Average Error: 15.4 → 1.2
Time: 6.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}} \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}} \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r152225 = g;
        double r152226 = 2.0;
        double r152227 = a;
        double r152228 = r152226 * r152227;
        double r152229 = r152225 / r152228;
        double r152230 = cbrt(r152229);
        return r152230;
}
↓
double f(double g, double a) {
        double r152231 = g;
        double r152232 = cbrt(r152231);
        double r152233 = r152232 * r152232;
        double r152234 = 2.0;
        double r152235 = r152233 / r152234;
        double r152236 = cbrt(r152235);
        double r152237 = sqrt(r152236);
        double r152238 = r152237 * r152237;
        double r152239 = cbrt(r152232);
        double r152240 = a;
        double r152241 = cbrt(r152240);
        double r152242 = r152239 / r152241;
        double r152243 = r152238 * r152242;
        return r152243;
}

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-cube-cbrt15.6

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

  4. Applied times-frac15.6

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

  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-sqr-sqrt1.2

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

  10. Final simplification1.2

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))