Average Error: 15.1 → 0.8
Time: 31.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]
double f(double g, double a) {
        double r16483701 = g;
        double r16483702 = 2.0;
        double r16483703 = a;
        double r16483704 = r16483702 * r16483703;
        double r16483705 = r16483701 / r16483704;
        double r16483706 = cbrt(r16483705);
        return r16483706;
}
↓
double f(double g, double a) {
        double r16483707 = g;
        double r16483708 = cbrt(r16483707);
        double r16483709 = 2.0;
        double r16483710 = a;
        double r16483711 = r16483709 * r16483710;
        double r16483712 = cbrt(r16483711);
        double r16483713 = r16483708 / r16483712;
        return r16483713;
}


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

Error

Bits error versus g

Bits error versus a

Derivation

  1. Initial program 15.1

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

  3. Applied cbrt-div0.8

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

  5. Applied *-un-lft-identity0.8

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

  6. Applied associate-/l*0.9

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

  8. Applied associate-/r/0.9

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

  10. Applied associate-*l/0.8

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

  11. Simplified0.8

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

  12. Final simplification0.8

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))