Average Error: 15.6 → 1.2
Time: 5.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\left(\sqrt{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}} \cdot \sqrt{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}}\right) \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\left(\sqrt{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}} \cdot \sqrt{\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}}
double f(double g, double a) {
        double r150847 = g;
        double r150848 = 2.0;
        double r150849 = a;
        double r150850 = r150848 * r150849;
        double r150851 = r150847 / r150850;
        double r150852 = cbrt(r150851);
        return r150852;
}
↓
double f(double g, double a) {
        double r150853 = g;
        double r150854 = cbrt(r150853);
        double r150855 = r150854 * r150854;
        double r150856 = cbrt(r150855);
        double r150857 = sqrt(r150856);
        double r150858 = r150857 * r150857;
        double r150859 = 1.0;
        double r150860 = 2.0;
        double r150861 = r150859 / r150860;
        double r150862 = cbrt(r150861);
        double r150863 = r150858 * r150862;
        double r150864 = cbrt(r150854);
        double r150865 = a;
        double r150866 = cbrt(r150865);
        double r150867 = r150864 / r150866;
        double r150868 = r150863 * r150867;
        return r150868;
}

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 15.6

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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-frac15.7

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

  5. Applied cbrt-prod5.9

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{a}}}\]
  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 add-sqr-sqrt1.2

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

  13. Final simplification1.2

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

Reproduce

herbie shell --seed 2019362 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))