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

Average Error: 0.1 → 0.1

Time: 8.0s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

↓

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

C

double f(double x, double y, double z) {
        double r313880 = x;
        double r313881 = 0.5;
        double r313882 = r313880 * r313881;
        double r313883 = y;
        double r313884 = 1.0;
        double r313885 = z;
        double r313886 = r313884 - r313885;
        double r313887 = log(r313885);
        double r313888 = r313886 + r313887;
        double r313889 = r313883 * r313888;
        double r313890 = r313882 + r313889;
        return r313890;
}

↓

double f(double x, double y, double z) {
        double r313891 = x;
        double r313892 = 0.5;
        double r313893 = r313891 * r313892;
        double r313894 = y;
        double r313895 = 1.0;
        double r313896 = z;
        double r313897 = r313895 - r313896;
        double r313898 = log(r313896);
        double r313899 = r313897 + r313898;
        double r313900 = r313894 * r313899;
        double r313901 = r313893 + r313900;
        return r313901;
}

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. Final simplification 0.1

   \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

Reproduce

herbie shell --seed 2020001 
(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)))))