Average Error: 15.8 → 0.9
Time: 19.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}
double f(double g, double a) {
        double r140408 = g;
        double r140409 = 2.0;
        double r140410 = a;
        double r140411 = r140409 * r140410;
        double r140412 = r140408 / r140411;
        double r140413 = cbrt(r140412);
        return r140413;
}
↓
double f(double g, double a) {
        double r140414 = 1.0;
        double r140415 = 2.0;
        double r140416 = a;
        double r140417 = r140415 * r140416;
        double r140418 = cbrt(r140417);
        double r140419 = g;
        double r140420 = cbrt(r140419);
        double r140421 = r140418 / r140420;
        double r140422 = r140414 / r140421;
        return r140422;
}

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 cbrt-div0.8

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

  5. Applied clear-num0.9

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

  6. Final simplification0.9

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))