Average Error: 1.0 → 0.0
Time: 12.8s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3 \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - \left(6 \cdot v\right) \cdot v}}\]
\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 \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - \left(6 \cdot v\right) \cdot v}}
double f(double v) {
        double r194359 = 4.0;
        double r194360 = 3.0;
        double r194361 = atan2(1.0, 0.0);
        double r194362 = r194360 * r194361;
        double r194363 = 1.0;
        double r194364 = v;
        double r194365 = r194364 * r194364;
        double r194366 = r194363 - r194365;
        double r194367 = r194362 * r194366;
        double r194368 = 2.0;
        double r194369 = 6.0;
        double r194370 = r194369 * r194365;
        double r194371 = r194368 - r194370;
        double r194372 = sqrt(r194371);
        double r194373 = r194367 * r194372;
        double r194374 = r194359 / r194373;
        return r194374;
}
↓
double f(double v) {
        double r194375 = 4.0;
        double r194376 = 3.0;
        double r194377 = atan2(1.0, 0.0);
        double r194378 = r194376 * r194377;
        double r194379 = r194375 / r194378;
        double r194380 = 1.0;
        double r194381 = v;
        double r194382 = r194381 * r194381;
        double r194383 = r194380 - r194382;
        double r194384 = r194379 / r194383;
        double r194385 = 2.0;
        double r194386 = 6.0;
        double r194387 = r194386 * r194381;
        double r194388 = r194387 * r194381;
        double r194389 = r194385 - r194388;
        double r194390 = sqrt(r194389);
        double r194391 = r194384 / r194390;
        return r194391;
}

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

    \[\leadsto \color{blue}{\frac{\frac{\frac{4}{\pi \cdot 3}}{1 - v \cdot v}}{\sqrt{2 - \left(v \cdot 6\right) \cdot v}}}\]

  3. Final simplification0.0

    \[\leadsto \frac{\frac{\frac{4}{3 \cdot \pi}}{1 - v \cdot v}}{\sqrt{2 - \left(6 \cdot v\right) \cdot v}}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))