Average Error: 1.0 → 0.0
Time: 13.0s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r7818371 = 4.0;
        double r7818372 = 3.0;
        double r7818373 = atan2(1.0, 0.0);
        double r7818374 = r7818372 * r7818373;
        double r7818375 = 1.0;
        double r7818376 = v;
        double r7818377 = r7818376 * r7818376;
        double r7818378 = r7818375 - r7818377;
        double r7818379 = r7818374 * r7818378;
        double r7818380 = 2.0;
        double r7818381 = 6.0;
        double r7818382 = r7818381 * r7818377;
        double r7818383 = r7818380 - r7818382;
        double r7818384 = sqrt(r7818383);
        double r7818385 = r7818379 * r7818384;
        double r7818386 = r7818371 / r7818385;
        return r7818386;
}
↓
double f(double v) {
        double r7818387 = 4.0;
        double r7818388 = atan2(1.0, 0.0);
        double r7818389 = 3.0;
        double r7818390 = r7818388 * r7818389;
        double r7818391 = 1.0;
        double r7818392 = v;
        double r7818393 = r7818392 * r7818392;
        double r7818394 = r7818391 - r7818393;
        double r7818395 = r7818390 * r7818394;
        double r7818396 = r7818387 / r7818395;
        double r7818397 = 2.0;
        double r7818398 = 6.0;
        double r7818399 = r7818398 * r7818393;
        double r7818400 = r7818397 - r7818399;
        double r7818401 = sqrt(r7818400);
        double r7818402 = r7818396 / r7818401;
        return r7818402;
}

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

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

Reproduce

herbie shell --seed 2019172 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))