Average Error: 15.5 → 1.2
Time: 8.5s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\right)
double f(double g, double a) {
        double r109338 = g;
        double r109339 = 2.0;
        double r109340 = a;
        double r109341 = r109339 * r109340;
        double r109342 = r109338 / r109341;
        double r109343 = cbrt(r109342);
        return r109343;
}
↓
double f(double g, double a) {
        double r109344 = g;
        double r109345 = cbrt(r109344);
        double r109346 = r109345 * r109345;
        double r109347 = cbrt(r109346);
        double r109348 = 1.0;
        double r109349 = 2.0;
        double r109350 = r109348 / r109349;
        double r109351 = cbrt(r109350);
        double r109352 = cbrt(r109345);
        double r109353 = a;
        double r109354 = cbrt(r109353);
        double r109355 = r109352 / r109354;
        double r109356 = r109351 * r109355;
        double r109357 = r109347 * r109356;
        return r109357;
}

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 add-cube-cbrt15.7

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

  4. Applied times-frac15.6

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

  5. Applied cbrt-prod5.7

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

  7. Applied cbrt-div1.2

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

  9. Applied div-inv1.2

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

  10. Applied cbrt-prod1.2

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

  12. Applied *-un-lft-identity1.2

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

  13. Final simplification1.2

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

Reproduce

herbie shell --seed 2019304 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))