Average Error: 15.4 → 0.9
Time: 10.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{1}}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{1}}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}
double f(double g, double a) {
        double r119560 = g;
        double r119561 = 2.0;
        double r119562 = a;
        double r119563 = r119561 * r119562;
        double r119564 = r119560 / r119563;
        double r119565 = cbrt(r119564);
        return r119565;
}
↓
double f(double g, double a) {
        double r119566 = 1.0;
        double r119567 = cbrt(r119566);
        double r119568 = 2.0;
        double r119569 = a;
        double r119570 = r119568 * r119569;
        double r119571 = cbrt(r119570);
        double r119572 = g;
        double r119573 = cbrt(r119572);
        double r119574 = r119571 / r119573;
        double r119575 = r119567 / r119574;
        return r119575;
}

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 15.4

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

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

  6. Applied cbrt-prod0.9

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

  7. Applied associate-/l*0.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019294 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))