Average Error: 15.1 → 0.8
Time: 16.0s
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 r5220979 = g;
        double r5220980 = 2.0;
        double r5220981 = a;
        double r5220982 = r5220980 * r5220981;
        double r5220983 = r5220979 / r5220982;
        double r5220984 = cbrt(r5220983);
        return r5220984;
}
↓
double f(double g, double a) {
        double r5220985 = g;
        double r5220986 = cbrt(r5220985);
        double r5220987 = 2.0;
        double r5220988 = a;
        double r5220989 = r5220987 * r5220988;
        double r5220990 = cbrt(r5220989);
        double r5220991 = r5220986 / r5220990;
        return r5220991;
}

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 15.1

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

  3. Applied cbrt-div0.8

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

  5. Applied *-un-lft-identity0.8

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

  6. Applied associate-/r*0.8

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

  7. Simplified0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019138 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))