Average Error: 1.0 → 0.0
Time: 3.3s
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 r184578 = 4.0;
        double r184579 = 3.0;
        double r184580 = atan2(1.0, 0.0);
        double r184581 = r184579 * r184580;
        double r184582 = 1.0;
        double r184583 = v;
        double r184584 = r184583 * r184583;
        double r184585 = r184582 - r184584;
        double r184586 = r184581 * r184585;
        double r184587 = 2.0;
        double r184588 = 6.0;
        double r184589 = r184588 * r184584;
        double r184590 = r184587 - r184589;
        double r184591 = sqrt(r184590);
        double r184592 = r184586 * r184591;
        double r184593 = r184578 / r184592;
        return r184593;
}
↓
double f(double v) {
        double r184594 = 4.0;
        double r184595 = 3.0;
        double r184596 = atan2(1.0, 0.0);
        double r184597 = r184595 * r184596;
        double r184598 = 1.0;
        double r184599 = v;
        double r184600 = r184599 * r184599;
        double r184601 = r184598 - r184600;
        double r184602 = r184597 * r184601;
        double r184603 = r184594 / r184602;
        double r184604 = 2.0;
        double r184605 = 6.0;
        double r184606 = r184605 * r184600;
        double r184607 = r184604 - r184606;
        double r184608 = sqrt(r184607);
        double r184609 = r184603 / r184608;
        return r184609;
}

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 2020035 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))