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

Average Error: 0.1 → 0.1

Time: 16.5s

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 r244837 = x;
        double r244838 = 0.5;
        double r244839 = r244837 * r244838;
        double r244840 = y;
        double r244841 = 1.0;
        double r244842 = z;
        double r244843 = r244841 - r244842;
        double r244844 = log(r244842);
        double r244845 = r244843 + r244844;
        double r244846 = r244840 * r244845;
        double r244847 = r244839 + r244846;
        return r244847;
}

↓

double f(double x, double y, double z) {
        double r244848 = x;
        double r244849 = 0.5;
        double r244850 = r244848 * r244849;
        double r244851 = y;
        double r244852 = 1.0;
        double r244853 = z;
        double r244854 = r244852 - r244853;
        double r244855 = log(r244853);
        double r244856 = r244854 + r244855;
        double r244857 = r244851 * r244856;
        double r244858 = r244850 + r244857;
        return r244858;
}

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 2019291 
(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)))))