Average Error: 15.7 → 1.3
Time: 6.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]
\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 \sqrt[3]{a}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)
double f(double g, double a) {
        double r146823 = g;
        double r146824 = 2.0;
        double r146825 = a;
        double r146826 = r146824 * r146825;
        double r146827 = r146823 / r146826;
        double r146828 = cbrt(r146827);
        return r146828;
}
↓
double f(double g, double a) {
        double r146829 = g;
        double r146830 = cbrt(r146829);
        double r146831 = r146830 * r146830;
        double r146832 = 2.0;
        double r146833 = r146831 / r146832;
        double r146834 = cbrt(r146833);
        double r146835 = 1.0;
        double r146836 = a;
        double r146837 = cbrt(r146836);
        double r146838 = r146837 * r146837;
        double r146839 = r146835 / r146838;
        double r146840 = cbrt(r146839);
        double r146841 = r146830 / r146837;
        double r146842 = cbrt(r146841);
        double r146843 = r146840 * r146842;
        double r146844 = r146834 * r146843;
        return r146844;
}

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 15.7

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

  3. Applied add-cube-cbrt15.9

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

  4. Applied times-frac15.8

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

  5. Applied cbrt-prod5.8

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

  7. Applied add-cube-cbrt5.9

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

  8. Applied *-un-lft-identity5.9

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

  9. Applied cbrt-prod5.9

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

  10. Applied times-frac5.9

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

  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. Final simplification1.3

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))