Average Error: 15.4 → 0.9
Time: 21.3s
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 r74362 = g;
        double r74363 = 2.0;
        double r74364 = a;
        double r74365 = r74363 * r74364;
        double r74366 = r74362 / r74365;
        double r74367 = cbrt(r74366);
        return r74367;
}
↓
double f(double g, double a) {
        double r74368 = 1.0;
        double r74369 = a;
        double r74370 = r74368 / r74369;
        double r74371 = cbrt(r74370);
        double r74372 = g;
        double r74373 = 2.0;
        double r74374 = r74372 / r74373;
        double r74375 = cbrt(r74374);
        double r74376 = r74371 * r74375;
        return r74376;
}

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 15.4

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

  3. Applied div-inv15.4

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

  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-frac0.9

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

  8. Applied cbrt-prod0.9

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

  9. Applied associate-*r*0.9

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

  10. Simplified0.9

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

  12. Applied cbrt-unprod0.9

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

  13. Simplified0.9

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

  14. Final simplification0.9

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))