Average Error: 14.6 → 0.8
Time: 12.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}
double f(double g, double a) {
        double r2154695 = g;
        double r2154696 = 2.0;
        double r2154697 = a;
        double r2154698 = r2154696 * r2154697;
        double r2154699 = r2154695 / r2154698;
        double r2154700 = cbrt(r2154699);
        return r2154700;
}
↓
double f(double g, double a) {
        double r2154701 = g;
        double r2154702 = cbrt(r2154701);
        double r2154703 = 2.0;
        double r2154704 = a;
        double r2154705 = r2154703 * r2154704;
        double r2154706 = cbrt(r2154705);
        double r2154707 = r2154702 / r2154706;
        return r2154707;
}

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 14.6

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

  3. Applied cbrt-div0.8

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

  4. Taylor expanded around 0 34.2

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

  5. Simplified0.8

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

  6. Final simplification0.8

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

Reproduce

herbie shell --seed 2019151 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))