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

Average Error: 0.1 → 0.1

Time: 15.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r15806807 = x;
        double r15806808 = 0.5;
        double r15806809 = r15806807 * r15806808;
        double r15806810 = y;
        double r15806811 = 1.0;
        double r15806812 = z;
        double r15806813 = r15806811 - r15806812;
        double r15806814 = log(r15806812);
        double r15806815 = r15806813 + r15806814;
        double r15806816 = r15806810 * r15806815;
        double r15806817 = r15806809 + r15806816;
        return r15806817;
}

↓

double f(double x, double y, double z) {
        double r15806818 = z;
        double r15806819 = log(r15806818);
        double r15806820 = 1.0;
        double r15806821 = r15806820 - r15806818;
        double r15806822 = r15806819 + r15806821;
        double r15806823 = y;
        double r15806824 = r15806822 * r15806823;
        double r15806825 = x;
        double r15806826 = 0.5;
        double r15806827 = r15806825 * r15806826;
        double r15806828 = r15806824 + r15806827;
        return r15806828;
}

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

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

Reproduce

herbie shell --seed 2019192 
(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)))))