Average Error: 15.4 → 0.9
Time: 19.4s
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 r97536 = g;
        double r97537 = 2.0;
        double r97538 = a;
        double r97539 = r97537 * r97538;
        double r97540 = r97536 / r97539;
        double r97541 = cbrt(r97540);
        return r97541;
}
↓
double f(double g, double a) {
        double r97542 = g;
        double r97543 = cbrt(r97542);
        double r97544 = 1.0;
        double r97545 = 2.0;
        double r97546 = a;
        double r97547 = r97545 * r97546;
        double r97548 = r97544 / r97547;
        double r97549 = cbrt(r97548);
        double r97550 = r97543 * r97549;
        return r97550;
}

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))))