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

Average Error: 0.1 → 0.1

Time: 19.7s

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 r14093410 = x;
        double r14093411 = 0.5;
        double r14093412 = r14093410 * r14093411;
        double r14093413 = y;
        double r14093414 = 1.0;
        double r14093415 = z;
        double r14093416 = r14093414 - r14093415;
        double r14093417 = log(r14093415);
        double r14093418 = r14093416 + r14093417;
        double r14093419 = r14093413 * r14093418;
        double r14093420 = r14093412 + r14093419;
        return r14093420;
}

↓

double f(double x, double y, double z) {
        double r14093421 = z;
        double r14093422 = log(r14093421);
        double r14093423 = 1.0;
        double r14093424 = r14093423 - r14093421;
        double r14093425 = r14093422 + r14093424;
        double r14093426 = y;
        double r14093427 = r14093425 * r14093426;
        double r14093428 = x;
        double r14093429 = 0.5;
        double r14093430 = r14093428 * r14093429;
        double r14093431 = r14093427 + r14093430;
        return r14093431;
}

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)))))