Average Error: 1.0 → 0.0
Time: 28.0s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]
\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
↓
\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}
double f(double v) {
        double r31666920 = 4.0;
        double r31666921 = 3.0;
        double r31666922 = atan2(1.0, 0.0);
        double r31666923 = r31666921 * r31666922;
        double r31666924 = 1.0;
        double r31666925 = v;
        double r31666926 = r31666925 * r31666925;
        double r31666927 = r31666924 - r31666926;
        double r31666928 = r31666923 * r31666927;
        double r31666929 = 2.0;
        double r31666930 = 6.0;
        double r31666931 = r31666930 * r31666926;
        double r31666932 = r31666929 - r31666931;
        double r31666933 = sqrt(r31666932);
        double r31666934 = r31666928 * r31666933;
        double r31666935 = r31666920 / r31666934;
        return r31666935;
}
↓
double f(double v) {
        double r31666936 = 1.3333333333333333;
        double r31666937 = atan2(1.0, 0.0);
        double r31666938 = v;
        double r31666939 = r31666938 * r31666938;
        double r31666940 = r31666939 * r31666937;
        double r31666941 = r31666937 - r31666940;
        double r31666942 = r31666936 / r31666941;
        double r31666943 = -6.0;
        double r31666944 = r31666943 * r31666939;
        double r31666945 = 2.0;
        double r31666946 = r31666944 + r31666945;
        double r31666947 = sqrt(r31666946);
        double r31666948 = r31666942 / r31666947;
        return r31666948;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 + -6 \cdot \left(v \cdot v\right)}}}\]

  3. Final simplification0.0

    \[\leadsto \frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]

Reproduce

herbie shell --seed 2019124 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))