Average Error: 15.9 → 1.2
Time: 6.2s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r117799 = g;
        double r117800 = 2.0;
        double r117801 = a;
        double r117802 = r117800 * r117801;
        double r117803 = r117799 / r117802;
        double r117804 = cbrt(r117803);
        return r117804;
}
↓
double f(double g, double a) {
        double r117805 = g;
        double r117806 = cbrt(r117805);
        double r117807 = r117806 * r117806;
        double r117808 = cbrt(r117807);
        double r117809 = 1.0;
        double r117810 = 2.0;
        double r117811 = r117809 / r117810;
        double r117812 = cbrt(r117811);
        double r117813 = r117808 * r117812;
        double r117814 = cbrt(r117806);
        double r117815 = r117808 * r117814;
        double r117816 = cbrt(r117815);
        double r117817 = a;
        double r117818 = cbrt(r117817);
        double r117819 = r117816 / r117818;
        double r117820 = r117813 * r117819;
        return r117820;
}

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 15.9

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

  3. Applied add-cube-cbrt16.1

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

  4. Applied times-frac16.1

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

  5. Applied cbrt-prod5.7

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

  7. Applied cbrt-div1.1

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

  9. Applied div-inv1.1

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

  10. Applied cbrt-prod1.2

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

  12. Applied add-cube-cbrt1.2

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

  13. Applied cbrt-prod1.2

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

  14. Final simplification1.2

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

Reproduce

herbie shell --seed 2020033 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))