Average Error: 1.0 → 0.0
Time: 8.6s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
\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 r5524548 = 4.0;
        double r5524549 = 3.0;
        double r5524550 = atan2(1.0, 0.0);
        double r5524551 = r5524549 * r5524550;
        double r5524552 = 1.0;
        double r5524553 = v;
        double r5524554 = r5524553 * r5524553;
        double r5524555 = r5524552 - r5524554;
        double r5524556 = r5524551 * r5524555;
        double r5524557 = 2.0;
        double r5524558 = 6.0;
        double r5524559 = r5524558 * r5524554;
        double r5524560 = r5524557 - r5524559;
        double r5524561 = sqrt(r5524560);
        double r5524562 = r5524556 * r5524561;
        double r5524563 = r5524548 / r5524562;
        return r5524563;
}
↓
double f(double v) {
        double r5524564 = 1.3333333333333333;
        double r5524565 = atan2(1.0, 0.0);
        double r5524566 = v;
        double r5524567 = r5524566 * r5524565;
        double r5524568 = r5524566 * r5524567;
        double r5524569 = r5524565 - r5524568;
        double r5524570 = r5524564 / r5524569;
        double r5524571 = 2.0;
        double r5524572 = r5524566 * r5524566;
        double r5524573 = 6.0;
        double r5524574 = r5524572 * r5524573;
        double r5524575 = r5524571 - r5524574;
        double r5524576 = sqrt(r5524575);
        double r5524577 = r5524570 / r5524576;
        return r5524577;
}

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 2019142 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))