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

Average Error: 0.1 → 0.1

Time: 11.9s

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 r349942 = x;
        double r349943 = 0.5;
        double r349944 = r349942 * r349943;
        double r349945 = y;
        double r349946 = 1.0;
        double r349947 = z;
        double r349948 = r349946 - r349947;
        double r349949 = log(r349947);
        double r349950 = r349948 + r349949;
        double r349951 = r349945 * r349950;
        double r349952 = r349944 + r349951;
        return r349952;
}

↓

double f(double x, double y, double z) {
        double r349953 = x;
        double r349954 = 0.5;
        double r349955 = r349953 * r349954;
        double r349956 = y;
        double r349957 = 1.0;
        double r349958 = z;
        double r349959 = r349957 - r349958;
        double r349960 = log(r349958);
        double r349961 = r349959 + r349960;
        double r349962 = r349956 * r349961;
        double r349963 = r349955 + r349962;
        return r349963;
}

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 2020043 
(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)))))