Average Error: 15.5 → 0.9
Time: 12.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{2}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{1}{2}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{a}}\right)
double f(double g, double a) {
        double r119560 = g;
        double r119561 = 2.0;
        double r119562 = a;
        double r119563 = r119561 * r119562;
        double r119564 = r119560 / r119563;
        double r119565 = cbrt(r119564);
        return r119565;
}
↓
double f(double g, double a) {
        double r119566 = 1.0;
        double r119567 = 2.0;
        double r119568 = r119566 / r119567;
        double r119569 = cbrt(r119568);
        double r119570 = g;
        double r119571 = cbrt(r119570);
        double r119572 = a;
        double r119573 = r119566 / r119572;
        double r119574 = cbrt(r119573);
        double r119575 = r119571 * r119574;
        double r119576 = r119569 * r119575;
        return r119576;
}

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 15.5

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

  3. Applied div-inv15.5

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

  4. Applied cbrt-prod0.8

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

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

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

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

  10. Simplified0.8

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

  12. Applied associate-*l*0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))