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

Average Error: 0.1 → 0.1

Time: 34.4s

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 r40654928 = x;
        double r40654929 = 0.5;
        double r40654930 = r40654928 * r40654929;
        double r40654931 = y;
        double r40654932 = 1.0;
        double r40654933 = z;
        double r40654934 = r40654932 - r40654933;
        double r40654935 = log(r40654933);
        double r40654936 = r40654934 + r40654935;
        double r40654937 = r40654931 * r40654936;
        double r40654938 = r40654930 + r40654937;
        return r40654938;
}

↓

double f(double x, double y, double z) {
        double r40654939 = x;
        double r40654940 = 0.5;
        double r40654941 = y;
        double r40654942 = 1.0;
        double r40654943 = z;
        double r40654944 = r40654942 - r40654943;
        double r40654945 = log(r40654943);
        double r40654946 = r40654944 + r40654945;
        double r40654947 = r40654941 * r40654946;
        double r40654948 = fma(r40654939, r40654940, r40654947);
        return r40654948;
}

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 2019173 +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)))))