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

Average Error: 0.1 → 0.1

Time: 12.6s

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 r6271714 = x;
        double r6271715 = 0.5;
        double r6271716 = r6271714 * r6271715;
        double r6271717 = y;
        double r6271718 = 1.0;
        double r6271719 = z;
        double r6271720 = r6271718 - r6271719;
        double r6271721 = log(r6271719);
        double r6271722 = r6271720 + r6271721;
        double r6271723 = r6271717 * r6271722;
        double r6271724 = r6271716 + r6271723;
        return r6271724;
}

↓

double f(double x, double y, double z) {
        double r6271725 = z;
        double r6271726 = log(r6271725);
        double r6271727 = 1.0;
        double r6271728 = r6271727 - r6271725;
        double r6271729 = r6271726 + r6271728;
        double r6271730 = y;
        double r6271731 = r6271729 * r6271730;
        double r6271732 = x;
        double r6271733 = 0.5;
        double r6271734 = r6271732 * r6271733;
        double r6271735 = r6271731 + r6271734;
        return r6271735;
}

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 2019156 
(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)))))