Average Error: 15.4 → 0.8
Time: 26.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}
double f(double g, double a) {
        double r4946193 = g;
        double r4946194 = 2.0;
        double r4946195 = a;
        double r4946196 = r4946194 * r4946195;
        double r4946197 = r4946193 / r4946196;
        double r4946198 = cbrt(r4946197);
        return r4946198;
}
↓
double f(double g, double a) {
        double r4946199 = g;
        double r4946200 = cbrt(r4946199);
        double r4946201 = 2.0;
        double r4946202 = a;
        double r4946203 = r4946201 * r4946202;
        double r4946204 = cbrt(r4946203);
        double r4946205 = r4946200 / r4946204;
        return r4946205;
}

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 cbrt-div0.8

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

  5. Applied div-inv0.8

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

  7. Applied un-div-inv0.8

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

  8. Final simplification0.8

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2.0 a))))