{
  "all_numerator_names": [
    "P1",
    "P2",
    "P3",
    "P4",
    "P5",
    "P6",
    "P8"
  ],
  "bound_exp": 1.2886909309951409,
  "bound_log": 0.2536269209592403,
  "certification_note": "No interval certificate was computed; this is numeric_refined only.",
  "certified": false,
  "degA": 125.23773921628612,
  "degA_rational": "472651158004937546429382156014863230202224713/3774031381935655613867715451591849269426432",
  "degQ": 140,
  "degree_ok": true,
  "denominator": [
    {
      "coeffs": [
        1,
        -3,
        8,
        -18,
        36,
        -62,
        97,
        -123,
        114,
        -73,
        31,
        -8,
        1
      ],
      "degree": 12,
      "multiplicity": 1,
      "name": "P7"
    },
    {
      "coeffs": [
        1,
        -4,
        10,
        -17,
        26,
        -47,
        119,
        -298,
        592,
        -878,
        963,
        -780,
        464,
        -199,
        59,
        -11,
        1
      ],
      "degree": 16,
      "multiplicity": 1,
      "name": "P9"
    },
    {
      "coeffs": [
        1,
        -7,
        30,
        -97,
        269,
        -679,
        1612,
        -3618,
        7646,
        -15180,
        28457,
        -50741,
        86189,
        -138288,
        206152,
        -279897,
        339335,
        -360911,
        331775,
        -260367,
        172556,
        -95554,
        43677,
        -16221,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "degree": 28,
      "multiplicity": 1,
      "name": "Q1"
    },
    {
      "coeffs": [
        1,
        -7,
        30,
        -96,
        255,
        -586,
        1212,
        -2360,
        4573,
        -9148,
        18749,
        -37783,
        71770,
        -124910,
        195848,
        -273368,
        335981,
        -359545,
        331349,
        -260271,
        172542,
        -95553,
        43677,
        -16221,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "degree": 28,
      "multiplicity": 1,
      "name": "Q2"
    },
    {
      "coeffs": [
        1,
        -7,
        31,
        -107,
        321,
        -867,
        2148,
        -4922,
        10497,
        -20908,
        38973,
        -68026,
        111075,
        -169111,
        238522,
        -308360,
        360033,
        -373190,
        337618,
        -262546,
        173171,
        -95678,
        43693,
        -16222,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "degree": 28,
      "multiplicity": 1,
      "name": "R0"
    },
    {
      "coeffs": [
        1,
        -7,
        29,
        -86,
        202,
        -387,
        618,
        -861,
        1256,
        -2589,
        7105,
        -19328,
        45963,
        -93546,
        163248,
        -244838,
        315271,
        -347265,
        325506,
        -258092,
        171927,
        -95429,
        43661,
        -16220,
        4786,
        -1084,
        178,
        -19,
        1
      ],
      "degree": 28,
      "multiplicity": 1,
      "name": "R2"
    }
  ],
  "gcd_ok": true,
  "grid_size": 32768,
  "integral": 0.008539029362185407,
  "integral_adaptive": null,
  "integral_grid": {
    "16384": 0.008539056894339791,
    "32768": 0.00853835534885583,
    "65536": 0.008539029362185407
  },
  "integral_mpmath_panel": {
    "reason": "mp_panels=0",
    "skipped": true
  },
  "label": "qstar_lp_grid32768_maxden1e7",
  "logM": 35.499229904931454,
  "message": "Optimization terminated successfully. (HiGHS Status 7: Optimal)",
  "numerator": [
    {
      "coeffs": [
        1,
        0
      ],
      "degree": 1,
      "name": "P1",
      "q": 26.511877484730615,
      "q_rational": "56823994/2143341"
    },
    {
      "coeffs": [
        -1,
        1
      ],
      "degree": 1,
      "name": "P2",
      "q": 23.782846008412744,
      "q_rational": "71890668/3022795"
    },
    {
      "coeffs": [
        1,
        1,
        -2,
        1
      ],
      "degree": 3,
      "name": "P3",
      "q": 0.9707094545190521,
      "q_rational": "7593829/7822968"
    },
    {
      "coeffs": [
        1,
        -2,
        4,
        -3,
        1
      ],
      "degree": 4,
      "name": "P4",
      "q": 4.526072775020114,
      "q_rational": "45179616/9982079"
    },
    {
      "coeffs": [
        1,
        -2,
        4,
        -7,
        13,
        -16,
        12,
        -5,
        1
      ],
      "degree": 8,
      "name": "P5",
      "q": 0.038326545650764404,
      "q_rational": "287519/7501824"
    },
    {
      "coeffs": [
        1,
        -3,
        8,
        -16,
        26,
        -27,
        17,
        -6,
        1
      ],
      "degree": 8,
      "name": "P6",
      "q": 4.173784226054273,
      "q_rational": "24396374/5845145"
    },
    {
      "coeffs": [
        1,
        -3,
        7,
        -14,
        30,
        -58,
        96,
        -123,
        114,
        -73,
        31,
        -8,
        1
      ],
      "degree": 12,
      "name": "P8",
      "q": 1.685809173822071,
      "q_rational": "12389192/7349107"
    }
  ],
  "parent": "targeted_qstar",
  "q_max_den": 10000000,
  "refined_from_bound_log": 0.25362691583095853,
  "schema": 1,
  "status": "numeric_refined",
  "success": true,
  "target": "0.2536331"
}