Average Error: 15.4 → 0.8
Time: 15.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r4603948 = g;
        double r4603949 = 2.0;
        double r4603950 = a;
        double r4603951 = r4603949 * r4603950;
        double r4603952 = r4603948 / r4603951;
        double r4603953 = cbrt(r4603952);
        return r4603953;
}
↓
double f(double g, double a) {
        double r4603954 = 0.5;
        double r4603955 = a;
        double r4603956 = r4603954 / r4603955;
        double r4603957 = cbrt(r4603956);
        double r4603958 = g;
        double r4603959 = cbrt(r4603958);
        double r4603960 = r4603957 * r4603959;
        return r4603960;
}

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 15.4

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

  3. Applied div-inv15.4

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

  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. Final simplification0.8

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

Reproduce

herbie shell --seed 2019164 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))