Average Error: 15.7 → 0.8
Time: 18.0s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{-\frac{-0.5}{a}} \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{-\frac{-0.5}{a}} \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r3726629 = g;
        double r3726630 = 2.0;
        double r3726631 = a;
        double r3726632 = r3726630 * r3726631;
        double r3726633 = r3726629 / r3726632;
        double r3726634 = cbrt(r3726633);
        return r3726634;
}
↓
double f(double g, double a) {
        double r3726635 = -0.5;
        double r3726636 = a;
        double r3726637 = r3726635 / r3726636;
        double r3726638 = -r3726637;
        double r3726639 = cbrt(r3726638);
        double r3726640 = g;
        double r3726641 = cbrt(r3726640);
        double r3726642 = r3726639 * r3726641;
        return r3726642;
}

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 15.7

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

  3. Applied div-inv15.7

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around -inf 34.9

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left({\left(\frac{-1}{a}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{-0.5}\right)}\]

  6. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{\frac{-1}{a}} \cdot \sqrt[3]{-0.5}\right)}\]
  7. Using strategy rm

  8. Applied cbrt-unprod0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{-1}{a} \cdot -0.5}}\]

  9. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{-\frac{-0.5}{a}}}\]

  10. Final simplification0.8

    \[\leadsto \sqrt[3]{-\frac{-0.5}{a}} \cdot \sqrt[3]{g}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))