Average Error: 1.0 → 0.0
Time: 11.6s
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 r115415 = 4.0;
        double r115416 = 3.0;
        double r115417 = atan2(1.0, 0.0);
        double r115418 = r115416 * r115417;
        double r115419 = 1.0;
        double r115420 = v;
        double r115421 = r115420 * r115420;
        double r115422 = r115419 - r115421;
        double r115423 = r115418 * r115422;
        double r115424 = 2.0;
        double r115425 = 6.0;
        double r115426 = r115425 * r115421;
        double r115427 = r115424 - r115426;
        double r115428 = sqrt(r115427);
        double r115429 = r115423 * r115428;
        double r115430 = r115415 / r115429;
        return r115430;
}
↓
double f(double v) {
        double r115431 = 4.0;
        double r115432 = 3.0;
        double r115433 = atan2(1.0, 0.0);
        double r115434 = r115432 * r115433;
        double r115435 = 1.0;
        double r115436 = v;
        double r115437 = r115436 * r115436;
        double r115438 = r115435 - r115437;
        double r115439 = r115434 * r115438;
        double r115440 = r115431 / r115439;
        double r115441 = 2.0;
        double r115442 = 6.0;
        double r115443 = r115442 * r115437;
        double r115444 = r115441 - r115443;
        double r115445 = sqrt(r115444);
        double r115446 = r115440 / r115445;
        return r115446;
}

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 2019306 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))