Average Error: 15.4 → 0.8
Time: 24.0s
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 r17468710 = g;
        double r17468711 = 2.0;
        double r17468712 = a;
        double r17468713 = r17468711 * r17468712;
        double r17468714 = r17468710 / r17468713;
        double r17468715 = cbrt(r17468714);
        return r17468715;
}
↓
double f(double g, double a) {
        double r17468716 = 0.5;
        double r17468717 = a;
        double r17468718 = r17468716 / r17468717;
        double r17468719 = cbrt(r17468718);
        double r17468720 = g;
        double r17468721 = cbrt(r17468720);
        double r17468722 = r17468719 * r17468721;
        return r17468722;
}

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 15.4

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

  6. Applied *-un-lft-identity0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{1}{a}}}\]
  10. Using strategy rm

  11. Applied associate-*l*0.8

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right)}\]
  12. Using strategy rm

  13. Applied cbrt-unprod0.8

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

  14. Simplified0.8

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

  15. Final simplification0.8

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))