Average Error: 15.2 → 0.9
Time: 33.5s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt{\frac{1}{2}}}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{\frac{1}{2}}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt{\frac{1}{2}}}{a}} \cdot \left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{\frac{1}{2}}}\right)
double f(double g, double a) {
        double r3734991 = g;
        double r3734992 = 2.0;
        double r3734993 = a;
        double r3734994 = r3734992 * r3734993;
        double r3734995 = r3734991 / r3734994;
        double r3734996 = cbrt(r3734995);
        return r3734996;
}
↓
double f(double g, double a) {
        double r3734997 = 0.5;
        double r3734998 = sqrt(r3734997);
        double r3734999 = a;
        double r3735000 = r3734998 / r3734999;
        double r3735001 = cbrt(r3735000);
        double r3735002 = g;
        double r3735003 = cbrt(r3735002);
        double r3735004 = cbrt(r3734998);
        double r3735005 = r3735003 * r3735004;
        double r3735006 = r3735001 * r3735005;
        return r3735006;
}

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 cbrt-div0.8

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\]
  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-sqr-sqrt0.8

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

  13. Applied times-frac0.8

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

  14. Applied cbrt-prod0.9

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

  15. Applied associate-*r*0.9

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

  16. Simplified0.9

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

  17. Final simplification0.9

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

Reproduce

herbie shell --seed 2019149 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))