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

Average Error: 0.1 → 0.1

Time: 7.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r336752 = x;
        double r336753 = 0.5;
        double r336754 = r336752 * r336753;
        double r336755 = y;
        double r336756 = 1.0;
        double r336757 = z;
        double r336758 = r336756 - r336757;
        double r336759 = log(r336757);
        double r336760 = r336758 + r336759;
        double r336761 = r336755 * r336760;
        double r336762 = r336754 + r336761;
        return r336762;
}

↓

double f(double x, double y, double z) {
        double r336763 = x;
        double r336764 = 0.5;
        double r336765 = r336763 * r336764;
        double r336766 = y;
        double r336767 = 1.0;
        double r336768 = z;
        double r336769 = r336767 - r336768;
        double r336770 = log(r336768);
        double r336771 = r336769 + r336770;
        double r336772 = r336766 * r336771;
        double r336773 = r336765 + r336772;
        return r336773;
}

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)))))