Average Error: 15.6 → 0.9
Time: 12.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}
double f(double g, double a) {
        double r111816 = g;
        double r111817 = 2.0;
        double r111818 = a;
        double r111819 = r111817 * r111818;
        double r111820 = r111816 / r111819;
        double r111821 = cbrt(r111820);
        return r111821;
}
↓
double f(double g, double a) {
        double r111822 = g;
        double r111823 = cbrt(r111822);
        double r111824 = 1.0;
        double r111825 = 2.0;
        double r111826 = a;
        double r111827 = r111825 * r111826;
        double r111828 = r111824 / r111827;
        double r111829 = cbrt(r111828);
        double r111830 = r111823 * r111829;
        return r111830;
}

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 15.6

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

  3. Applied div-inv15.6

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

  4. Applied cbrt-prod0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2020042 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))