Average Error: 15.8 → 0.8
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 r91314 = g;
        double r91315 = 2.0;
        double r91316 = a;
        double r91317 = r91315 * r91316;
        double r91318 = r91314 / r91317;
        double r91319 = cbrt(r91318);
        return r91319;
}
↓
double f(double g, double a) {
        double r91320 = g;
        double r91321 = cbrt(r91320);
        double r91322 = 1.0;
        double r91323 = 2.0;
        double r91324 = a;
        double r91325 = r91323 * r91324;
        double r91326 = r91322 / r91325;
        double r91327 = cbrt(r91326);
        double r91328 = r91321 * r91327;
        return r91328;
}

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 15.8

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

  3. Applied div-inv15.8

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

  4. Applied cbrt-prod0.8

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

  6. Applied *-un-lft-identity0.8

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

  7. Applied cbrt-prod0.8

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

  8. Applied associate-*l*0.8

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

  9. Final simplification0.8

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

Reproduce

herbie shell --seed 2019199 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))