Average Error: 15.4 → 0.9
Time: 19.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{\frac{1}{\sqrt{\sqrt[3]{2} \cdot \sqrt[3]{2}}}}}{\frac{\sqrt[3]{\sqrt{2} \cdot a}}{\sqrt[3]{\frac{g}{\sqrt{\sqrt[3]{2}}}}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{\frac{1}{\sqrt{\sqrt[3]{2} \cdot \sqrt[3]{2}}}}}{\frac{\sqrt[3]{\sqrt{2} \cdot a}}{\sqrt[3]{\frac{g}{\sqrt{\sqrt[3]{2}}}}}}
double f(double g, double a) {
        double r6801352 = g;
        double r6801353 = 2.0;
        double r6801354 = a;
        double r6801355 = r6801353 * r6801354;
        double r6801356 = r6801352 / r6801355;
        double r6801357 = cbrt(r6801356);
        return r6801357;
}
↓
double f(double g, double a) {
        double r6801358 = 1.0;
        double r6801359 = 2.0;
        double r6801360 = cbrt(r6801359);
        double r6801361 = r6801360 * r6801360;
        double r6801362 = sqrt(r6801361);
        double r6801363 = r6801358 / r6801362;
        double r6801364 = cbrt(r6801363);
        double r6801365 = sqrt(r6801359);
        double r6801366 = a;
        double r6801367 = r6801365 * r6801366;
        double r6801368 = cbrt(r6801367);
        double r6801369 = g;
        double r6801370 = sqrt(r6801360);
        double r6801371 = r6801369 / r6801370;
        double r6801372 = cbrt(r6801371);
        double r6801373 = r6801368 / r6801372;
        double r6801374 = r6801364 / r6801373;
        return r6801374;
}

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 15.4

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

  3. Applied add-sqr-sqrt15.5

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

  4. Applied associate-*l*15.4

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

  5. Applied associate-/r*15.4

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

  6. Applied cbrt-div0.9

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

  8. Applied add-cube-cbrt0.9

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

  9. Applied sqrt-prod0.9

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

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

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

  11. Applied times-frac1.0

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

  12. Applied cbrt-prod0.9

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

  13. Applied associate-/l*0.9

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

  14. Final simplification0.9

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

Reproduce

herbie shell --seed 2019158 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))