Average Error: 15.4 → 0.9
Time: 21.6s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}
double f(double g, double a) {
        double r96393 = g;
        double r96394 = 2.0;
        double r96395 = a;
        double r96396 = r96394 * r96395;
        double r96397 = r96393 / r96396;
        double r96398 = cbrt(r96397);
        return r96398;
}
↓
double f(double g, double a) {
        double r96399 = g;
        double r96400 = cbrt(r96399);
        double r96401 = 1.0;
        double r96402 = 2.0;
        double r96403 = a;
        double r96404 = r96402 * r96403;
        double r96405 = r96401 / r96404;
        double r96406 = cbrt(r96405);
        double r96407 = r96400 * r96406;
        return r96407;
}

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 div-inv15.4

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

  4. Applied cbrt-prod0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))