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

Average Error: 0.1 → 0.1

Time: 30.8s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r16829230 = x;
        double r16829231 = 0.5;
        double r16829232 = r16829230 * r16829231;
        double r16829233 = y;
        double r16829234 = 1.0;
        double r16829235 = z;
        double r16829236 = r16829234 - r16829235;
        double r16829237 = log(r16829235);
        double r16829238 = r16829236 + r16829237;
        double r16829239 = r16829233 * r16829238;
        double r16829240 = r16829232 + r16829239;
        return r16829240;
}

↓

double f(double x, double y, double z) {
        double r16829241 = x;
        double r16829242 = 0.5;
        double r16829243 = y;
        double r16829244 = 1.0;
        double r16829245 = z;
        double r16829246 = log(r16829245);
        double r16829247 = r16829245 - r16829246;
        double r16829248 = r16829244 - r16829247;
        double r16829249 = r16829243 * r16829248;
        double r16829250 = fma(r16829241, r16829242, r16829249);
        return r16829250;
}

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

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019163 +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)))))