Average Error: 15.4 → 0.9
Time: 21.9s
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 r102983 = g;
        double r102984 = 2.0;
        double r102985 = a;
        double r102986 = r102984 * r102985;
        double r102987 = r102983 / r102986;
        double r102988 = cbrt(r102987);
        return r102988;
}
↓
double f(double g, double a) {
        double r102989 = g;
        double r102990 = cbrt(r102989);
        double r102991 = 1.0;
        double r102992 = 2.0;
        double r102993 = a;
        double r102994 = r102992 * r102993;
        double r102995 = r102991 / r102994;
        double r102996 = cbrt(r102995);
        double r102997 = r102990 * r102996;
        return r102997;
}

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. Final simplification0.9

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))