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

Average Error: 0.1 → 0.1

Time: 8.4s

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 r338716 = x;
        double r338717 = 0.5;
        double r338718 = r338716 * r338717;
        double r338719 = y;
        double r338720 = 1.0;
        double r338721 = z;
        double r338722 = r338720 - r338721;
        double r338723 = log(r338721);
        double r338724 = r338722 + r338723;
        double r338725 = r338719 * r338724;
        double r338726 = r338718 + r338725;
        return r338726;
}

↓

double f(double x, double y, double z) {
        double r338727 = x;
        double r338728 = 0.5;
        double r338729 = r338727 * r338728;
        double r338730 = y;
        double r338731 = 1.0;
        double r338732 = z;
        double r338733 = r338731 - r338732;
        double r338734 = log(r338732);
        double r338735 = r338733 + r338734;
        double r338736 = r338730 * r338735;
        double r338737 = r338729 + r338736;
        return r338737;
}

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 2020001 
(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)))))