Average Error: 14.6 → 0.9
Time: 12.6s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{g}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{g}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r2529263 = g;
        double r2529264 = 2.0;
        double r2529265 = a;
        double r2529266 = r2529264 * r2529265;
        double r2529267 = r2529263 / r2529266;
        double r2529268 = cbrt(r2529267);
        return r2529268;
}
↓
double f(double g, double a) {
        double r2529269 = 0.5;
        double r2529270 = cbrt(r2529269);
        double r2529271 = g;
        double r2529272 = cbrt(r2529271);
        double r2529273 = r2529270 * r2529272;
        double r2529274 = a;
        double r2529275 = cbrt(r2529274);
        double r2529276 = r2529273 / r2529275;
        return r2529276;
}

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 14.6

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

  3. Applied div-inv14.6

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

  4. Applied cbrt-prod0.8

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

  5. Simplified0.8

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

  7. Applied cbrt-div0.9

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

  8. Applied associate-*r/0.9

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

  9. Final simplification0.9

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))