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

Average Error: 0.1 → 0.1

Time: 21.4s

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 r12567951 = x;
        double r12567952 = 0.5;
        double r12567953 = r12567951 * r12567952;
        double r12567954 = y;
        double r12567955 = 1.0;
        double r12567956 = z;
        double r12567957 = r12567955 - r12567956;
        double r12567958 = log(r12567956);
        double r12567959 = r12567957 + r12567958;
        double r12567960 = r12567954 * r12567959;
        double r12567961 = r12567953 + r12567960;
        return r12567961;
}

↓

double f(double x, double y, double z) {
        double r12567962 = z;
        double r12567963 = log(r12567962);
        double r12567964 = 1.0;
        double r12567965 = r12567964 - r12567962;
        double r12567966 = r12567963 + r12567965;
        double r12567967 = y;
        double r12567968 = r12567966 * r12567967;
        double r12567969 = x;
        double r12567970 = 0.5;
        double r12567971 = r12567969 * r12567970;
        double r12567972 = r12567968 + r12567971;
        return r12567972;
}

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 2019172 
(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)))))