System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2

Average Error: 0.1 → 0.1

Time: 26.1s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

↓

\[\mathsf{fma}\left(x, 0.5, y \cdot \left(1 - \left(z - \log z\right)\right)\right)\]

C

double f(double x, double y, double z) {
        double r18733586 = x;
        double r18733587 = 0.5;
        double r18733588 = r18733586 * r18733587;
        double r18733589 = y;
        double r18733590 = 1.0;
        double r18733591 = z;
        double r18733592 = r18733590 - r18733591;
        double r18733593 = log(r18733591);
        double r18733594 = r18733592 + r18733593;
        double r18733595 = r18733589 * r18733594;
        double r18733596 = r18733588 + r18733595;
        return r18733596;
}

↓

double f(double x, double y, double z) {
        double r18733597 = x;
        double r18733598 = 0.5;
        double r18733599 = y;
        double r18733600 = 1.0;
        double r18733601 = z;
        double r18733602 = log(r18733601);
        double r18733603 = r18733601 - r18733602;
        double r18733604 = r18733600 - r18733603;
        double r18733605 = r18733599 * r18733604;
        double r18733606 = fma(r18733597, r18733598, r18733605);
        return r18733606;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

1. Initial program 0.1

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.5, \left(1 - \left(z - \log z\right)\right) \cdot y\right)}\]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(x, 0.5, y \cdot \left(1 - \left(z - \log z\right)\right)\right)\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))