Average Error: 15.6 → 0.9
Time: 19.6s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{1}{\frac{\sqrt[3]{a \cdot 2}}{\sqrt[3]{g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{1}{\frac{\sqrt[3]{a \cdot 2}}{\sqrt[3]{g}}}
double f(double g, double a) {
        double r3054021 = g;
        double r3054022 = 2.0;
        double r3054023 = a;
        double r3054024 = r3054022 * r3054023;
        double r3054025 = r3054021 / r3054024;
        double r3054026 = cbrt(r3054025);
        return r3054026;
}
↓
double f(double g, double a) {
        double r3054027 = 1.0;
        double r3054028 = a;
        double r3054029 = 2.0;
        double r3054030 = r3054028 * r3054029;
        double r3054031 = cbrt(r3054030);
        double r3054032 = g;
        double r3054033 = cbrt(r3054032);
        double r3054034 = r3054031 / r3054033;
        double r3054035 = r3054027 / r3054034;
        return r3054035;
}

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 15.6

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

  3. Applied cbrt-div0.9

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

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

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

  6. Applied associate-/l*0.9

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

  7. Taylor expanded around 0 34.4

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

  8. Simplified0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))