Average Error: 14.9 → 0.9
Time: 16.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}\right)
double f(double g, double a) {
        double r11012745 = g;
        double r11012746 = 2.0;
        double r11012747 = a;
        double r11012748 = r11012746 * r11012747;
        double r11012749 = r11012745 / r11012748;
        double r11012750 = cbrt(r11012749);
        return r11012750;
}
↓
double f(double g, double a) {
        double r11012751 = 0.5;
        double r11012752 = cbrt(r11012751);
        double r11012753 = a;
        double r11012754 = r11012752 / r11012753;
        double r11012755 = cbrt(r11012754);
        double r11012756 = g;
        double r11012757 = cbrt(r11012756);
        double r11012758 = r11012752 * r11012752;
        double r11012759 = cbrt(r11012758);
        double r11012760 = r11012757 * r11012759;
        double r11012761 = r11012755 * r11012760;
        return r11012761;
}

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 14.9

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

  3. Applied cbrt-div0.9

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

  5. Applied div-inv0.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube0.9

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

  8. Applied cbrt-undiv0.9

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

  9. Simplified0.8

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

  11. Applied *-un-lft-identity0.8

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

  12. Applied add-cube-cbrt0.8

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

  13. Applied times-frac0.8

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

  14. Applied cbrt-prod0.9

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

  15. Applied associate-*r*0.9

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

  16. Final simplification0.9

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

Reproduce

herbie shell --seed 2019112 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))