Average Error: 1.0 → 0.0
Time: 20.2s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{1}{\pi} \cdot \frac{\frac{\frac{4}{3}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{1}{\pi} \cdot \frac{\frac{\frac{4}{3}}{1 - v \cdot v}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r5340908 = 4.0;
        double r5340909 = 3.0;
        double r5340910 = atan2(1.0, 0.0);
        double r5340911 = r5340909 * r5340910;
        double r5340912 = 1.0;
        double r5340913 = v;
        double r5340914 = r5340913 * r5340913;
        double r5340915 = r5340912 - r5340914;
        double r5340916 = r5340911 * r5340915;
        double r5340917 = 2.0;
        double r5340918 = 6.0;
        double r5340919 = r5340918 * r5340914;
        double r5340920 = r5340917 - r5340919;
        double r5340921 = sqrt(r5340920);
        double r5340922 = r5340916 * r5340921;
        double r5340923 = r5340908 / r5340922;
        return r5340923;
}
↓
double f(double v) {
        double r5340924 = 1.0;
        double r5340925 = atan2(1.0, 0.0);
        double r5340926 = r5340924 / r5340925;
        double r5340927 = 1.3333333333333333;
        double r5340928 = v;
        double r5340929 = r5340928 * r5340928;
        double r5340930 = r5340924 - r5340929;
        double r5340931 = r5340927 / r5340930;
        double r5340932 = 2.0;
        double r5340933 = 6.0;
        double r5340934 = r5340933 * r5340929;
        double r5340935 = r5340932 - r5340934;
        double r5340936 = sqrt(r5340935);
        double r5340937 = r5340931 / r5340936;
        double r5340938 = r5340926 * r5340937;
        return r5340938;
}

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. Using strategy rm

  4. Applied *-un-lft-identity0.0

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

  5. Applied *-un-lft-identity0.0

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

  6. Applied distribute-rgt-out--0.0

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

  7. Applied *-un-lft-identity0.0

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

  8. Applied times-frac0.0

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

  9. Applied times-frac0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019130 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))