Average Error: 15.4 → 0.9
Time: 19.6s
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 r112548 = g;
        double r112549 = 2.0;
        double r112550 = a;
        double r112551 = r112549 * r112550;
        double r112552 = r112548 / r112551;
        double r112553 = cbrt(r112552);
        return r112553;
}
↓
double f(double g, double a) {
        double r112554 = g;
        double r112555 = cbrt(r112554);
        double r112556 = 1.0;
        double r112557 = 2.0;
        double r112558 = a;
        double r112559 = r112557 * r112558;
        double r112560 = r112556 / r112559;
        double r112561 = cbrt(r112560);
        double r112562 = r112555 * r112561;
        return r112562;
}

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 2019325 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))