Average Error: 1.0 → 0.0
Time: 7.4s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r189885 = 4.0;
        double r189886 = 3.0;
        double r189887 = atan2(1.0, 0.0);
        double r189888 = r189886 * r189887;
        double r189889 = 1.0;
        double r189890 = v;
        double r189891 = r189890 * r189890;
        double r189892 = r189889 - r189891;
        double r189893 = r189888 * r189892;
        double r189894 = 2.0;
        double r189895 = 6.0;
        double r189896 = r189895 * r189891;
        double r189897 = r189894 - r189896;
        double r189898 = sqrt(r189897);
        double r189899 = r189893 * r189898;
        double r189900 = r189885 / r189899;
        return r189900;
}
↓
double f(double v) {
        double r189901 = 4.0;
        double r189902 = sqrt(r189901);
        double r189903 = 3.0;
        double r189904 = atan2(1.0, 0.0);
        double r189905 = r189903 * r189904;
        double r189906 = 1.0;
        double r189907 = v;
        double r189908 = r189907 * r189907;
        double r189909 = r189906 - r189908;
        double r189910 = r189905 * r189909;
        double r189911 = r189902 / r189910;
        double r189912 = 2.0;
        double r189913 = 6.0;
        double r189914 = r189913 * r189908;
        double r189915 = r189912 - r189914;
        double r189916 = sqrt(r189915);
        double r189917 = r189902 / r189916;
        double r189918 = r189911 * r189917;
        return r189918;
}

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 add-sqr-sqrt1.0

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

  4. Applied times-frac0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))