Average Error: 15.5 → 0.8
Time: 12.2s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)
double f(double g, double a) {
        double r135590 = g;
        double r135591 = 2.0;
        double r135592 = a;
        double r135593 = r135591 * r135592;
        double r135594 = r135590 / r135593;
        double r135595 = cbrt(r135594);
        return r135595;
}
↓
double f(double g, double a) {
        double r135596 = g;
        double r135597 = cbrt(r135596);
        double r135598 = -0.5;
        double r135599 = cbrt(r135598);
        double r135600 = -1.0;
        double r135601 = a;
        double r135602 = r135600 / r135601;
        double r135603 = cbrt(r135602);
        double r135604 = r135599 * r135603;
        double r135605 = r135597 * r135604;
        return r135605;
}

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 15.5

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

  3. Applied div-inv15.5

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

  4. Applied cbrt-prod0.8

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

  5. Taylor expanded around -inf 34.2

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left({\left(\frac{-1}{a}\right)}^{\frac{1}{3}} \cdot \sqrt[3]{-0.5}\right)}\]

  6. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)}\]

  7. Final simplification0.8

    \[\leadsto \sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)\]

Reproduce

herbie shell --seed 2019350 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))