Average Error: 15.6 → 1.2
Time: 5.5s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r160257 = g;
        double r160258 = 2.0;
        double r160259 = a;
        double r160260 = r160258 * r160259;
        double r160261 = r160257 / r160260;
        double r160262 = cbrt(r160261);
        return r160262;
}
↓
double f(double g, double a) {
        double r160263 = g;
        double r160264 = cbrt(r160263);
        double r160265 = r160264 * r160264;
        double r160266 = 2.0;
        double r160267 = r160265 / r160266;
        double r160268 = cbrt(r160267);
        double r160269 = cbrt(r160265);
        double r160270 = cbrt(r160264);
        double r160271 = r160269 * r160270;
        double r160272 = cbrt(r160271);
        double r160273 = a;
        double r160274 = cbrt(r160273);
        double r160275 = r160272 / r160274;
        double r160276 = r160268 * r160275;
        return r160276;
}

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-prod5.7

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

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

  10. Applied cbrt-prod1.2

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

  11. Final simplification1.2

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

Reproduce

herbie shell --seed 2020027 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))