Average Error: 1.0 → 0.0
Time: 25.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi \cdot \pi - \left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right)}}{\frac{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}{\pi + \pi \cdot \left(v \cdot v\right)}}\]
\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 \cdot \pi - \left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right)}}{\frac{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}{\pi + \pi \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r4925261 = 4.0;
        double r4925262 = 3.0;
        double r4925263 = atan2(1.0, 0.0);
        double r4925264 = r4925262 * r4925263;
        double r4925265 = 1.0;
        double r4925266 = v;
        double r4925267 = r4925266 * r4925266;
        double r4925268 = r4925265 - r4925267;
        double r4925269 = r4925264 * r4925268;
        double r4925270 = 2.0;
        double r4925271 = 6.0;
        double r4925272 = r4925271 * r4925267;
        double r4925273 = r4925270 - r4925272;
        double r4925274 = sqrt(r4925273);
        double r4925275 = r4925269 * r4925274;
        double r4925276 = r4925261 / r4925275;
        return r4925276;
}
↓
double f(double v) {
        double r4925277 = 1.3333333333333333;
        double r4925278 = atan2(1.0, 0.0);
        double r4925279 = r4925278 * r4925278;
        double r4925280 = v;
        double r4925281 = r4925280 * r4925280;
        double r4925282 = r4925278 * r4925281;
        double r4925283 = r4925282 * r4925282;
        double r4925284 = r4925279 - r4925283;
        double r4925285 = r4925277 / r4925284;
        double r4925286 = 2.0;
        double r4925287 = 6.0;
        double r4925288 = r4925281 * r4925287;
        double r4925289 = r4925286 - r4925288;
        double r4925290 = sqrt(r4925289);
        double r4925291 = r4925278 + r4925282;
        double r4925292 = r4925290 / r4925291;
        double r4925293 = r4925285 / r4925292;
        return r4925293;
}

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

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

  4. Applied flip--0.0

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

  5. Applied associate-/r/0.0

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

  6. Applied associate-/l*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019138 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))