Average Error: 1.0 → 0.0
Time: 13.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
\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 r5479532 = 4.0;
        double r5479533 = 3.0;
        double r5479534 = atan2(1.0, 0.0);
        double r5479535 = r5479533 * r5479534;
        double r5479536 = 1.0;
        double r5479537 = v;
        double r5479538 = r5479537 * r5479537;
        double r5479539 = r5479536 - r5479538;
        double r5479540 = r5479535 * r5479539;
        double r5479541 = 2.0;
        double r5479542 = 6.0;
        double r5479543 = r5479542 * r5479538;
        double r5479544 = r5479541 - r5479543;
        double r5479545 = sqrt(r5479544);
        double r5479546 = r5479540 * r5479545;
        double r5479547 = r5479532 / r5479546;
        return r5479547;
}
↓
double f(double v) {
        double r5479548 = 1.3333333333333333;
        double r5479549 = atan2(1.0, 0.0);
        double r5479550 = v;
        double r5479551 = r5479550 * r5479549;
        double r5479552 = r5479550 * r5479551;
        double r5479553 = r5479549 - r5479552;
        double r5479554 = r5479548 / r5479553;
        double r5479555 = 2.0;
        double r5479556 = r5479550 * r5479550;
        double r5479557 = 6.0;
        double r5479558 = r5479556 * r5479557;
        double r5479559 = r5479555 - r5479558;
        double r5479560 = sqrt(r5479559);
        double r5479561 = r5479554 / r5479560;
        return r5479561;
}

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 2019143 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))