Average Error: 1.0 → 0.0
Time: 12.7s
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 r119604 = 4.0;
        double r119605 = 3.0;
        double r119606 = atan2(1.0, 0.0);
        double r119607 = r119605 * r119606;
        double r119608 = 1.0;
        double r119609 = v;
        double r119610 = r119609 * r119609;
        double r119611 = r119608 - r119610;
        double r119612 = r119607 * r119611;
        double r119613 = 2.0;
        double r119614 = 6.0;
        double r119615 = r119614 * r119610;
        double r119616 = r119613 - r119615;
        double r119617 = sqrt(r119616);
        double r119618 = r119612 * r119617;
        double r119619 = r119604 / r119618;
        return r119619;
}
↓
double f(double v) {
        double r119620 = 4.0;
        double r119621 = 3.0;
        double r119622 = atan2(1.0, 0.0);
        double r119623 = r119621 * r119622;
        double r119624 = 1.0;
        double r119625 = v;
        double r119626 = r119625 * r119625;
        double r119627 = r119624 - r119626;
        double r119628 = r119623 * r119627;
        double r119629 = r119620 / r119628;
        double r119630 = 2.0;
        double r119631 = 6.0;
        double r119632 = r119631 * r119626;
        double r119633 = r119630 - r119632;
        double r119634 = sqrt(r119633);
        double r119635 = r119629 / r119634;
        return r119635;
}

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 2019235 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))