Average Error: 1.0 → 0.0
Time: 15.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 + \log \left(e^{-6 \cdot \left(v \cdot v\right)}\right)}}\]
\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}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 + \log \left(e^{-6 \cdot \left(v \cdot v\right)}\right)}}
double f(double v) {
        double r4905447 = 4.0;
        double r4905448 = 3.0;
        double r4905449 = atan2(1.0, 0.0);
        double r4905450 = r4905448 * r4905449;
        double r4905451 = 1.0;
        double r4905452 = v;
        double r4905453 = r4905452 * r4905452;
        double r4905454 = r4905451 - r4905453;
        double r4905455 = r4905450 * r4905454;
        double r4905456 = 2.0;
        double r4905457 = 6.0;
        double r4905458 = r4905457 * r4905453;
        double r4905459 = r4905456 - r4905458;
        double r4905460 = sqrt(r4905459);
        double r4905461 = r4905455 * r4905460;
        double r4905462 = r4905447 / r4905461;
        return r4905462;
}
↓
double f(double v) {
        double r4905463 = 1.3333333333333333;
        double r4905464 = atan2(1.0, 0.0);
        double r4905465 = v;
        double r4905466 = r4905465 * r4905464;
        double r4905467 = r4905465 * r4905466;
        double r4905468 = r4905464 - r4905467;
        double r4905469 = r4905463 / r4905468;
        double r4905470 = 2.0;
        double r4905471 = -6.0;
        double r4905472 = r4905465 * r4905465;
        double r4905473 = r4905471 * r4905472;
        double r4905474 = exp(r4905473);
        double r4905475 = log(r4905474);
        double r4905476 = r4905470 + r4905475;
        double r4905477 = sqrt(r4905476);
        double r4905478 = r4905469 / r4905477;
        return r4905478;
}

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 add-log-exp0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))