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

Average Error: 0.1 → 0.1

Time: 8.3s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r370927 = x;
        double r370928 = 0.5;
        double r370929 = r370927 * r370928;
        double r370930 = y;
        double r370931 = 1.0;
        double r370932 = z;
        double r370933 = r370931 - r370932;
        double r370934 = log(r370932);
        double r370935 = r370933 + r370934;
        double r370936 = r370930 * r370935;
        double r370937 = r370929 + r370936;
        return r370937;
}

↓

double f(double x, double y, double z) {
        double r370938 = x;
        double r370939 = 0.5;
        double r370940 = r370938 * r370939;
        double r370941 = y;
        double r370942 = 1.0;
        double r370943 = z;
        double r370944 = r370942 - r370943;
        double r370945 = log(r370943);
        double r370946 = r370944 + r370945;
        double r370947 = r370941 * r370946;
        double r370948 = r370940 + r370947;
        return r370948;
}

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 2020046 
(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)))))