Average Error: 1.0 → 0.0
Time: 18.8s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{1}{\frac{\pi - \left(v \cdot v\right) \cdot \pi}{\frac{4}{3}}}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}\]
\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{1}{\frac{\pi - \left(v \cdot v\right) \cdot \pi}{\frac{4}{3}}}}{\sqrt{-6 \cdot \left(v \cdot v\right) + 2}}
double f(double v) {
        double r5497474 = 4.0;
        double r5497475 = 3.0;
        double r5497476 = atan2(1.0, 0.0);
        double r5497477 = r5497475 * r5497476;
        double r5497478 = 1.0;
        double r5497479 = v;
        double r5497480 = r5497479 * r5497479;
        double r5497481 = r5497478 - r5497480;
        double r5497482 = r5497477 * r5497481;
        double r5497483 = 2.0;
        double r5497484 = 6.0;
        double r5497485 = r5497484 * r5497480;
        double r5497486 = r5497483 - r5497485;
        double r5497487 = sqrt(r5497486);
        double r5497488 = r5497482 * r5497487;
        double r5497489 = r5497474 / r5497488;
        return r5497489;
}
↓
double f(double v) {
        double r5497490 = 1.0;
        double r5497491 = atan2(1.0, 0.0);
        double r5497492 = v;
        double r5497493 = r5497492 * r5497492;
        double r5497494 = r5497493 * r5497491;
        double r5497495 = r5497491 - r5497494;
        double r5497496 = 1.3333333333333333;
        double r5497497 = r5497495 / r5497496;
        double r5497498 = r5497490 / r5497497;
        double r5497499 = -6.0;
        double r5497500 = r5497499 * r5497493;
        double r5497501 = 2.0;
        double r5497502 = r5497500 + r5497501;
        double r5497503 = sqrt(r5497502);
        double r5497504 = r5497498 / r5497503;
        return r5497504;
}

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

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

  4. Applied clear-num0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))