Average Error: 15.5 → 0.8
Time: 20.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{g}{2}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\frac{g}{2}}
double f(double g, double a) {
        double r132291 = g;
        double r132292 = 2.0;
        double r132293 = a;
        double r132294 = r132292 * r132293;
        double r132295 = r132291 / r132294;
        double r132296 = cbrt(r132295);
        return r132296;
}
↓
double f(double g, double a) {
        double r132297 = 1.0;
        double r132298 = a;
        double r132299 = r132297 / r132298;
        double r132300 = cbrt(r132299);
        double r132301 = g;
        double r132302 = 2.0;
        double r132303 = r132301 / r132302;
        double r132304 = cbrt(r132303);
        double r132305 = r132300 * r132304;
        return r132305;
}

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 15.5

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

  3. Applied div-inv15.5

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

  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 add-cube-cbrt0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

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

  10. Simplified0.8

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

  12. Applied cbrt-unprod0.8

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

  13. Simplified0.8

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

  14. Final simplification0.8

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))