Average Error: 15.5 → 0.9
Time: 17.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a}} \cdot \sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a}} \cdot \sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}\right)
double f(double g, double a) {
        double r5110833 = g;
        double r5110834 = 2.0;
        double r5110835 = a;
        double r5110836 = r5110834 * r5110835;
        double r5110837 = r5110833 / r5110836;
        double r5110838 = cbrt(r5110837);
        return r5110838;
}
↓
double f(double g, double a) {
        double r5110839 = g;
        double r5110840 = cbrt(r5110839);
        double r5110841 = 0.5;
        double r5110842 = cbrt(r5110841);
        double r5110843 = a;
        double r5110844 = r5110842 / r5110843;
        double r5110845 = cbrt(r5110844);
        double r5110846 = r5110842 * r5110842;
        double r5110847 = cbrt(r5110846);
        double r5110848 = r5110845 * r5110847;
        double r5110849 = r5110840 * r5110848;
        return r5110849;
}

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 15.5

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

  3. Applied div-inv15.5

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

  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 *-un-lft-identity0.8

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

  8. Applied add-cube-cbrt0.8

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

  9. Applied times-frac0.8

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

  10. Applied cbrt-prod0.9

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

  11. Simplified0.9

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

  12. Final simplification0.9

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

Reproduce

herbie shell --seed 2019141 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))