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 r344030 = x;
        double r344031 = 0.5;
        double r344032 = r344030 * r344031;
        double r344033 = y;
        double r344034 = 1.0;
        double r344035 = z;
        double r344036 = r344034 - r344035;
        double r344037 = log(r344035);
        double r344038 = r344036 + r344037;
        double r344039 = r344033 * r344038;
        double r344040 = r344032 + r344039;
        return r344040;
}

↓

double f(double x, double y, double z) {
        double r344041 = x;
        double r344042 = 0.5;
        double r344043 = y;
        double r344044 = 1.0;
        double r344045 = z;
        double r344046 = r344044 - r344045;
        double r344047 = log(r344045);
        double r344048 = r344046 + r344047;
        double r344049 = r344043 * r344048;
        double r344050 = fma(r344041, r344042, r344049);
        return r344050;
}

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 2020034 +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)))))