Average Error: 15.6 → 0.9
Time: 13.2s
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 r145675 = g;
        double r145676 = 2.0;
        double r145677 = a;
        double r145678 = r145676 * r145677;
        double r145679 = r145675 / r145678;
        double r145680 = cbrt(r145679);
        return r145680;
}
↓
double f(double g, double a) {
        double r145681 = g;
        double r145682 = cbrt(r145681);
        double r145683 = 1.0;
        double r145684 = 2.0;
        double r145685 = a;
        double r145686 = r145684 * r145685;
        double r145687 = r145683 / r145686;
        double r145688 = cbrt(r145687);
        double r145689 = r145682 * r145688;
        return r145689;
}

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 15.6

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

  3. Applied div-inv15.6

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

  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 2020042 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))