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

Average Error: 0.1 → 0.1

Time: 32.7s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

↓

\[\mathsf{fma}\left(x, 0.5, y \cdot \left(1.0 - \left(z - \log z\right)\right)\right)\]

C

double f(double x, double y, double z) {
        double r18495706 = x;
        double r18495707 = 0.5;
        double r18495708 = r18495706 * r18495707;
        double r18495709 = y;
        double r18495710 = 1.0;
        double r18495711 = z;
        double r18495712 = r18495710 - r18495711;
        double r18495713 = log(r18495711);
        double r18495714 = r18495712 + r18495713;
        double r18495715 = r18495709 * r18495714;
        double r18495716 = r18495708 + r18495715;
        return r18495716;
}

↓

double f(double x, double y, double z) {
        double r18495717 = x;
        double r18495718 = 0.5;
        double r18495719 = y;
        double r18495720 = 1.0;
        double r18495721 = z;
        double r18495722 = log(r18495721);
        double r18495723 = r18495721 - r18495722;
        double r18495724 = r18495720 - r18495723;
        double r18495725 = r18495719 * r18495724;
        double r18495726 = fma(r18495717, r18495718, r18495725);
        return r18495726;
}

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

   \[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.5, \left(1.0 - \left(z - \log z\right)\right) \cdot y\right)}\]

3. Final simplification 0.1

   \[\leadsto \mathsf{fma}\left(x, 0.5, y \cdot \left(1.0 - \left(z - \log z\right)\right)\right)\]

Reproduce

herbie shell --seed 2019163 +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)))))