Average Error: 15.5 → 0.9
Time: 11.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{a}}\right)
double f(double g, double a) {
        double r143900 = g;
        double r143901 = 2.0;
        double r143902 = a;
        double r143903 = r143901 * r143902;
        double r143904 = r143900 / r143903;
        double r143905 = cbrt(r143904);
        return r143905;
}
↓
double f(double g, double a) {
        double r143906 = g;
        double r143907 = cbrt(r143906);
        double r143908 = 1.0;
        double r143909 = 2.0;
        double r143910 = r143908 / r143909;
        double r143911 = cbrt(r143910);
        double r143912 = a;
        double r143913 = r143908 / r143912;
        double r143914 = cbrt(r143913);
        double r143915 = r143911 * r143914;
        double r143916 = r143907 * r143915;
        return r143916;
}

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 15.5

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

  3. Applied div-inv15.5

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

  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 add-cube-cbrt0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.9

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

  9. Simplified0.9

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

  10. Simplified0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2019235 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))