Average Error: 14.9 → 0.9
Time: 21.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{g}{2}} \cdot \sqrt[3]{\frac{1}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{g}{2}} \cdot \sqrt[3]{\frac{1}{a}}
double f(double g, double a) {
        double r99952 = g;
        double r99953 = 2.0;
        double r99954 = a;
        double r99955 = r99953 * r99954;
        double r99956 = r99952 / r99955;
        double r99957 = cbrt(r99956);
        return r99957;
}
↓
double f(double g, double a) {
        double r99958 = g;
        double r99959 = 2.0;
        double r99960 = r99958 / r99959;
        double r99961 = cbrt(r99960);
        double r99962 = 1.0;
        double r99963 = a;
        double r99964 = r99962 / r99963;
        double r99965 = cbrt(r99964);
        double r99966 = r99961 * r99965;
        return r99966;
}

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 14.9

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

  3. Applied div-inv15.0

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

  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-frac0.9

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

  8. Applied cbrt-prod0.9

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

  9. Applied associate-*r*0.9

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

  10. Simplified0.9

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

  12. Applied cbrt-unprod0.9

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

  13. Simplified0.9

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

  14. Final simplification0.9

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))