Average Error: 14.9 → 0.9
Time: 28.8s
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 r28402800 = g;
        double r28402801 = 2.0;
        double r28402802 = a;
        double r28402803 = r28402801 * r28402802;
        double r28402804 = r28402800 / r28402803;
        double r28402805 = cbrt(r28402804);
        return r28402805;
}
↓
double f(double g, double a) {
        double r28402806 = g;
        double r28402807 = cbrt(r28402806);
        double r28402808 = 1.0;
        double r28402809 = 2.0;
        double r28402810 = a;
        double r28402811 = r28402809 * r28402810;
        double r28402812 = r28402808 / r28402811;
        double r28402813 = cbrt(r28402812);
        double r28402814 = r28402807 * r28402813;
        return r28402814;
}

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 14.9

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

  3. Applied div-inv14.9

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

  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 2019119 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))