Average Error: 1.0 → 0.0
Time: 12.9s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r6999881 = 4.0;
        double r6999882 = 3.0;
        double r6999883 = atan2(1.0, 0.0);
        double r6999884 = r6999882 * r6999883;
        double r6999885 = 1.0;
        double r6999886 = v;
        double r6999887 = r6999886 * r6999886;
        double r6999888 = r6999885 - r6999887;
        double r6999889 = r6999884 * r6999888;
        double r6999890 = 2.0;
        double r6999891 = 6.0;
        double r6999892 = r6999891 * r6999887;
        double r6999893 = r6999890 - r6999892;
        double r6999894 = sqrt(r6999893);
        double r6999895 = r6999889 * r6999894;
        double r6999896 = r6999881 / r6999895;
        return r6999896;
}
↓
double f(double v) {
        double r6999897 = 4.0;
        double r6999898 = atan2(1.0, 0.0);
        double r6999899 = 3.0;
        double r6999900 = r6999898 * r6999899;
        double r6999901 = 1.0;
        double r6999902 = v;
        double r6999903 = r6999902 * r6999902;
        double r6999904 = r6999901 - r6999903;
        double r6999905 = r6999900 * r6999904;
        double r6999906 = r6999897 / r6999905;
        double r6999907 = 2.0;
        double r6999908 = 6.0;
        double r6999909 = r6999908 * r6999903;
        double r6999910 = r6999907 - r6999909;
        double r6999911 = sqrt(r6999910);
        double r6999912 = r6999906 / r6999911;
        return r6999912;
}

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. Using strategy rm

  3. Applied associate-/r*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))