Average Error: 15.3 → 0.8
Time: 16.6s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\frac{1}{2}}{a}} \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r15857548 = g;
        double r15857549 = 2.0;
        double r15857550 = a;
        double r15857551 = r15857549 * r15857550;
        double r15857552 = r15857548 / r15857551;
        double r15857553 = cbrt(r15857552);
        return r15857553;
}
↓
double f(double g, double a) {
        double r15857554 = 0.5;
        double r15857555 = a;
        double r15857556 = r15857554 / r15857555;
        double r15857557 = cbrt(r15857556);
        double r15857558 = g;
        double r15857559 = cbrt(r15857558);
        double r15857560 = r15857557 * r15857559;
        return r15857560;
}

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-inv15.4

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

  4. Applied cbrt-prod0.9

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

  5. Taylor expanded around inf 33.9

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

  6. Simplified0.9

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

  8. Applied cbrt-unprod0.8

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

  9. Simplified0.8

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

  10. Final simplification0.8

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

Reproduce

herbie shell --seed 2019107 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))