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

Average Error: 0.1 → 0.1

Time: 19.3s

Precision: 64

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 r175316 = x;
        double r175317 = 0.5;
        double r175318 = r175316 * r175317;
        double r175319 = y;
        double r175320 = 1.0;
        double r175321 = z;
        double r175322 = r175320 - r175321;
        double r175323 = log(r175321);
        double r175324 = r175322 + r175323;
        double r175325 = r175319 * r175324;
        double r175326 = r175318 + r175325;
        return r175326;
}

↓

double f(double x, double y, double z) {
        double r175327 = x;
        double r175328 = 0.5;
        double r175329 = r175327 * r175328;
        double r175330 = y;
        double r175331 = 1.0;
        double r175332 = z;
        double r175333 = r175331 - r175332;
        double r175334 = log(r175332);
        double r175335 = r175333 + r175334;
        double r175336 = r175330 * r175335;
        double r175337 = r175329 + r175336;
        return r175337;
}

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 2019304 +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)))))