Average Error: 1.0 → 0.0
Time: 15.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\left(\pi \cdot \pi + \left(\left(\left(\pi \cdot v\right) \cdot v\right) \cdot \left(\left(\pi \cdot v\right) \cdot v\right) + \pi \cdot \left(\left(\pi \cdot v\right) \cdot v\right)\right)\right) \cdot \frac{\frac{4}{3}}{\left(\pi \cdot \pi\right) \cdot \pi - \left(\left(\left(\pi \cdot \pi\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot \left(v \cdot v\right)}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}}\]
\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{\left(\pi \cdot \pi + \left(\left(\left(\pi \cdot v\right) \cdot v\right) \cdot \left(\left(\pi \cdot v\right) \cdot v\right) + \pi \cdot \left(\left(\pi \cdot v\right) \cdot v\right)\right)\right) \cdot \frac{\frac{4}{3}}{\left(\pi \cdot \pi\right) \cdot \pi - \left(\left(\left(\pi \cdot \pi\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot \left(v \cdot v\right)}}{\sqrt{2 + \left(v \cdot v\right) \cdot -6}}
double f(double v) {
        double r4728348 = 4.0;
        double r4728349 = 3.0;
        double r4728350 = atan2(1.0, 0.0);
        double r4728351 = r4728349 * r4728350;
        double r4728352 = 1.0;
        double r4728353 = v;
        double r4728354 = r4728353 * r4728353;
        double r4728355 = r4728352 - r4728354;
        double r4728356 = r4728351 * r4728355;
        double r4728357 = 2.0;
        double r4728358 = 6.0;
        double r4728359 = r4728358 * r4728354;
        double r4728360 = r4728357 - r4728359;
        double r4728361 = sqrt(r4728360);
        double r4728362 = r4728356 * r4728361;
        double r4728363 = r4728348 / r4728362;
        return r4728363;
}
↓
double f(double v) {
        double r4728364 = atan2(1.0, 0.0);
        double r4728365 = r4728364 * r4728364;
        double r4728366 = v;
        double r4728367 = r4728364 * r4728366;
        double r4728368 = r4728367 * r4728366;
        double r4728369 = r4728368 * r4728368;
        double r4728370 = r4728364 * r4728368;
        double r4728371 = r4728369 + r4728370;
        double r4728372 = r4728365 + r4728371;
        double r4728373 = 1.3333333333333333;
        double r4728374 = r4728365 * r4728364;
        double r4728375 = r4728366 * r4728366;
        double r4728376 = r4728375 * r4728375;
        double r4728377 = r4728374 * r4728376;
        double r4728378 = r4728377 * r4728375;
        double r4728379 = r4728374 - r4728378;
        double r4728380 = r4728373 / r4728379;
        double r4728381 = r4728372 * r4728380;
        double r4728382 = 2.0;
        double r4728383 = -6.0;
        double r4728384 = r4728375 * r4728383;
        double r4728385 = r4728382 + r4728384;
        double r4728386 = sqrt(r4728385);
        double r4728387 = r4728381 / r4728386;
        return r4728387;
}

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

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

  4. Applied flip3--0.0

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

  5. Applied associate-/r/0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))