Average Error: 16.0 → 0.8
Time: 40.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{0.5}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a}}\right) \cdot \sqrt[3]{0.5}
double f(double g, double a) {
        double r5293861 = g;
        double r5293862 = 2.0;
        double r5293863 = a;
        double r5293864 = r5293862 * r5293863;
        double r5293865 = r5293861 / r5293864;
        double r5293866 = cbrt(r5293865);
        return r5293866;
}
↓
double f(double g, double a) {
        double r5293867 = g;
        double r5293868 = cbrt(r5293867);
        double r5293869 = 1.0;
        double r5293870 = a;
        double r5293871 = r5293869 / r5293870;
        double r5293872 = cbrt(r5293871);
        double r5293873 = r5293868 * r5293872;
        double r5293874 = 0.5;
        double r5293875 = cbrt(r5293874);
        double r5293876 = r5293873 * r5293875;
        return r5293876;
}

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 16.0

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

  3. Applied cbrt-div0.8

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

  5. Applied div-inv0.9

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

  7. Applied add-cbrt-cube0.9

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

  8. Applied cbrt-undiv0.9

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

  9. Simplified0.8

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

  10. Taylor expanded around 0 49.1

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

  11. Simplified0.8

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

  12. Final simplification0.8

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))