Average Error: 14.8 → 0.8
Time: 11.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{\frac{1}{a}}{2}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{\frac{\frac{1}{a}}{2}}
double f(double g, double a) {
        double r130127 = g;
        double r130128 = 2.0;
        double r130129 = a;
        double r130130 = r130128 * r130129;
        double r130131 = r130127 / r130130;
        double r130132 = cbrt(r130131);
        return r130132;
}
↓
double f(double g, double a) {
        double r130133 = g;
        double r130134 = cbrt(r130133);
        double r130135 = 1.0;
        double r130136 = a;
        double r130137 = r130135 / r130136;
        double r130138 = 2.0;
        double r130139 = r130137 / r130138;
        double r130140 = cbrt(r130139);
        double r130141 = r130134 * r130140;
        return r130141;
}

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

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Derivation

  1. Initial program 14.8

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]

  2. Simplified14.8

    \[\leadsto \color{blue}{\sqrt[3]{\frac{g}{a \cdot 2}}}\]
  3. Using strategy rm

  4. Applied div-inv14.8

    \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{a \cdot 2}}}\]

  5. Applied cbrt-prod0.8

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}}\]

  6. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{\frac{1}{a}}{2}}}\]

  7. Final simplification0.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{\frac{1}{a}}{2}}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))