Average Error: 15.2 → 0.9
Time: 11.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a} \cdot {\left(\sqrt[3]{0.5}\right)}^{3}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a} \cdot {\left(\sqrt[3]{0.5}\right)}^{3}}
double f(double g, double a) {
        double r99934 = g;
        double r99935 = 2.0;
        double r99936 = a;
        double r99937 = r99935 * r99936;
        double r99938 = r99934 / r99937;
        double r99939 = cbrt(r99938);
        return r99939;
}
↓
double f(double g, double a) {
        double r99940 = g;
        double r99941 = cbrt(r99940);
        double r99942 = 1.0;
        double r99943 = a;
        double r99944 = r99942 / r99943;
        double r99945 = 0.5;
        double r99946 = cbrt(r99945);
        double r99947 = 3.0;
        double r99948 = pow(r99946, r99947);
        double r99949 = r99944 * r99948;
        double r99950 = cbrt(r99949);
        double r99951 = r99941 * r99950;
        return r99951;
}

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 15.2

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

  3. Applied div-inv15.2

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around 0 34.6

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

  6. Simplified0.9

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

  8. Applied add-cbrt-cube1.0

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

  9. Simplified0.9

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

  10. Final simplification0.9

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))