Average Error: 15.8 → 1.3
Time: 5.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\left(\sqrt[3]{\sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right) \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\left(\sqrt[3]{\sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right) \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r143714 = g;
        double r143715 = 2.0;
        double r143716 = a;
        double r143717 = r143715 * r143716;
        double r143718 = r143714 / r143717;
        double r143719 = cbrt(r143718);
        return r143719;
}
↓
double f(double g, double a) {
        double r143720 = g;
        double r143721 = cbrt(r143720);
        double r143722 = r143721 * r143721;
        double r143723 = 2.0;
        double r143724 = r143722 / r143723;
        double r143725 = cbrt(r143724);
        double r143726 = cbrt(r143721);
        double r143727 = r143726 * r143726;
        double r143728 = r143727 * r143726;
        double r143729 = cbrt(r143728);
        double r143730 = a;
        double r143731 = cbrt(r143730);
        double r143732 = r143729 / r143731;
        double r143733 = r143725 * r143732;
        return r143733;
}

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 add-cube-cbrt16.0

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

  4. Applied times-frac16.0

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

  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 cbrt-div1.2

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

  9. Applied add-cube-cbrt1.3

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

  10. Final simplification1.3

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

Reproduce

herbie shell --seed 2020083 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))