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 r6968905 = 4.0;
        double r6968906 = 3.0;
        double r6968907 = atan2(1.0, 0.0);
        double r6968908 = r6968906 * r6968907;
        double r6968909 = 1.0;
        double r6968910 = v;
        double r6968911 = r6968910 * r6968910;
        double r6968912 = r6968909 - r6968911;
        double r6968913 = r6968908 * r6968912;
        double r6968914 = 2.0;
        double r6968915 = 6.0;
        double r6968916 = r6968915 * r6968911;
        double r6968917 = r6968914 - r6968916;
        double r6968918 = sqrt(r6968917);
        double r6968919 = r6968913 * r6968918;
        double r6968920 = r6968905 / r6968919;
        return r6968920;
}
↓
double f(double v) {
        double r6968921 = 4.0;
        double r6968922 = atan2(1.0, 0.0);
        double r6968923 = 3.0;
        double r6968924 = r6968922 * r6968923;
        double r6968925 = 1.0;
        double r6968926 = v;
        double r6968927 = r6968926 * r6968926;
        double r6968928 = r6968925 - r6968927;
        double r6968929 = r6968924 * r6968928;
        double r6968930 = r6968921 / r6968929;
        double r6968931 = 2.0;
        double r6968932 = 6.0;
        double r6968933 = r6968932 * r6968927;
        double r6968934 = r6968931 - r6968933;
        double r6968935 = sqrt(r6968934);
        double r6968936 = r6968930 / r6968935;
        return r6968936;
}

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)))))))