Average Error: 15.8 → 0.9
Time: 10.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\frac{\sqrt[3]{\frac{-1}{g}}}{\sqrt[3]{-1}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\frac{\sqrt[3]{\frac{-1}{g}}}{\sqrt[3]{-1}}}
double f(double g, double a) {
        double r76674 = g;
        double r76675 = 2.0;
        double r76676 = a;
        double r76677 = r76675 * r76676;
        double r76678 = r76674 / r76677;
        double r76679 = cbrt(r76678);
        return r76679;
}
↓
double f(double g, double a) {
        double r76680 = 1.0;
        double r76681 = 2.0;
        double r76682 = a;
        double r76683 = r76681 * r76682;
        double r76684 = cbrt(r76683);
        double r76685 = r76680 / r76684;
        double r76686 = -1.0;
        double r76687 = g;
        double r76688 = r76686 / r76687;
        double r76689 = cbrt(r76688);
        double r76690 = cbrt(r76686);
        double r76691 = r76689 / r76690;
        double r76692 = r76685 / r76691;
        return r76692;
}

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 15.8

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

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

  6. Applied cbrt-prod0.8

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

  7. Applied associate-/l*0.8

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

  9. Applied div-inv0.9

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

  10. Applied associate-/r*0.9

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

  11. Simplified0.9

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

  12. Taylor expanded around -inf 34.8

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

  13. Simplified0.9

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

  14. Final simplification0.9

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

Reproduce

herbie shell --seed 2019212 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))