Average Error: 15.9 → 0.9
Time: 11.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\frac{1}{\sqrt[3]{g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\frac{1}{\sqrt[3]{g}}}
double f(double g, double a) {
        double r126175 = g;
        double r126176 = 2.0;
        double r126177 = a;
        double r126178 = r126176 * r126177;
        double r126179 = r126175 / r126178;
        double r126180 = cbrt(r126179);
        return r126180;
}
↓
double f(double g, double a) {
        double r126181 = 1.0;
        double r126182 = 2.0;
        double r126183 = a;
        double r126184 = r126182 * r126183;
        double r126185 = cbrt(r126184);
        double r126186 = r126181 / r126185;
        double r126187 = g;
        double r126188 = cbrt(r126187);
        double r126189 = r126181 / r126188;
        double r126190 = r126186 / r126189;
        return r126190;
}

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 15.9

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

  3. Applied cbrt-div0.8

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

  5. Applied clear-num0.9

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}}\]
  6. Using strategy rm

  7. Applied div-inv0.9

    \[\leadsto \frac{1}{\color{blue}{\sqrt[3]{2 \cdot a} \cdot \frac{1}{\sqrt[3]{g}}}}\]

  8. Applied associate-/r*0.9

    \[\leadsto \color{blue}{\frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\frac{1}{\sqrt[3]{g}}}}\]

  9. Final simplification0.9

    \[\leadsto \frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\frac{1}{\sqrt[3]{g}}}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))