Average Error: 1.0 → 0.0
Time: 7.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 - v \cdot \left(v \cdot 6\right)}}\]
\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 - v \cdot \left(v \cdot 6\right)}}
double f(double v) {
        double r2245648 = 4.0;
        double r2245649 = 3.0;
        double r2245650 = atan2(1.0, 0.0);
        double r2245651 = r2245649 * r2245650;
        double r2245652 = 1.0;
        double r2245653 = v;
        double r2245654 = r2245653 * r2245653;
        double r2245655 = r2245652 - r2245654;
        double r2245656 = r2245651 * r2245655;
        double r2245657 = 2.0;
        double r2245658 = 6.0;
        double r2245659 = r2245658 * r2245654;
        double r2245660 = r2245657 - r2245659;
        double r2245661 = sqrt(r2245660);
        double r2245662 = r2245656 * r2245661;
        double r2245663 = r2245648 / r2245662;
        return r2245663;
}
↓
double f(double v) {
        double r2245664 = 1.3333333333333333;
        double r2245665 = atan2(1.0, 0.0);
        double r2245666 = v;
        double r2245667 = r2245666 * r2245666;
        double r2245668 = r2245667 * r2245665;
        double r2245669 = r2245665 - r2245668;
        double r2245670 = r2245664 / r2245669;
        double r2245671 = 2.0;
        double r2245672 = 6.0;
        double r2245673 = r2245666 * r2245672;
        double r2245674 = r2245666 * r2245673;
        double r2245675 = r2245671 - r2245674;
        double r2245676 = sqrt(r2245675);
        double r2245677 = r2245670 / r2245676;
        return r2245677;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))