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

Average Error: 0.1 → 0.1

Time: 14.9s

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 r197050 = x;
        double r197051 = 0.5;
        double r197052 = r197050 * r197051;
        double r197053 = y;
        double r197054 = 1.0;
        double r197055 = z;
        double r197056 = r197054 - r197055;
        double r197057 = log(r197055);
        double r197058 = r197056 + r197057;
        double r197059 = r197053 * r197058;
        double r197060 = r197052 + r197059;
        return r197060;
}

↓

double f(double x, double y, double z) {
        double r197061 = z;
        double r197062 = log(r197061);
        double r197063 = 1.0;
        double r197064 = r197063 - r197061;
        double r197065 = r197062 + r197064;
        double r197066 = y;
        double r197067 = r197065 * r197066;
        double r197068 = x;
        double r197069 = 0.5;
        double r197070 = r197068 * r197069;
        double r197071 = r197067 + r197070;
        return r197071;
}

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 2019195 
(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)))))