Average Error: 15.4 → 0.9
Time: 16.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{a \cdot 2}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{a \cdot 2}}
double f(double g, double a) {
        double r3252093 = g;
        double r3252094 = 2.0;
        double r3252095 = a;
        double r3252096 = r3252094 * r3252095;
        double r3252097 = r3252093 / r3252096;
        double r3252098 = cbrt(r3252097);
        return r3252098;
}
↓
double f(double g, double a) {
        double r3252099 = g;
        double r3252100 = cbrt(r3252099);
        double r3252101 = 1.0;
        double r3252102 = a;
        double r3252103 = 2.0;
        double r3252104 = r3252102 * r3252103;
        double r3252105 = cbrt(r3252104);
        double r3252106 = r3252101 / r3252105;
        double r3252107 = r3252100 * r3252106;
        return r3252107;
}

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.4

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

  3. Applied cbrt-div0.9

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

  5. Applied clear-num0.9

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}}\]
  6. Using strategy rm

  7. Applied div-inv0.9

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

  8. Applied add-cube-cbrt0.9

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

  9. Applied times-frac0.9

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

  10. Simplified0.9

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

  11. Simplified0.9

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

  12. Final simplification0.9

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))