Average Error: 1.0 → 0.0
Time: 14.6s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r271438 = 4.0;
        double r271439 = 3.0;
        double r271440 = atan2(1.0, 0.0);
        double r271441 = r271439 * r271440;
        double r271442 = 1.0;
        double r271443 = v;
        double r271444 = r271443 * r271443;
        double r271445 = r271442 - r271444;
        double r271446 = r271441 * r271445;
        double r271447 = 2.0;
        double r271448 = 6.0;
        double r271449 = r271448 * r271444;
        double r271450 = r271447 - r271449;
        double r271451 = sqrt(r271450);
        double r271452 = r271446 * r271451;
        double r271453 = r271438 / r271452;
        return r271453;
}
↓
double f(double v) {
        double r271454 = 4.0;
        double r271455 = sqrt(r271454);
        double r271456 = 3.0;
        double r271457 = atan2(1.0, 0.0);
        double r271458 = r271456 * r271457;
        double r271459 = 1.0;
        double r271460 = v;
        double r271461 = r271460 * r271460;
        double r271462 = r271459 - r271461;
        double r271463 = r271458 * r271462;
        double r271464 = r271455 / r271463;
        double r271465 = 2.0;
        double r271466 = 6.0;
        double r271467 = r271466 * r271461;
        double r271468 = r271465 - r271467;
        double r271469 = sqrt(r271468);
        double r271470 = r271455 / r271469;
        double r271471 = r271464 * r271470;
        return r271471;
}

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 add-sqr-sqrt1.0

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

  4. Applied times-frac0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))