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

Average Error: 0.1 → 0.1

Time: 7.6s

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 r310876 = x;
        double r310877 = 0.5;
        double r310878 = r310876 * r310877;
        double r310879 = y;
        double r310880 = 1.0;
        double r310881 = z;
        double r310882 = r310880 - r310881;
        double r310883 = log(r310881);
        double r310884 = r310882 + r310883;
        double r310885 = r310879 * r310884;
        double r310886 = r310878 + r310885;
        return r310886;
}

↓

double f(double x, double y, double z) {
        double r310887 = x;
        double r310888 = 0.5;
        double r310889 = r310887 * r310888;
        double r310890 = y;
        double r310891 = 1.0;
        double r310892 = z;
        double r310893 = r310891 - r310892;
        double r310894 = log(r310892);
        double r310895 = r310893 + r310894;
        double r310896 = r310890 * r310895;
        double r310897 = r310889 + r310896;
        return r310897;
}

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 2020049 
(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)))))