Average Error: 1.0 → 0.0
Time: 8.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
\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}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}
double f(double v) {
        double r2615482 = 4.0;
        double r2615483 = 3.0;
        double r2615484 = atan2(1.0, 0.0);
        double r2615485 = r2615483 * r2615484;
        double r2615486 = 1.0;
        double r2615487 = v;
        double r2615488 = r2615487 * r2615487;
        double r2615489 = r2615486 - r2615488;
        double r2615490 = r2615485 * r2615489;
        double r2615491 = 2.0;
        double r2615492 = 6.0;
        double r2615493 = r2615492 * r2615488;
        double r2615494 = r2615491 - r2615493;
        double r2615495 = sqrt(r2615494);
        double r2615496 = r2615490 * r2615495;
        double r2615497 = r2615482 / r2615496;
        return r2615497;
}
↓
double f(double v) {
        double r2615498 = 1.3333333333333333;
        double r2615499 = atan2(1.0, 0.0);
        double r2615500 = v;
        double r2615501 = r2615500 * r2615499;
        double r2615502 = r2615500 * r2615501;
        double r2615503 = r2615499 - r2615502;
        double r2615504 = r2615498 / r2615503;
        double r2615505 = 2.0;
        double r2615506 = r2615500 * r2615500;
        double r2615507 = 6.0;
        double r2615508 = r2615506 * r2615507;
        double r2615509 = r2615505 - r2615508;
        double r2615510 = sqrt(r2615509);
        double r2615511 = r2615504 / r2615510;
        return r2615511;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019152 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))