Average Error: 15.4 → 1.2
Time: 5.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \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 r150676 = g;
        double r150677 = 2.0;
        double r150678 = a;
        double r150679 = r150677 * r150678;
        double r150680 = r150676 / r150679;
        double r150681 = cbrt(r150680);
        return r150681;
}
↓
double f(double g, double a) {
        double r150682 = g;
        double r150683 = cbrt(r150682);
        double r150684 = r150683 * r150683;
        double r150685 = 2.0;
        double r150686 = r150684 / r150685;
        double r150687 = cbrt(r150686);
        double r150688 = cbrt(r150684);
        double r150689 = cbrt(r150683);
        double r150690 = r150688 * r150689;
        double r150691 = cbrt(r150690);
        double r150692 = a;
        double r150693 = cbrt(r150692);
        double r150694 = r150691 / r150693;
        double r150695 = r150687 * r150694;
        return r150695;
}

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 15.4

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

  3. Applied add-cube-cbrt15.6

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

  4. Applied times-frac15.5

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

  5. Applied cbrt-prod5.6

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{a}}}\]
  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 add-cube-cbrt1.2

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

  10. Applied cbrt-prod1.2

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

  11. Final simplification1.2

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

Reproduce

herbie shell --seed 2020024 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))