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

Average Error: 0.1 → 0.1

Time: 16.2s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

↓

\[\mathsf{fma}\left(y, \left(1.0 + \log z\right) - z, 0.5 \cdot x\right)\]

C

double f(double x, double y, double z) {
        double r4857394 = x;
        double r4857395 = 0.5;
        double r4857396 = r4857394 * r4857395;
        double r4857397 = y;
        double r4857398 = 1.0;
        double r4857399 = z;
        double r4857400 = r4857398 - r4857399;
        double r4857401 = log(r4857399);
        double r4857402 = r4857400 + r4857401;
        double r4857403 = r4857397 * r4857402;
        double r4857404 = r4857396 + r4857403;
        return r4857404;
}

↓

double f(double x, double y, double z) {
        double r4857405 = y;
        double r4857406 = 1.0;
        double r4857407 = z;
        double r4857408 = log(r4857407);
        double r4857409 = r4857406 + r4857408;
        double r4857410 = r4857409 - r4857407;
        double r4857411 = 0.5;
        double r4857412 = x;
        double r4857413 = r4857411 * r4857412;
        double r4857414 = fma(r4857405, r4857410, r4857413);
        return r4857414;
}

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

   \[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(1.0 + \log z\right) - z, x \cdot 0.5\right)}\]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(y, \left(1.0 + \log z\right) - z, 0.5 \cdot x\right)\]

Reproduce

herbie shell --seed 2019156 +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)))))