Average Error: 1.0 → 0.0
Time: 14.2s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
\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}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}
double f(double v) {
        double r7038846 = 4.0;
        double r7038847 = 3.0;
        double r7038848 = atan2(1.0, 0.0);
        double r7038849 = r7038847 * r7038848;
        double r7038850 = 1.0;
        double r7038851 = v;
        double r7038852 = r7038851 * r7038851;
        double r7038853 = r7038850 - r7038852;
        double r7038854 = r7038849 * r7038853;
        double r7038855 = 2.0;
        double r7038856 = 6.0;
        double r7038857 = r7038856 * r7038852;
        double r7038858 = r7038855 - r7038857;
        double r7038859 = sqrt(r7038858);
        double r7038860 = r7038854 * r7038859;
        double r7038861 = r7038846 / r7038860;
        return r7038861;
}
↓
double f(double v) {
        double r7038862 = 1.3333333333333333;
        double r7038863 = atan2(1.0, 0.0);
        double r7038864 = v;
        double r7038865 = r7038864 * r7038863;
        double r7038866 = r7038864 * r7038865;
        double r7038867 = r7038863 - r7038866;
        double r7038868 = r7038862 / r7038867;
        double r7038869 = 2.0;
        double r7038870 = r7038864 * r7038864;
        double r7038871 = 6.0;
        double r7038872 = r7038870 * r7038871;
        double r7038873 = r7038869 - r7038872;
        double r7038874 = sqrt(r7038873);
        double r7038875 = r7038868 / r7038874;
        return r7038875;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))