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

Average Error: 0.1 → 0.1

Time: 5.5s

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 r266415 = x;
        double r266416 = 0.5;
        double r266417 = r266415 * r266416;
        double r266418 = y;
        double r266419 = 1.0;
        double r266420 = z;
        double r266421 = r266419 - r266420;
        double r266422 = log(r266420);
        double r266423 = r266421 + r266422;
        double r266424 = r266418 * r266423;
        double r266425 = r266417 + r266424;
        return r266425;
}

↓

double f(double x, double y, double z) {
        double r266426 = x;
        double r266427 = 0.5;
        double r266428 = r266426 * r266427;
        double r266429 = y;
        double r266430 = 1.0;
        double r266431 = z;
        double r266432 = r266430 - r266431;
        double r266433 = log(r266431);
        double r266434 = r266432 + r266433;
        double r266435 = r266429 * r266434;
        double r266436 = r266428 + r266435;
        return r266436;
}

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 2020065 +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)))))