Average Error: 15.2 → 0.9
Time: 10.6s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r123334 = g;
        double r123335 = 2.0;
        double r123336 = a;
        double r123337 = r123335 * r123336;
        double r123338 = r123334 / r123337;
        double r123339 = cbrt(r123338);
        return r123339;
}
↓
double f(double g, double a) {
        double r123340 = 1.0;
        double r123341 = 2.0;
        double r123342 = a;
        double r123343 = r123341 * r123342;
        double r123344 = r123340 / r123343;
        double r123345 = cbrt(r123344);
        double r123346 = g;
        double r123347 = cbrt(r123346);
        double r123348 = r123345 * r123347;
        return r123348;
}

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 15.2

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

  3. Applied div-inv15.3

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

  4. Applied cbrt-prod0.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]
  5. Using strategy rm

  6. Applied *-commutative0.9

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

  7. Final simplification0.9

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

Reproduce

herbie shell --seed 2019303 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))