Average Error: 1.0 → 0.0
Time: 6.1s
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 r2862445 = 4.0;
        double r2862446 = 3.0;
        double r2862447 = atan2(1.0, 0.0);
        double r2862448 = r2862446 * r2862447;
        double r2862449 = 1.0;
        double r2862450 = v;
        double r2862451 = r2862450 * r2862450;
        double r2862452 = r2862449 - r2862451;
        double r2862453 = r2862448 * r2862452;
        double r2862454 = 2.0;
        double r2862455 = 6.0;
        double r2862456 = r2862455 * r2862451;
        double r2862457 = r2862454 - r2862456;
        double r2862458 = sqrt(r2862457);
        double r2862459 = r2862453 * r2862458;
        double r2862460 = r2862445 / r2862459;
        return r2862460;
}
↓
double f(double v) {
        double r2862461 = 1.3333333333333333;
        double r2862462 = atan2(1.0, 0.0);
        double r2862463 = v;
        double r2862464 = r2862463 * r2862463;
        double r2862465 = r2862464 * r2862462;
        double r2862466 = r2862462 - r2862465;
        double r2862467 = r2862461 / r2862466;
        double r2862468 = 2.0;
        double r2862469 = 6.0;
        double r2862470 = r2862463 * r2862469;
        double r2862471 = r2862463 * r2862470;
        double r2862472 = r2862468 - r2862471;
        double r2862473 = sqrt(r2862472);
        double r2862474 = r2862467 / r2862473;
        return r2862474;
}

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 2019154 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))