Average Error: 1.0 → 0.0
Time: 14.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{3}}{\pi \cdot \left(1 - v \cdot v\right)}\]
\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{\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}{3}}{\pi \cdot \left(1 - v \cdot v\right)}
double f(double v) {
        double r248550 = 4.0;
        double r248551 = 3.0;
        double r248552 = atan2(1.0, 0.0);
        double r248553 = r248551 * r248552;
        double r248554 = 1.0;
        double r248555 = v;
        double r248556 = r248555 * r248555;
        double r248557 = r248554 - r248556;
        double r248558 = r248553 * r248557;
        double r248559 = 2.0;
        double r248560 = 6.0;
        double r248561 = r248560 * r248556;
        double r248562 = r248559 - r248561;
        double r248563 = sqrt(r248562);
        double r248564 = r248558 * r248563;
        double r248565 = r248550 / r248564;
        return r248565;
}
↓
double f(double v) {
        double r248566 = 4.0;
        double r248567 = 2.0;
        double r248568 = 6.0;
        double r248569 = v;
        double r248570 = r248569 * r248569;
        double r248571 = r248568 * r248570;
        double r248572 = r248567 - r248571;
        double r248573 = sqrt(r248572);
        double r248574 = r248566 / r248573;
        double r248575 = 3.0;
        double r248576 = r248574 / r248575;
        double r248577 = atan2(1.0, 0.0);
        double r248578 = 1.0;
        double r248579 = r248578 - r248570;
        double r248580 = r248577 * r248579;
        double r248581 = r248576 / r248580;
        return r248581;
}

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 *-un-lft-identity1.0

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

  4. Applied times-frac0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019291 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))