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

Average Error: 0.1 → 0.1

Time: 17.1s

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 r203747 = x;
        double r203748 = 0.5;
        double r203749 = r203747 * r203748;
        double r203750 = y;
        double r203751 = 1.0;
        double r203752 = z;
        double r203753 = r203751 - r203752;
        double r203754 = log(r203752);
        double r203755 = r203753 + r203754;
        double r203756 = r203750 * r203755;
        double r203757 = r203749 + r203756;
        return r203757;
}

↓

double f(double x, double y, double z) {
        double r203758 = x;
        double r203759 = 0.5;
        double r203760 = y;
        double r203761 = 1.0;
        double r203762 = z;
        double r203763 = r203761 - r203762;
        double r203764 = log(r203762);
        double r203765 = r203763 + r203764;
        double r203766 = r203760 * r203765;
        double r203767 = fma(r203758, r203759, r203766);
        return r203767;
}

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 2019209 +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)))))