Average Error: 1.0 → 0.0
Time: 5.5s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\frac{4}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r292263 = 4.0;
        double r292264 = 3.0;
        double r292265 = atan2(1.0, 0.0);
        double r292266 = r292264 * r292265;
        double r292267 = 1.0;
        double r292268 = v;
        double r292269 = r292268 * r292268;
        double r292270 = r292267 - r292269;
        double r292271 = r292266 * r292270;
        double r292272 = 2.0;
        double r292273 = 6.0;
        double r292274 = r292273 * r292269;
        double r292275 = r292272 - r292274;
        double r292276 = sqrt(r292275);
        double r292277 = r292271 * r292276;
        double r292278 = r292263 / r292277;
        return r292278;
}
↓
double f(double v) {
        double r292279 = 4.0;
        double r292280 = 3.0;
        double r292281 = atan2(1.0, 0.0);
        double r292282 = r292280 * r292281;
        double r292283 = 1.0;
        double r292284 = v;
        double r292285 = r292284 * r292284;
        double r292286 = r292283 - r292285;
        double r292287 = r292282 * r292286;
        double r292288 = r292279 / r292287;
        double r292289 = 2.0;
        double r292290 = 6.0;
        double r292291 = r292290 * r292285;
        double r292292 = r292289 - r292291;
        double r292293 = sqrt(r292292);
        double r292294 = r292288 / r292293;
        return r292294;
}

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 associate-/r*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))