Average Error: 15.8 → 0.9
Time: 18.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{\sqrt[3]{\sqrt[3]{\frac{1}{2}}}}{a}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}} \cdot \sqrt[3]{g}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\frac{\sqrt[3]{\sqrt[3]{\frac{1}{2}}}}{a}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}} \cdot \sqrt[3]{g}\right)
double f(double g, double a) {
        double r4480869 = g;
        double r4480870 = 2.0;
        double r4480871 = a;
        double r4480872 = r4480870 * r4480871;
        double r4480873 = r4480869 / r4480872;
        double r4480874 = cbrt(r4480873);
        return r4480874;
}
↓
double f(double g, double a) {
        double r4480875 = 0.5;
        double r4480876 = cbrt(r4480875);
        double r4480877 = cbrt(r4480876);
        double r4480878 = a;
        double r4480879 = r4480877 / r4480878;
        double r4480880 = cbrt(r4480879);
        double r4480881 = r4480876 * r4480876;
        double r4480882 = cbrt(r4480881);
        double r4480883 = cbrt(r4480882);
        double r4480884 = r4480880 * r4480883;
        double r4480885 = g;
        double r4480886 = cbrt(r4480885);
        double r4480887 = r4480882 * r4480886;
        double r4480888 = r4480884 * r4480887;
        return r4480888;
}

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 15.8

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

  3. Applied div-inv15.8

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

  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 *-un-lft-identity0.8

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

  8. Applied add-cube-cbrt0.8

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

  9. Applied times-frac0.8

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

  10. Applied cbrt-prod0.9

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

  11. Applied associate-*r*0.9

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

  12. Simplified0.9

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

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

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

  15. Applied add-cube-cbrt0.9

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

  16. Applied cbrt-prod0.9

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

  17. Applied times-frac0.9

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

  18. Applied cbrt-prod0.9

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

  19. Simplified0.9

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

  20. Final simplification0.9

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

Reproduce

herbie shell --seed 2019142 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))