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

Average Error: 0.1 → 0.1

Time: 5.8s

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 r282175 = x;
        double r282176 = 0.5;
        double r282177 = r282175 * r282176;
        double r282178 = y;
        double r282179 = 1.0;
        double r282180 = z;
        double r282181 = r282179 - r282180;
        double r282182 = log(r282180);
        double r282183 = r282181 + r282182;
        double r282184 = r282178 * r282183;
        double r282185 = r282177 + r282184;
        return r282185;
}

↓

double f(double x, double y, double z) {
        double r282186 = x;
        double r282187 = 0.5;
        double r282188 = r282186 * r282187;
        double r282189 = y;
        double r282190 = 1.0;
        double r282191 = z;
        double r282192 = r282190 - r282191;
        double r282193 = log(r282191);
        double r282194 = r282192 + r282193;
        double r282195 = r282189 * r282194;
        double r282196 = r282188 + r282195;
        return r282196;
}

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 2020034 
(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)))))