Average Error: 14.9 → 0.8
Time: 28.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}
double f(double g, double a) {
        double r19517822 = g;
        double r19517823 = 2.0;
        double r19517824 = a;
        double r19517825 = r19517823 * r19517824;
        double r19517826 = r19517822 / r19517825;
        double r19517827 = cbrt(r19517826);
        return r19517827;
}
↓
double f(double g, double a) {
        double r19517828 = g;
        double r19517829 = cbrt(r19517828);
        double r19517830 = a;
        double r19517831 = 2.0;
        double r19517832 = r19517830 * r19517831;
        double r19517833 = cbrt(r19517832);
        double r19517834 = r19517829 / r19517833;
        return r19517834;
}

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 14.9

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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 *-un-lft-identity0.8

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

  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 *-un-lft-identity0.9

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

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

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

  10. Applied times-frac0.9

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

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

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

  12. Applied times-frac0.9

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

  13. Simplified0.9

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

  14. Simplified0.8

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

  15. Final simplification0.8

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

Reproduce

herbie shell --seed 2019124 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))