Average Error: 1.0 → 0.0
Time: 10.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r3788715 = 4.0;
        double r3788716 = 3.0;
        double r3788717 = atan2(1.0, 0.0);
        double r3788718 = r3788716 * r3788717;
        double r3788719 = 1.0;
        double r3788720 = v;
        double r3788721 = r3788720 * r3788720;
        double r3788722 = r3788719 - r3788721;
        double r3788723 = r3788718 * r3788722;
        double r3788724 = 2.0;
        double r3788725 = 6.0;
        double r3788726 = r3788725 * r3788721;
        double r3788727 = r3788724 - r3788726;
        double r3788728 = sqrt(r3788727);
        double r3788729 = r3788723 * r3788728;
        double r3788730 = r3788715 / r3788729;
        return r3788730;
}
↓
double f(double v) {
        double r3788731 = 1.3333333333333333;
        double r3788732 = atan2(1.0, 0.0);
        double r3788733 = v;
        double r3788734 = r3788733 * r3788733;
        double r3788735 = r3788734 * r3788732;
        double r3788736 = r3788732 - r3788735;
        double r3788737 = r3788731 / r3788736;
        double r3788738 = 2.0;
        double r3788739 = 6.0;
        double r3788740 = r3788739 * r3788734;
        double r3788741 = r3788738 - r3788740;
        double r3788742 = sqrt(r3788741);
        double r3788743 = r3788737 / r3788742;
        return r3788743;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019139 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))