Average Error: 1.0 → 0.0
Time: 4.5s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{1}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{1}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r206341 = 4.0;
        double r206342 = 3.0;
        double r206343 = atan2(1.0, 0.0);
        double r206344 = r206342 * r206343;
        double r206345 = 1.0;
        double r206346 = v;
        double r206347 = r206346 * r206346;
        double r206348 = r206345 - r206347;
        double r206349 = r206344 * r206348;
        double r206350 = 2.0;
        double r206351 = 6.0;
        double r206352 = r206351 * r206347;
        double r206353 = r206350 - r206352;
        double r206354 = sqrt(r206353);
        double r206355 = r206349 * r206354;
        double r206356 = r206341 / r206355;
        return r206356;
}
↓
double f(double v) {
        double r206357 = 1.0;
        double r206358 = 3.0;
        double r206359 = atan2(1.0, 0.0);
        double r206360 = r206358 * r206359;
        double r206361 = 1.0;
        double r206362 = v;
        double r206363 = r206362 * r206362;
        double r206364 = r206361 - r206363;
        double r206365 = r206360 * r206364;
        double r206366 = r206357 / r206365;
        double r206367 = 4.0;
        double r206368 = 2.0;
        double r206369 = 6.0;
        double r206370 = r206369 * r206363;
        double r206371 = r206368 - r206370;
        double r206372 = sqrt(r206371);
        double r206373 = r206367 / r206372;
        double r206374 = r206366 * r206373;
        return r206374;
}

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. Using strategy rm

  3. Applied *-un-lft-identity1.0

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

  4. Applied times-frac0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020056 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))