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

Average Error: 0.1 → 0.1

Time: 18.7s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r13676548 = x;
        double r13676549 = 0.5;
        double r13676550 = r13676548 * r13676549;
        double r13676551 = y;
        double r13676552 = 1.0;
        double r13676553 = z;
        double r13676554 = r13676552 - r13676553;
        double r13676555 = log(r13676553);
        double r13676556 = r13676554 + r13676555;
        double r13676557 = r13676551 * r13676556;
        double r13676558 = r13676550 + r13676557;
        return r13676558;
}

↓

double f(double x, double y, double z) {
        double r13676559 = y;
        double r13676560 = z;
        double r13676561 = log(r13676560);
        double r13676562 = r13676559 * r13676561;
        double r13676563 = 1.0;
        double r13676564 = r13676563 - r13676560;
        double r13676565 = r13676564 * r13676559;
        double r13676566 = r13676562 + r13676565;
        double r13676567 = x;
        double r13676568 = 0.5;
        double r13676569 = r13676567 * r13676568;
        double r13676570 = r13676566 + r13676569;
        return r13676570;
}

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. Using strategy rm

3. Applied distribute-rgt-in 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019179 
(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)))))