Average Error: 15.6 → 0.9
Time: 15.2s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{1}{a} \cdot \sqrt{\frac{1}{2}}} \cdot \sqrt[3]{\sqrt{\frac{1}{2}}}\right) \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\frac{1}{a} \cdot \sqrt{\frac{1}{2}}} \cdot \sqrt[3]{\sqrt{\frac{1}{2}}}\right) \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r6608796 = g;
        double r6608797 = 2.0;
        double r6608798 = a;
        double r6608799 = r6608797 * r6608798;
        double r6608800 = r6608796 / r6608799;
        double r6608801 = cbrt(r6608800);
        return r6608801;
}
↓
double f(double g, double a) {
        double r6608802 = 1.0;
        double r6608803 = a;
        double r6608804 = r6608802 / r6608803;
        double r6608805 = 0.5;
        double r6608806 = sqrt(r6608805);
        double r6608807 = r6608804 * r6608806;
        double r6608808 = cbrt(r6608807);
        double r6608809 = cbrt(r6608806);
        double r6608810 = r6608808 * r6608809;
        double r6608811 = g;
        double r6608812 = cbrt(r6608811);
        double r6608813 = r6608810 * r6608812;
        return r6608813;
}

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 15.6

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

  3. Applied div-inv15.6

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

  4. Applied cbrt-prod0.9

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

  5. Simplified0.8

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

  7. Applied *-commutative0.8

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

  9. Applied *-un-lft-identity0.8

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

  10. Applied add-sqr-sqrt0.8

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

  11. Applied times-frac0.8

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

  12. Applied cbrt-prod0.9

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

  13. Simplified0.9

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

  15. Applied div-inv0.9

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

  16. Final simplification0.9

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

Reproduce

herbie shell --seed 2019168 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))