Average Error: 15.4 → 0.8
Time: 16.8s
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 r3678706 = g;
        double r3678707 = 2.0;
        double r3678708 = a;
        double r3678709 = r3678707 * r3678708;
        double r3678710 = r3678706 / r3678709;
        double r3678711 = cbrt(r3678710);
        return r3678711;
}
↓
double f(double g, double a) {
        double r3678712 = 0.5;
        double r3678713 = a;
        double r3678714 = r3678712 / r3678713;
        double r3678715 = cbrt(r3678714);
        double r3678716 = g;
        double r3678717 = cbrt(r3678716);
        double r3678718 = r3678715 * r3678717;
        return r3678718;
}

Error

Bits error versus g

Bits error versus a

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