Average Error: 15.7 → 0.9
Time: 18.4s
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 r5656054 = g;
        double r5656055 = 2.0;
        double r5656056 = a;
        double r5656057 = r5656055 * r5656056;
        double r5656058 = r5656054 / r5656057;
        double r5656059 = cbrt(r5656058);
        return r5656059;
}
↓
double f(double g, double a) {
        double r5656060 = g;
        double r5656061 = cbrt(r5656060);
        double r5656062 = 1.0;
        double r5656063 = 2.0;
        double r5656064 = a;
        double r5656065 = r5656063 * r5656064;
        double r5656066 = r5656062 / r5656065;
        double r5656067 = cbrt(r5656066);
        double r5656068 = r5656061 * r5656067;
        return r5656068;
}

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 15.7

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

  3. Applied div-inv15.7

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

  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 2019169 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))