Average Error: 15.8 → 0.9
Time: 18.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}
double f(double g, double a) {
        double r96702 = g;
        double r96703 = 2.0;
        double r96704 = a;
        double r96705 = r96703 * r96704;
        double r96706 = r96702 / r96705;
        double r96707 = cbrt(r96706);
        return r96707;
}
↓
double f(double g, double a) {
        double r96708 = 1.0;
        double r96709 = 2.0;
        double r96710 = a;
        double r96711 = r96709 * r96710;
        double r96712 = cbrt(r96711);
        double r96713 = g;
        double r96714 = cbrt(r96713);
        double r96715 = r96712 / r96714;
        double r96716 = r96708 / r96715;
        return r96716;
}

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 15.8

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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 clear-num0.9

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

  6. Final simplification0.9

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))