Average Error: 15.1 → 1.2
Time: 5.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\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}}
double f(double g, double a) {
        double r160139 = g;
        double r160140 = 2.0;
        double r160141 = a;
        double r160142 = r160140 * r160141;
        double r160143 = r160139 / r160142;
        double r160144 = cbrt(r160143);
        return r160144;
}
↓
double f(double g, double a) {
        double r160145 = g;
        double r160146 = cbrt(r160145);
        double r160147 = r160146 * r160146;
        double r160148 = cbrt(r160147);
        double r160149 = 1.0;
        double r160150 = 2.0;
        double r160151 = r160149 / r160150;
        double r160152 = cbrt(r160151);
        double r160153 = r160148 * r160152;
        double r160154 = cbrt(r160146);
        double r160155 = a;
        double r160156 = cbrt(r160155);
        double r160157 = r160154 / r160156;
        double r160158 = r160153 * r160157;
        return r160158;
}

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 15.1

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

  3. Applied add-cube-cbrt15.3

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

  4. Applied times-frac15.3

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

  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 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. Final simplification1.2

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

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))