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

Average Error: 0.1 → 0.1

Time: 7.6s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

↓

\[\mathsf{fma}\left(x, 0.5, y \cdot \left(\left(1 - z\right) + \log z\right)\right)\]

C

double f(double x, double y, double z) {
        double r247554 = x;
        double r247555 = 0.5;
        double r247556 = r247554 * r247555;
        double r247557 = y;
        double r247558 = 1.0;
        double r247559 = z;
        double r247560 = r247558 - r247559;
        double r247561 = log(r247559);
        double r247562 = r247560 + r247561;
        double r247563 = r247557 * r247562;
        double r247564 = r247556 + r247563;
        return r247564;
}

↓

double f(double x, double y, double z) {
        double r247565 = x;
        double r247566 = 0.5;
        double r247567 = y;
        double r247568 = 1.0;
        double r247569 = z;
        double r247570 = r247568 - r247569;
        double r247571 = log(r247569);
        double r247572 = r247570 + r247571;
        double r247573 = r247567 * r247572;
        double r247574 = fma(r247565, r247566, r247573);
        return r247574;
}

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. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.5, y \cdot \left(\left(1 - z\right) + \log z\right)\right)}\]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(x, 0.5, y \cdot \left(\left(1 - z\right) + \log z\right)\right)\]

Reproduce

herbie shell --seed 2020001 +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)))))