Average Error: 15.2 → 0.9
Time: 21.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{1}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right)
double f(double g, double a) {
        double r64580 = g;
        double r64581 = 2.0;
        double r64582 = a;
        double r64583 = r64581 * r64582;
        double r64584 = r64580 / r64583;
        double r64585 = cbrt(r64584);
        return r64585;
}
↓
double f(double g, double a) {
        double r64586 = 1.0;
        double r64587 = a;
        double r64588 = r64586 / r64587;
        double r64589 = cbrt(r64588);
        double r64590 = g;
        double r64591 = cbrt(r64590);
        double r64592 = 2.0;
        double r64593 = r64586 / r64592;
        double r64594 = cbrt(r64593);
        double r64595 = r64591 * r64594;
        double r64596 = r64589 * r64595;
        return r64596;
}

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 15.2

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

  6. Applied add-cube-cbrt0.9

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

  7. Applied times-frac0.9

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

  8. Applied cbrt-prod0.9

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

  9. Applied associate-*r*0.9

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

  10. Simplified0.9

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

  11. Final simplification0.9

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))