Average Error: 16.1 → 1.2
Time: 6.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\left(\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right) \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\left(\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right) \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r138694 = g;
        double r138695 = 2.0;
        double r138696 = a;
        double r138697 = r138695 * r138696;
        double r138698 = r138694 / r138697;
        double r138699 = cbrt(r138698);
        return r138699;
}
↓
double f(double g, double a) {
        double r138700 = g;
        double r138701 = cbrt(r138700);
        double r138702 = r138701 * r138701;
        double r138703 = cbrt(r138702);
        double r138704 = cbrt(r138701);
        double r138705 = r138703 * r138704;
        double r138706 = r138705 * r138701;
        double r138707 = 2.0;
        double r138708 = r138706 / r138707;
        double r138709 = cbrt(r138708);
        double r138710 = a;
        double r138711 = cbrt(r138710);
        double r138712 = r138704 / r138711;
        double r138713 = r138709 * r138712;
        return r138713;
}

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 16.1

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

  3. Applied add-cube-cbrt16.3

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

  4. Applied times-frac16.3

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

  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-div1.2

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

  9. Applied add-cube-cbrt1.2

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

  10. Applied cbrt-prod1.2

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

  11. Final simplification1.2

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))