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

Average Error: 0.1 → 0.1

Time: 22.0s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

↓

\[\left(y \cdot \log z + \left(1.0 - z\right) \cdot y\right) + x \cdot 0.5\]

C

double f(double x, double y, double z) {
        double r16133002 = x;
        double r16133003 = 0.5;
        double r16133004 = r16133002 * r16133003;
        double r16133005 = y;
        double r16133006 = 1.0;
        double r16133007 = z;
        double r16133008 = r16133006 - r16133007;
        double r16133009 = log(r16133007);
        double r16133010 = r16133008 + r16133009;
        double r16133011 = r16133005 * r16133010;
        double r16133012 = r16133004 + r16133011;
        return r16133012;
}

↓

double f(double x, double y, double z) {
        double r16133013 = y;
        double r16133014 = z;
        double r16133015 = log(r16133014);
        double r16133016 = r16133013 * r16133015;
        double r16133017 = 1.0;
        double r16133018 = r16133017 - r16133014;
        double r16133019 = r16133018 * r16133013;
        double r16133020 = r16133016 + r16133019;
        double r16133021 = x;
        double r16133022 = 0.5;
        double r16133023 = r16133021 * r16133022;
        double r16133024 = r16133020 + r16133023;
        return r16133024;
}

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

   \[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]
2. Using strategy rm

3. Applied distribute-rgt-in 0.1

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(1.0 - z\right) \cdot y + \log z \cdot y\right)}\]

4. Final simplification 0.1

   \[\leadsto \left(y \cdot \log z + \left(1.0 - z\right) \cdot y\right) + x \cdot 0.5\]

Reproduce

herbie shell --seed 2019162 
(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)))))