Average Error: 1.0 → 0.0
Time: 3.9s
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 r241557 = 4.0;
        double r241558 = 3.0;
        double r241559 = atan2(1.0, 0.0);
        double r241560 = r241558 * r241559;
        double r241561 = 1.0;
        double r241562 = v;
        double r241563 = r241562 * r241562;
        double r241564 = r241561 - r241563;
        double r241565 = r241560 * r241564;
        double r241566 = 2.0;
        double r241567 = 6.0;
        double r241568 = r241567 * r241563;
        double r241569 = r241566 - r241568;
        double r241570 = sqrt(r241569);
        double r241571 = r241565 * r241570;
        double r241572 = r241557 / r241571;
        return r241572;
}
↓
double f(double v) {
        double r241573 = 4.0;
        double r241574 = sqrt(r241573);
        double r241575 = 3.0;
        double r241576 = atan2(1.0, 0.0);
        double r241577 = r241575 * r241576;
        double r241578 = 1.0;
        double r241579 = v;
        double r241580 = r241579 * r241579;
        double r241581 = r241578 - r241580;
        double r241582 = r241577 * r241581;
        double r241583 = r241574 / r241582;
        double r241584 = 2.0;
        double r241585 = 6.0;
        double r241586 = r241585 * r241580;
        double r241587 = r241584 - r241586;
        double r241588 = sqrt(r241587);
        double r241589 = r241574 / r241588;
        double r241590 = r241583 * r241589;
        return r241590;
}

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 2020024 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))