Average Error: 1.0 → 0.0
Time: 4.8s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r282737 = 4.0;
        double r282738 = 3.0;
        double r282739 = atan2(1.0, 0.0);
        double r282740 = r282738 * r282739;
        double r282741 = 1.0;
        double r282742 = v;
        double r282743 = r282742 * r282742;
        double r282744 = r282741 - r282743;
        double r282745 = r282740 * r282744;
        double r282746 = 2.0;
        double r282747 = 6.0;
        double r282748 = r282747 * r282743;
        double r282749 = r282746 - r282748;
        double r282750 = sqrt(r282749);
        double r282751 = r282745 * r282750;
        double r282752 = r282737 / r282751;
        return r282752;
}
↓
double f(double v) {
        double r282753 = 4.0;
        double r282754 = 3.0;
        double r282755 = atan2(1.0, 0.0);
        double r282756 = r282754 * r282755;
        double r282757 = 1.0;
        double r282758 = v;
        double r282759 = r282758 * r282758;
        double r282760 = r282757 - r282759;
        double r282761 = r282756 * r282760;
        double r282762 = r282753 / r282761;
        double r282763 = 2.0;
        double r282764 = 6.0;
        double r282765 = r282764 * r282759;
        double r282766 = r282763 - r282765;
        double r282767 = sqrt(r282766);
        double r282768 = r282762 / r282767;
        return r282768;
}

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

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

Reproduce

herbie shell --seed 2020081 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))