Average Error: 15.3 → 0.9
Time: 15.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{\sqrt{\frac{1}{2}}}{a}} \cdot \sqrt[3]{\sqrt{\frac{1}{2}}}\right) \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\frac{\sqrt{\frac{1}{2}}}{a}} \cdot \sqrt[3]{\sqrt{\frac{1}{2}}}\right) \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r4228677 = g;
        double r4228678 = 2.0;
        double r4228679 = a;
        double r4228680 = r4228678 * r4228679;
        double r4228681 = r4228677 / r4228680;
        double r4228682 = cbrt(r4228681);
        return r4228682;
}
↓
double f(double g, double a) {
        double r4228683 = 0.5;
        double r4228684 = sqrt(r4228683);
        double r4228685 = a;
        double r4228686 = r4228684 / r4228685;
        double r4228687 = cbrt(r4228686);
        double r4228688 = cbrt(r4228684);
        double r4228689 = r4228687 * r4228688;
        double r4228690 = g;
        double r4228691 = cbrt(r4228690);
        double r4228692 = r4228689 * r4228691;
        return r4228692;
}

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 15.3

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

  3. Applied div-inv15.3

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

  4. Applied cbrt-prod0.9

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

  5. Simplified0.8

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

  7. Applied *-un-lft-identity0.8

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

  8. Applied add-sqr-sqrt0.8

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

  9. Applied times-frac0.8

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

  10. Applied cbrt-prod0.9

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

  11. Simplified0.9

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

  12. Final simplification0.9

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))