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

Average Error: 0.1 → 0.1

Time: 14.6s

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 r270835 = x;
        double r270836 = 0.5;
        double r270837 = r270835 * r270836;
        double r270838 = y;
        double r270839 = 1.0;
        double r270840 = z;
        double r270841 = r270839 - r270840;
        double r270842 = log(r270840);
        double r270843 = r270841 + r270842;
        double r270844 = r270838 * r270843;
        double r270845 = r270837 + r270844;
        return r270845;
}

↓

double f(double x, double y, double z) {
        double r270846 = x;
        double r270847 = 0.5;
        double r270848 = r270846 * r270847;
        double r270849 = y;
        double r270850 = 1.0;
        double r270851 = z;
        double r270852 = r270850 - r270851;
        double r270853 = log(r270851);
        double r270854 = r270852 + r270853;
        double r270855 = r270849 * r270854;
        double r270856 = r270848 + r270855;
        return r270856;
}

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 2019351 +o rules:numerics
(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)))))