Average Error: 14.8 → 0.8
Time: 12.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}
double f(double g, double a) {
        double r99152 = g;
        double r99153 = 2.0;
        double r99154 = a;
        double r99155 = r99153 * r99154;
        double r99156 = r99152 / r99155;
        double r99157 = cbrt(r99156);
        return r99157;
}
↓
double f(double g, double a) {
        double r99158 = g;
        double r99159 = cbrt(r99158);
        double r99160 = a;
        double r99161 = 2.0;
        double r99162 = r99160 * r99161;
        double r99163 = cbrt(r99162);
        double r99164 = r99159 / r99163;
        return r99164;
}

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 14.8

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

  3. Applied cbrt-div0.8

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

  4. Simplified0.8

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

  5. Final simplification0.8

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))