Average Error: 15.9 → 1.4
Time: 6.2s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}}\right) \cdot \sqrt[3]{\sqrt[3]{g}}\right)}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}} \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}}\right) \cdot \sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}}\right) \cdot \sqrt[3]{\sqrt[3]{g}}\right)}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r216281 = g;
        double r216282 = 2.0;
        double r216283 = a;
        double r216284 = r216282 * r216283;
        double r216285 = r216281 / r216284;
        double r216286 = cbrt(r216285);
        return r216286;
}
↓
double f(double g, double a) {
        double r216287 = g;
        double r216288 = cbrt(r216287);
        double r216289 = r216288 * r216288;
        double r216290 = cbrt(r216289);
        double r216291 = cbrt(r216290);
        double r216292 = r216291 * r216291;
        double r216293 = r216292 * r216291;
        double r216294 = cbrt(r216288);
        double r216295 = r216293 * r216294;
        double r216296 = r216288 * r216295;
        double r216297 = 2.0;
        double r216298 = r216296 / r216297;
        double r216299 = cbrt(r216298);
        double r216300 = a;
        double r216301 = cbrt(r216300);
        double r216302 = r216294 / r216301;
        double r216303 = r216299 * r216302;
        return r216303;
}

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 15.9

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

  3. Applied add-cube-cbrt16.1

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

  4. Applied times-frac16.1

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

  5. Applied cbrt-prod5.6

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{a}}}\]
  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 add-cube-cbrt1.2

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

  10. Applied cbrt-prod1.2

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

  12. Applied add-cube-cbrt1.4

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

  13. Final simplification1.4

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

Reproduce

herbie shell --seed 2020060 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))