Average Error: 15.8 → 0.8
Time: 16.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{1}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{1}{a}}
double f(double g, double a) {
        double r123770 = g;
        double r123771 = 2.0;
        double r123772 = a;
        double r123773 = r123771 * r123772;
        double r123774 = r123770 / r123773;
        double r123775 = cbrt(r123774);
        return r123775;
}
↓
double f(double g, double a) {
        double r123776 = 1.0;
        double r123777 = 2.0;
        double r123778 = r123776 / r123777;
        double r123779 = cbrt(r123778);
        double r123780 = g;
        double r123781 = cbrt(r123780);
        double r123782 = r123779 * r123781;
        double r123783 = a;
        double r123784 = r123776 / r123783;
        double r123785 = cbrt(r123784);
        double r123786 = r123782 * r123785;
        return r123786;
}

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 div-inv15.8

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

  4. Applied cbrt-prod0.9

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

  6. Applied *-un-lft-identity0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

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

  10. Simplified0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2020043 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))