Average Error: 15.4 → 0.9
Time: 22.5s
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 r5115151 = g;
        double r5115152 = 2.0;
        double r5115153 = a;
        double r5115154 = r5115152 * r5115153;
        double r5115155 = r5115151 / r5115154;
        double r5115156 = cbrt(r5115155);
        return r5115156;
}
↓
double f(double g, double a) {
        double r5115157 = 1.0;
        double r5115158 = 2.0;
        double r5115159 = cbrt(r5115158);
        double r5115160 = r5115159 * r5115159;
        double r5115161 = sqrt(r5115160);
        double r5115162 = r5115157 / r5115161;
        double r5115163 = cbrt(r5115162);
        double r5115164 = sqrt(r5115158);
        double r5115165 = a;
        double r5115166 = r5115164 * r5115165;
        double r5115167 = cbrt(r5115166);
        double r5115168 = g;
        double r5115169 = sqrt(r5115159);
        double r5115170 = r5115168 / r5115169;
        double r5115171 = cbrt(r5115170);
        double r5115172 = r5115167 / r5115171;
        double r5115173 = r5115163 / r5115172;
        return r5115173;
}

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 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))