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

Average Error: 0.1 → 0.1

Time: 17.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r246268 = x;
        double r246269 = 0.5;
        double r246270 = r246268 * r246269;
        double r246271 = y;
        double r246272 = 1.0;
        double r246273 = z;
        double r246274 = r246272 - r246273;
        double r246275 = log(r246273);
        double r246276 = r246274 + r246275;
        double r246277 = r246271 * r246276;
        double r246278 = r246270 + r246277;
        return r246278;
}

↓

double f(double x, double y, double z) {
        double r246279 = z;
        double r246280 = log(r246279);
        double r246281 = 1.0;
        double r246282 = r246281 - r246279;
        double r246283 = r246280 + r246282;
        double r246284 = y;
        double r246285 = r246283 * r246284;
        double r246286 = x;
        double r246287 = 0.5;
        double r246288 = r246286 * r246287;
        double r246289 = r246285 + r246288;
        return r246289;
}

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. Simplified 0.1

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))