Average Error: 15.2 → 0.8
Time: 31.0s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r20839345 = g;
        double r20839346 = 2.0;
        double r20839347 = a;
        double r20839348 = r20839346 * r20839347;
        double r20839349 = r20839345 / r20839348;
        double r20839350 = cbrt(r20839349);
        return r20839350;
}
↓
double f(double g, double a) {
        double r20839351 = 0.5;
        double r20839352 = a;
        double r20839353 = r20839351 / r20839352;
        double r20839354 = cbrt(r20839353);
        double r20839355 = g;
        double r20839356 = cbrt(r20839355);
        double r20839357 = r20839354 * r20839356;
        return r20839357;
}

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 15.2

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

  3. Applied cbrt-div0.9

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

  5. Applied *-un-lft-identity0.9

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

  6. Applied associate-/l*0.9

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

  8. Applied div-inv0.9

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

  9. Applied *-un-lft-identity0.9

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

  10. Applied times-frac0.9

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

  11. Simplified0.9

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

  13. Applied add-cbrt-cube0.9

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

  14. Applied cbrt-undiv0.9

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

  15. Simplified0.8

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

  16. Final simplification0.8

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))