Average Error: 1.0 → 0.0
Time: 5.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r286891 = 4.0;
        double r286892 = 3.0;
        double r286893 = atan2(1.0, 0.0);
        double r286894 = r286892 * r286893;
        double r286895 = 1.0;
        double r286896 = v;
        double r286897 = r286896 * r286896;
        double r286898 = r286895 - r286897;
        double r286899 = r286894 * r286898;
        double r286900 = 2.0;
        double r286901 = 6.0;
        double r286902 = r286901 * r286897;
        double r286903 = r286900 - r286902;
        double r286904 = sqrt(r286903);
        double r286905 = r286899 * r286904;
        double r286906 = r286891 / r286905;
        return r286906;
}
↓
double f(double v) {
        double r286907 = 4.0;
        double r286908 = 3.0;
        double r286909 = atan2(1.0, 0.0);
        double r286910 = r286908 * r286909;
        double r286911 = 1.0;
        double r286912 = v;
        double r286913 = r286912 * r286912;
        double r286914 = r286911 - r286913;
        double r286915 = r286910 * r286914;
        double r286916 = r286907 / r286915;
        double r286917 = 2.0;
        double r286918 = 6.0;
        double r286919 = r286918 * r286913;
        double r286920 = r286917 - r286919;
        double r286921 = sqrt(r286920);
        double r286922 = r286916 / r286921;
        return r286922;
}

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

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

Reproduce

herbie shell --seed 2020021 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))