Average Error: 14.7 → 0.9
Time: 16.5s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r5439707 = g;
        double r5439708 = 2.0;
        double r5439709 = a;
        double r5439710 = r5439708 * r5439709;
        double r5439711 = r5439707 / r5439710;
        double r5439712 = cbrt(r5439711);
        return r5439712;
}
↓
double f(double g, double a) {
        double r5439713 = 0.5;
        double r5439714 = cbrt(r5439713);
        double r5439715 = 1.0;
        double r5439716 = a;
        double r5439717 = r5439715 / r5439716;
        double r5439718 = cbrt(r5439717);
        double r5439719 = r5439714 * r5439718;
        double r5439720 = g;
        double r5439721 = cbrt(r5439720);
        double r5439722 = r5439719 * r5439721;
        return r5439722;
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied div-inv14.7

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

  4. Applied cbrt-prod0.9

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

  5. Simplified0.8

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

  7. Applied div-inv0.9

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

  8. Applied cbrt-prod0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2019162 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))