Average Error: 1.0 → 0.0
Time: 5.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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 r291377 = 4.0;
        double r291378 = 3.0;
        double r291379 = atan2(1.0, 0.0);
        double r291380 = r291378 * r291379;
        double r291381 = 1.0;
        double r291382 = v;
        double r291383 = r291382 * r291382;
        double r291384 = r291381 - r291383;
        double r291385 = r291380 * r291384;
        double r291386 = 2.0;
        double r291387 = 6.0;
        double r291388 = r291387 * r291383;
        double r291389 = r291386 - r291388;
        double r291390 = sqrt(r291389);
        double r291391 = r291385 * r291390;
        double r291392 = r291377 / r291391;
        return r291392;
}
↓
double f(double v) {
        double r291393 = 4.0;
        double r291394 = 3.0;
        double r291395 = atan2(1.0, 0.0);
        double r291396 = r291394 * r291395;
        double r291397 = 1.0;
        double r291398 = v;
        double r291399 = r291398 * r291398;
        double r291400 = r291397 - r291399;
        double r291401 = r291396 * r291400;
        double r291402 = r291393 / r291401;
        double r291403 = 2.0;
        double r291404 = 6.0;
        double r291405 = r291404 * r291399;
        double r291406 = r291403 - r291405;
        double r291407 = sqrt(r291406);
        double r291408 = r291402 / r291407;
        return r291408;
}

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)))))))