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

Average Error: 0.1 → 0.1

Time: 5.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r304775 = x;
        double r304776 = 0.5;
        double r304777 = r304775 * r304776;
        double r304778 = y;
        double r304779 = 1.0;
        double r304780 = z;
        double r304781 = r304779 - r304780;
        double r304782 = log(r304780);
        double r304783 = r304781 + r304782;
        double r304784 = r304778 * r304783;
        double r304785 = r304777 + r304784;
        return r304785;
}

↓

double f(double x, double y, double z) {
        double r304786 = y;
        double r304787 = 1.0;
        double r304788 = z;
        double r304789 = r304787 - r304788;
        double r304790 = log(r304788);
        double r304791 = r304789 + r304790;
        double r304792 = r304786 * r304791;
        double r304793 = x;
        double r304794 = 0.5;
        double r304795 = r304793 * r304794;
        double r304796 = r304792 + r304795;
        return r304796;
}

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 +-commutative 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020083 
(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)))))