Average Error: 1.0 → 0.0
Time: 9.1s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{1}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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 r207246 = 4.0;
        double r207247 = 3.0;
        double r207248 = atan2(1.0, 0.0);
        double r207249 = r207247 * r207248;
        double r207250 = 1.0;
        double r207251 = v;
        double r207252 = r207251 * r207251;
        double r207253 = r207250 - r207252;
        double r207254 = r207249 * r207253;
        double r207255 = 2.0;
        double r207256 = 6.0;
        double r207257 = r207256 * r207252;
        double r207258 = r207255 - r207257;
        double r207259 = sqrt(r207258);
        double r207260 = r207254 * r207259;
        double r207261 = r207246 / r207260;
        return r207261;
}
↓
double f(double v) {
        double r207262 = 1.0;
        double r207263 = 3.0;
        double r207264 = atan2(1.0, 0.0);
        double r207265 = r207263 * r207264;
        double r207266 = 1.0;
        double r207267 = v;
        double r207268 = r207267 * r207267;
        double r207269 = r207266 - r207268;
        double r207270 = r207265 * r207269;
        double r207271 = r207262 / r207270;
        double r207272 = 4.0;
        double r207273 = 2.0;
        double r207274 = 6.0;
        double r207275 = r207274 * r207268;
        double r207276 = r207273 - r207275;
        double r207277 = sqrt(r207276);
        double r207278 = r207272 / r207277;
        double r207279 = r207271 * r207278;
        return r207279;
}

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 2020042 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))