000",
      "E_f64": 1.0,
      "E_decimal": "1.000000000000000000000000000000000000000",
      "I_f64": 1.0,
      "I_decimal": "1.000000000000000000000000000000000000000",
      "a_f64": 1.0,
      "a_decimal": "1.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-small",
      "kind": "small",
      "inputs": {
        "P": "10",
        "a": "0.5",
        "L": "1",
        "E": "1000",
        "I": "0.01"
      },
      "delta_f64": -0.03125,
      "delta_decimal": "-0.03125000000000000000000000000000000000000",
      "P_f64": 10.0,
      "P_decimal": "10.00000000000000000000000000000000000000",
      "L_f64": 1.0,
      "L_decimal": "1.000000000000000000000000000000000000000",
      "E_f64": 1000.0,
      "E_decimal": "1000.000000000000000000000000000000000000",
      "I_f64": 0.01,
      "I_decimal": "0.01000000000000000000000000000000000000000",
      "a_f64": 0.5,
      "a_decimal": "0.5000000000000000000000000000000000000000"
    },
    {
      "id": "o3-stiff",
      "kind": "stiff",
      "inputs": {
        "P": "500",
        "a": "1",
        "L": "1.5",
        "E": "210e9",
        "I": "2e-4"
      },
      "delta_f64": -1.6741071428571428e-06,
      "delta_decimal": "-0.000001674107142857142857142857142857142857143",
      "P_f64": 500.0,
      "P_decimal": "500.0000000000000000000000000000000000000",
      "L_f64": 1.5,
      "L_decimal": "1.500000000000000000000000000000000000000",
      "E_f64": 210000000000.0,
      "E_decimal": "210000000000.0000000000000000000000000000",
      "I_f64": 0.0002,
      "I_decimal": "0.0002000000000000000000000000000000000000000",
      "a_f64": 1.0,
      "a_decimal": "1.000000000000000000000000000000000000000"
    },
    {
      "id": "o3-long",
      "kind": "long",
      "inputs": {
        "P": "200",
        "a": "1.5",
        "L": "4",
        "E": "70e9",
        "I": "5e-5"
      },
      "delta_f64": -8.571428571428571e-05,
      "delta_decimal": "-0.00008571428571428571428571428571428571428571",
      "P_f64": 200.0,
      "P_decimal": "200.0000000000000000000000000000000000000",
      "L_f64": 4.0,
      "L_decimal": "4.000000000000000000000000000000000000000",
      "E_f64": 70000000000.0,
      "E_decimal": "70000000000.00000000000000000000000000000",
      "I_f64": 5e-05,
      "I_decimal": "0.00005000000000000000000000000000000000000000",
      "a_f64": 1.5,
      "a_decimal": "1.500000000000000000000000000000000000000"
    }
  ]
}