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

Average Error: 0.1 → 0.1

Time: 7.4s

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 r295471 = x;
        double r295472 = 0.5;
        double r295473 = r295471 * r295472;
        double r295474 = y;
        double r295475 = 1.0;
        double r295476 = z;
        double r295477 = r295475 - r295476;
        double r295478 = log(r295476);
        double r295479 = r295477 + r295478;
        double r295480 = r295474 * r295479;
        double r295481 = r295473 + r295480;
        return r295481;
}

↓

double f(double x, double y, double z) {
        double r295482 = x;
        double r295483 = 0.5;
        double r295484 = y;
        double r295485 = 1.0;
        double r295486 = z;
        double r295487 = r295485 - r295486;
        double r295488 = log(r295486);
        double r295489 = r295487 + r295488;
        double r295490 = r295484 * r295489;
        double r295491 = fma(r295482, r295483, r295490);
        return r295491;
}

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 2020001 +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)))))