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

Average Error: 0.1 → 0.1

Time: 6.1s

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 r316924 = x;
        double r316925 = 0.5;
        double r316926 = r316924 * r316925;
        double r316927 = y;
        double r316928 = 1.0;
        double r316929 = z;
        double r316930 = r316928 - r316929;
        double r316931 = log(r316929);
        double r316932 = r316930 + r316931;
        double r316933 = r316927 * r316932;
        double r316934 = r316926 + r316933;
        return r316934;
}

↓

double f(double x, double y, double z) {
        double r316935 = x;
        double r316936 = 0.5;
        double r316937 = y;
        double r316938 = 1.0;
        double r316939 = z;
        double r316940 = r316938 - r316939;
        double r316941 = log(r316939);
        double r316942 = r316940 + r316941;
        double r316943 = r316937 * r316942;
        double r316944 = fma(r316935, r316936, r316943);
        return r316944;
}

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 2019362 +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)))))