Average Error: 14.9 → 0.9
Time: 18.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}}\right)
double f(double g, double a) {
        double r14655943 = g;
        double r14655944 = 2.0;
        double r14655945 = a;
        double r14655946 = r14655944 * r14655945;
        double r14655947 = r14655943 / r14655946;
        double r14655948 = cbrt(r14655947);
        return r14655948;
}
↓
double f(double g, double a) {
        double r14655949 = 0.5;
        double r14655950 = cbrt(r14655949);
        double r14655951 = a;
        double r14655952 = r14655950 / r14655951;
        double r14655953 = cbrt(r14655952);
        double r14655954 = g;
        double r14655955 = cbrt(r14655954);
        double r14655956 = r14655950 * r14655950;
        double r14655957 = cbrt(r14655956);
        double r14655958 = r14655955 * r14655957;
        double r14655959 = r14655953 * r14655958;
        return r14655959;
}

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 14.9

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

  3. Applied cbrt-div0.9

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

  5. Applied div-inv0.9

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

  7. Applied add-cbrt-cube0.9

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

  8. Applied cbrt-undiv0.9

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

  9. Simplified0.8

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

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

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

  12. Applied add-cube-cbrt0.8

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

  13. Applied times-frac0.8

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

  14. Applied cbrt-prod0.9

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

  15. Applied associate-*r*0.9

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

  16. Final simplification0.9

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

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))