Average Error: 15.4 → 0.9
Time: 19.8s
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 r125546 = g;
        double r125547 = 2.0;
        double r125548 = a;
        double r125549 = r125547 * r125548;
        double r125550 = r125546 / r125549;
        double r125551 = cbrt(r125550);
        return r125551;
}
↓
double f(double g, double a) {
        double r125552 = g;
        double r125553 = cbrt(r125552);
        double r125554 = 1.0;
        double r125555 = 2.0;
        double r125556 = a;
        double r125557 = r125555 * r125556;
        double r125558 = r125554 / r125557;
        double r125559 = cbrt(r125558);
        double r125560 = r125553 * r125559;
        return r125560;
}

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