Average Error: 15.4 → 0.9
Time: 21.4s
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 r113701 = g;
        double r113702 = 2.0;
        double r113703 = a;
        double r113704 = r113702 * r113703;
        double r113705 = r113701 / r113704;
        double r113706 = cbrt(r113705);
        return r113706;
}
↓
double f(double g, double a) {
        double r113707 = g;
        double r113708 = cbrt(r113707);
        double r113709 = 1.0;
        double r113710 = 2.0;
        double r113711 = a;
        double r113712 = r113710 * r113711;
        double r113713 = r113709 / r113712;
        double r113714 = cbrt(r113713);
        double r113715 = r113708 * r113714;
        return r113715;
}

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))))