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

Average Error: 0.1 → 0.1

Time: 5.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r322678 = x;
        double r322679 = 0.5;
        double r322680 = r322678 * r322679;
        double r322681 = y;
        double r322682 = 1.0;
        double r322683 = z;
        double r322684 = r322682 - r322683;
        double r322685 = log(r322683);
        double r322686 = r322684 + r322685;
        double r322687 = r322681 * r322686;
        double r322688 = r322680 + r322687;
        return r322688;
}

↓

double f(double x, double y, double z) {
        double r322689 = x;
        double r322690 = 0.5;
        double r322691 = r322689 * r322690;
        double r322692 = y;
        double r322693 = 1.0;
        double r322694 = z;
        double r322695 = r322693 - r322694;
        double r322696 = log(r322694);
        double r322697 = r322695 + r322696;
        double r322698 = r322692 * r322697;
        double r322699 = r322691 + r322698;
        return r322699;
}

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 2020046 
(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)))))