Average Error: 16.5 → 0.9
Time: 12.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}
double f(double g, double a) {
        double r105350 = g;
        double r105351 = 2.0;
        double r105352 = a;
        double r105353 = r105351 * r105352;
        double r105354 = r105350 / r105353;
        double r105355 = cbrt(r105354);
        return r105355;
}
↓
double f(double g, double a) {
        double r105356 = g;
        double r105357 = cbrt(r105356);
        double r105358 = 2.0;
        double r105359 = a;
        double r105360 = r105358 * r105359;
        double r105361 = cbrt(r105360);
        double r105362 = r105357 / r105361;
        return r105362;
}

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 16.5

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

  3. Applied cbrt-div0.9

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

  4. Final simplification0.9

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))