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

Average Error: 0.1 → 0.1

Time: 8.7s

Precision: 64

Math

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

↓

\[x \cdot \frac{1}{2} + y \cdot \left(\left(1 - z\right) + \log z\right)\]

C

double f(double x, double y, double z) {
        double r177523 = x;
        double r177524 = 0.5;
        double r177525 = r177523 * r177524;
        double r177526 = y;
        double r177527 = 1.0;
        double r177528 = z;
        double r177529 = r177527 - r177528;
        double r177530 = log(r177528);
        double r177531 = r177529 + r177530;
        double r177532 = r177526 * r177531;
        double r177533 = r177525 + r177532;
        return r177533;
}

↓

double f(double x, double y, double z) {
        double r177534 = x;
        double r177535 = 1.0;
        double r177536 = 2.0;
        double r177537 = r177535 / r177536;
        double r177538 = r177534 * r177537;
        double r177539 = y;
        double r177540 = z;
        double r177541 = r177535 - r177540;
        double r177542 = log(r177540);
        double r177543 = r177541 + r177542;
        double r177544 = r177539 * r177543;
        double r177545 = r177538 + r177544;
        return r177545;
}

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

   \[\leadsto \color{blue}{x \cdot \frac{1}{2} + y \cdot \left(\left(1 - z\right) + \log z\right)}\]

3. Final simplification 0.1

   \[\leadsto x \cdot \frac{1}{2} + y \cdot \left(\left(1 - z\right) + \log z\right)\]

Reproduce

herbie shell --seed 2019304 
(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)))))