Average Error: 14.6 → 0.8
Time: 18.7s
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 r3804803 = g;
        double r3804804 = 2.0;
        double r3804805 = a;
        double r3804806 = r3804804 * r3804805;
        double r3804807 = r3804803 / r3804806;
        double r3804808 = cbrt(r3804807);
        return r3804808;
}
↓
double f(double g, double a) {
        double r3804809 = g;
        double r3804810 = cbrt(r3804809);
        double r3804811 = 2.0;
        double r3804812 = a;
        double r3804813 = r3804811 * r3804812;
        double r3804814 = cbrt(r3804813);
        double r3804815 = r3804810 / r3804814;
        return r3804815;
}

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))))