Average Error: 1.0 → 0.0
Time: 8.6s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\frac{\left({1}^{3} - {v}^{6}\right) \cdot \left(3 \cdot \pi\right)}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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}{\frac{\left({1}^{3} - {v}^{6}\right) \cdot \left(3 \cdot \pi\right)}{1 \cdot 1 + \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + 1 \cdot \left(v \cdot v\right)\right)}}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r288754 = 4.0;
        double r288755 = 3.0;
        double r288756 = atan2(1.0, 0.0);
        double r288757 = r288755 * r288756;
        double r288758 = 1.0;
        double r288759 = v;
        double r288760 = r288759 * r288759;
        double r288761 = r288758 - r288760;
        double r288762 = r288757 * r288761;
        double r288763 = 2.0;
        double r288764 = 6.0;
        double r288765 = r288764 * r288760;
        double r288766 = r288763 - r288765;
        double r288767 = sqrt(r288766);
        double r288768 = r288762 * r288767;
        double r288769 = r288754 / r288768;
        return r288769;
}
↓
double f(double v) {
        double r288770 = 4.0;
        double r288771 = 1.0;
        double r288772 = 3.0;
        double r288773 = pow(r288771, r288772);
        double r288774 = v;
        double r288775 = 6.0;
        double r288776 = pow(r288774, r288775);
        double r288777 = r288773 - r288776;
        double r288778 = 3.0;
        double r288779 = atan2(1.0, 0.0);
        double r288780 = r288778 * r288779;
        double r288781 = r288777 * r288780;
        double r288782 = r288771 * r288771;
        double r288783 = r288774 * r288774;
        double r288784 = r288783 * r288783;
        double r288785 = r288771 * r288783;
        double r288786 = r288784 + r288785;
        double r288787 = r288782 + r288786;
        double r288788 = r288781 / r288787;
        double r288789 = r288770 / r288788;
        double r288790 = 2.0;
        double r288791 = 6.0;
        double r288792 = r288791 * r288783;
        double r288793 = r288790 - r288792;
        double r288794 = sqrt(r288793);
        double r288795 = r288789 / r288794;
        return r288795;
}

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. Using strategy rm

  5. Applied flip3--0.0

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

  6. Applied associate-*r/0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))