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

Average Error: 0.1 → 0.1

Time: 27.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r17319109 = x;
        double r17319110 = 0.5;
        double r17319111 = r17319109 * r17319110;
        double r17319112 = y;
        double r17319113 = 1.0;
        double r17319114 = z;
        double r17319115 = r17319113 - r17319114;
        double r17319116 = log(r17319114);
        double r17319117 = r17319115 + r17319116;
        double r17319118 = r17319112 * r17319117;
        double r17319119 = r17319111 + r17319118;
        return r17319119;
}

↓

double f(double x, double y, double z) {
        double r17319120 = z;
        double r17319121 = log(r17319120);
        double r17319122 = 1.0;
        double r17319123 = r17319122 - r17319120;
        double r17319124 = r17319121 + r17319123;
        double r17319125 = y;
        double r17319126 = r17319124 * r17319125;
        double r17319127 = x;
        double r17319128 = 0.5;
        double r17319129 = r17319127 * r17319128;
        double r17319130 = r17319126 + r17319129;
        return r17319130;
}

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. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019163 
(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)))))