Average Error: 15.1 → 0.9
Time: 16.6s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \frac{\sqrt[3]{\frac{1}{2}}}{\sqrt[3]{a}}\]
double f(double g, double a) {
        double r24928556 = g;
        double r24928557 = 2.0;
        double r24928558 = a;
        double r24928559 = r24928557 * r24928558;
        double r24928560 = r24928556 / r24928559;
        double r24928561 = cbrt(r24928560);
        return r24928561;
}
↓
double f(double g, double a) {
        double r24928562 = g;
        double r24928563 = cbrt(r24928562);
        double r24928564 = 0.5;
        double r24928565 = cbrt(r24928564);
        double r24928566 = a;
        double r24928567 = cbrt(r24928566);
        double r24928568 = r24928565 / r24928567;
        double r24928569 = r24928563 * r24928568;
        return r24928569;
}


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

Error

Bits error versus g

Bits error versus a

Derivation

  1. Initial program 15.1

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

  3. Applied div-inv15.1

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

  4. Applied cbrt-prod0.9

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

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

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

  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. Simplified0.8

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

  11. Applied cbrt-div0.9

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

  12. Applied associate-*r/0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2019102 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))