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

Average Error: 0.1 → 0.1

Time: 23.8s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z) {
        double r11703205 = x;
        double r11703206 = 0.5;
        double r11703207 = r11703205 * r11703206;
        double r11703208 = y;
        double r11703209 = 1.0;
        double r11703210 = z;
        double r11703211 = r11703209 - r11703210;
        double r11703212 = log(r11703210);
        double r11703213 = r11703211 + r11703212;
        double r11703214 = r11703208 * r11703213;
        double r11703215 = r11703207 + r11703214;
        return r11703215;
}

↓

double f(double x, double y, double z) {
        double r11703216 = y;
        double r11703217 = z;
        double r11703218 = log(r11703217);
        double r11703219 = 1.0;
        double r11703220 = r11703219 - r11703217;
        double r11703221 = r11703218 + r11703220;
        double r11703222 = 0.5;
        double r11703223 = x;
        double r11703224 = r11703222 * r11703223;
        double r11703225 = fma(r11703216, r11703221, r11703224);
        return r11703225;
}

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

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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)))))