Average Error: 15.7 → 0.9
Time: 16.0s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{g}{2}} \cdot \sqrt[3]{\frac{1}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{g}{2}} \cdot \sqrt[3]{\frac{1}{a}}
double f(double g, double a) {
        double r6168580 = g;
        double r6168581 = 2.0;
        double r6168582 = a;
        double r6168583 = r6168581 * r6168582;
        double r6168584 = r6168580 / r6168583;
        double r6168585 = cbrt(r6168584);
        return r6168585;
}
↓
double f(double g, double a) {
        double r6168586 = g;
        double r6168587 = 2.0;
        double r6168588 = r6168586 / r6168587;
        double r6168589 = cbrt(r6168588);
        double r6168590 = 1.0;
        double r6168591 = a;
        double r6168592 = r6168590 / r6168591;
        double r6168593 = cbrt(r6168592);
        double r6168594 = r6168589 * r6168593;
        return r6168594;
}

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 15.7

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

  3. Applied div-inv15.7

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

  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-frac0.9

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

  8. Applied cbrt-prod0.9

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

  9. Applied associate-*r*0.9

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

  11. Applied cbrt-unprod0.9

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

  12. Simplified0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2019179 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))