Average Error: 14.7 → 0.8
Time: 16.1s
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 r5407129 = g;
        double r5407130 = 2.0;
        double r5407131 = a;
        double r5407132 = r5407130 * r5407131;
        double r5407133 = r5407129 / r5407132;
        double r5407134 = cbrt(r5407133);
        return r5407134;
}
↓
double f(double g, double a) {
        double r5407135 = 0.5;
        double r5407136 = a;
        double r5407137 = r5407135 / r5407136;
        double r5407138 = cbrt(r5407137);
        double r5407139 = g;
        double r5407140 = cbrt(r5407139);
        double r5407141 = r5407138 * r5407140;
        return r5407141;
}

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 14.7

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

  3. Applied div-inv14.7

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

  4. Applied cbrt-prod0.9

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

  5. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{\frac{1}{2}}{a}}}\]
  6. Using strategy rm

  7. Applied *-commutative0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))