Average Error: 15.3 → 0.9
Time: 20.5s
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 r16498803 = g;
        double r16498804 = 2.0;
        double r16498805 = a;
        double r16498806 = r16498804 * r16498805;
        double r16498807 = r16498803 / r16498806;
        double r16498808 = cbrt(r16498807);
        return r16498808;
}
↓
double f(double g, double a) {
        double r16498809 = g;
        double r16498810 = cbrt(r16498809);
        double r16498811 = 1.0;
        double r16498812 = 2.0;
        double r16498813 = a;
        double r16498814 = r16498812 * r16498813;
        double r16498815 = r16498811 / r16498814;
        double r16498816 = cbrt(r16498815);
        double r16498817 = r16498810 * r16498816;
        return r16498817;
}

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 15.3

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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 2019107 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))