Average Error: 1.0 → 0.0
Time: 11.2s
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 r4596513 = 4.0;
        double r4596514 = 3.0;
        double r4596515 = atan2(1.0, 0.0);
        double r4596516 = r4596514 * r4596515;
        double r4596517 = 1.0;
        double r4596518 = v;
        double r4596519 = r4596518 * r4596518;
        double r4596520 = r4596517 - r4596519;
        double r4596521 = r4596516 * r4596520;
        double r4596522 = 2.0;
        double r4596523 = 6.0;
        double r4596524 = r4596523 * r4596519;
        double r4596525 = r4596522 - r4596524;
        double r4596526 = sqrt(r4596525);
        double r4596527 = r4596521 * r4596526;
        double r4596528 = r4596513 / r4596527;
        return r4596528;
}
↓
double f(double v) {
        double r4596529 = 1.3333333333333333;
        double r4596530 = atan2(1.0, 0.0);
        double r4596531 = v;
        double r4596532 = r4596531 * r4596531;
        double r4596533 = r4596532 * r4596530;
        double r4596534 = r4596530 - r4596533;
        double r4596535 = r4596529 / r4596534;
        double r4596536 = 2.0;
        double r4596537 = 6.0;
        double r4596538 = r4596531 * r4596537;
        double r4596539 = r4596531 * r4596538;
        double r4596540 = r4596536 - r4596539;
        double r4596541 = sqrt(r4596540);
        double r4596542 = r4596535 / r4596541;
        return r4596542;
}

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 2019153 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))