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

Average Error: 0.1 → 0.1

Time: 6.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r390150 = x;
        double r390151 = 0.5;
        double r390152 = r390150 * r390151;
        double r390153 = y;
        double r390154 = 1.0;
        double r390155 = z;
        double r390156 = r390154 - r390155;
        double r390157 = log(r390155);
        double r390158 = r390156 + r390157;
        double r390159 = r390153 * r390158;
        double r390160 = r390152 + r390159;
        return r390160;
}

↓

double f(double x, double y, double z) {
        double r390161 = x;
        double r390162 = 0.5;
        double r390163 = r390161 * r390162;
        double r390164 = y;
        double r390165 = 1.0;
        double r390166 = z;
        double r390167 = r390165 - r390166;
        double r390168 = log(r390166);
        double r390169 = r390167 + r390168;
        double r390170 = r390164 * r390169;
        double r390171 = r390163 + r390170;
        return r390171;
}

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. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019362 
(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)))))