Average Error: 15.3 → 1.3
Time: 5.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \left(1 \cdot \sqrt[3]{a}\right)}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \left(1 \cdot \sqrt[3]{a}\right)}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)
double f(double g, double a) {
        double r160928 = g;
        double r160929 = 2.0;
        double r160930 = a;
        double r160931 = r160929 * r160930;
        double r160932 = r160928 / r160931;
        double r160933 = cbrt(r160932);
        return r160933;
}
↓
double f(double g, double a) {
        double r160934 = g;
        double r160935 = cbrt(r160934);
        double r160936 = r160935 * r160935;
        double r160937 = 2.0;
        double r160938 = r160936 / r160937;
        double r160939 = cbrt(r160938);
        double r160940 = 1.0;
        double r160941 = a;
        double r160942 = cbrt(r160941);
        double r160943 = r160940 * r160942;
        double r160944 = r160942 * r160943;
        double r160945 = r160940 / r160944;
        double r160946 = cbrt(r160945);
        double r160947 = r160935 / r160942;
        double r160948 = cbrt(r160947);
        double r160949 = r160946 * r160948;
        double r160950 = r160939 * r160949;
        return r160950;
}

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 15.3

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

  3. Applied add-cube-cbrt15.4

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

  4. Applied times-frac15.4

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

  5. Applied cbrt-prod5.5

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

  7. Applied add-cube-cbrt5.6

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

  8. Applied *-un-lft-identity5.6

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

  9. Applied cbrt-prod5.6

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

  10. Applied times-frac5.6

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

  11. Applied cbrt-prod1.3

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

  12. Simplified1.3

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

  14. Applied *-un-lft-identity1.3

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

  15. Final simplification1.3

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

Reproduce

herbie shell --seed 2020057 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))