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

Average Error: 0.1 → 0.1

Time: 18.0s

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 r231722 = x;
        double r231723 = 0.5;
        double r231724 = r231722 * r231723;
        double r231725 = y;
        double r231726 = 1.0;
        double r231727 = z;
        double r231728 = r231726 - r231727;
        double r231729 = log(r231727);
        double r231730 = r231728 + r231729;
        double r231731 = r231725 * r231730;
        double r231732 = r231724 + r231731;
        return r231732;
}

↓

double f(double x, double y, double z) {
        double r231733 = x;
        double r231734 = 0.5;
        double r231735 = r231733 * r231734;
        double r231736 = y;
        double r231737 = 1.0;
        double r231738 = z;
        double r231739 = r231737 - r231738;
        double r231740 = log(r231738);
        double r231741 = r231739 + r231740;
        double r231742 = r231736 * r231741;
        double r231743 = r231735 + r231742;
        return r231743;
}

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 2019212 
(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)))))