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

Average Error: 0.1 → 0.1

Time: 19.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r191359 = x;
        double r191360 = 0.5;
        double r191361 = r191359 * r191360;
        double r191362 = y;
        double r191363 = 1.0;
        double r191364 = z;
        double r191365 = r191363 - r191364;
        double r191366 = log(r191364);
        double r191367 = r191365 + r191366;
        double r191368 = r191362 * r191367;
        double r191369 = r191361 + r191368;
        return r191369;
}

↓

double f(double x, double y, double z) {
        double r191370 = x;
        double r191371 = 0.5;
        double r191372 = y;
        double r191373 = 1.0;
        double r191374 = z;
        double r191375 = r191373 - r191374;
        double r191376 = log(r191374);
        double r191377 = r191375 + r191376;
        double r191378 = r191372 * r191377;
        double r191379 = fma(r191370, r191371, r191378);
        return r191379;
}

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

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

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

  (+ (* x 0.5) (* y (+ (- 1 z) (log z)))))