Average Error: 16.2 → 0.8
Time: 12.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{\sqrt{1}}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \sqrt[3]{\frac{\sqrt{1}}{a}}
double f(double g, double a) {
        double r119712 = g;
        double r119713 = 2.0;
        double r119714 = a;
        double r119715 = r119713 * r119714;
        double r119716 = r119712 / r119715;
        double r119717 = cbrt(r119716);
        return r119717;
}
↓
double f(double g, double a) {
        double r119718 = g;
        double r119719 = cbrt(r119718);
        double r119720 = 1.0;
        double r119721 = 2.0;
        double r119722 = r119720 / r119721;
        double r119723 = cbrt(r119722);
        double r119724 = r119719 * r119723;
        double r119725 = sqrt(r119720);
        double r119726 = a;
        double r119727 = r119725 / r119726;
        double r119728 = cbrt(r119727);
        double r119729 = r119724 * r119728;
        return r119729;
}

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 16.2

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

  3. Applied div-inv16.2

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

  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-sqr-sqrt0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

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

  10. Simplified0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2019351 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))