Average Error: 1.0 → 0.0
Time: 13.5s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{1 - v \cdot v} \cdot \frac{1}{\pi}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}\]
\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{\frac{4}{3}}{1 - v \cdot v} \cdot \frac{1}{\pi}}{\sqrt{\left(v \cdot v\right) \cdot -6 + 2}}
double f(double v) {
        double r62937896 = 4.0;
        double r62937897 = 3.0;
        double r62937898 = atan2(1.0, 0.0);
        double r62937899 = r62937897 * r62937898;
        double r62937900 = 1.0;
        double r62937901 = v;
        double r62937902 = r62937901 * r62937901;
        double r62937903 = r62937900 - r62937902;
        double r62937904 = r62937899 * r62937903;
        double r62937905 = 2.0;
        double r62937906 = 6.0;
        double r62937907 = r62937906 * r62937902;
        double r62937908 = r62937905 - r62937907;
        double r62937909 = sqrt(r62937908);
        double r62937910 = r62937904 * r62937909;
        double r62937911 = r62937896 / r62937910;
        return r62937911;
}
↓
double f(double v) {
        double r62937912 = 1.3333333333333333;
        double r62937913 = 1.0;
        double r62937914 = v;
        double r62937915 = r62937914 * r62937914;
        double r62937916 = r62937913 - r62937915;
        double r62937917 = r62937912 / r62937916;
        double r62937918 = atan2(1.0, 0.0);
        double r62937919 = r62937913 / r62937918;
        double r62937920 = r62937917 * r62937919;
        double r62937921 = -6.0;
        double r62937922 = r62937915 * r62937921;
        double r62937923 = 2.0;
        double r62937924 = r62937922 + r62937923;
        double r62937925 = sqrt(r62937924);
        double r62937926 = r62937920 / r62937925;
        return r62937926;
}

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

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

  5. Applied distribute-rgt-out--0.0

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

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

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

  7. Applied times-frac0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))