Average Error: 15.4 → 1.2
Time: 6.3s
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 r172968 = g;
        double r172969 = 2.0;
        double r172970 = a;
        double r172971 = r172969 * r172970;
        double r172972 = r172968 / r172971;
        double r172973 = cbrt(r172972);
        return r172973;
}
↓
double f(double g, double a) {
        double r172974 = g;
        double r172975 = cbrt(r172974);
        double r172976 = r172975 * r172975;
        double r172977 = 2.0;
        double r172978 = r172976 / r172977;
        double r172979 = cbrt(r172978);
        double r172980 = sqrt(r172979);
        double r172981 = r172980 * r172980;
        double r172982 = cbrt(r172975);
        double r172983 = a;
        double r172984 = cbrt(r172983);
        double r172985 = r172982 / r172984;
        double r172986 = r172981 * r172985;
        return r172986;
}

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