Average Error: 1.0 → 0.0
Time: 9.8s
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 r293460 = 4.0;
        double r293461 = 3.0;
        double r293462 = atan2(1.0, 0.0);
        double r293463 = r293461 * r293462;
        double r293464 = 1.0;
        double r293465 = v;
        double r293466 = r293465 * r293465;
        double r293467 = r293464 - r293466;
        double r293468 = r293463 * r293467;
        double r293469 = 2.0;
        double r293470 = 6.0;
        double r293471 = r293470 * r293466;
        double r293472 = r293469 - r293471;
        double r293473 = sqrt(r293472);
        double r293474 = r293468 * r293473;
        double r293475 = r293460 / r293474;
        return r293475;
}
↓
double f(double v) {
        double r293476 = 4.0;
        double r293477 = sqrt(r293476);
        double r293478 = 3.0;
        double r293479 = atan2(1.0, 0.0);
        double r293480 = r293478 * r293479;
        double r293481 = 1.0;
        double r293482 = v;
        double r293483 = r293482 * r293482;
        double r293484 = r293481 - r293483;
        double r293485 = r293480 * r293484;
        double r293486 = r293477 / r293485;
        double r293487 = 2.0;
        double r293488 = 6.0;
        double r293489 = r293488 * r293483;
        double r293490 = r293487 - r293489;
        double r293491 = sqrt(r293490);
        double r293492 = r293477 / r293491;
        double r293493 = r293486 * r293492;
        return r293493;
}

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