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

Average Error: 0.1 → 0.1

Time: 5.0s

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 r271021 = x;
        double r271022 = 0.5;
        double r271023 = r271021 * r271022;
        double r271024 = y;
        double r271025 = 1.0;
        double r271026 = z;
        double r271027 = r271025 - r271026;
        double r271028 = log(r271026);
        double r271029 = r271027 + r271028;
        double r271030 = r271024 * r271029;
        double r271031 = r271023 + r271030;
        return r271031;
}

↓

double f(double x, double y, double z) {
        double r271032 = x;
        double r271033 = 0.5;
        double r271034 = y;
        double r271035 = 1.0;
        double r271036 = z;
        double r271037 = r271035 - r271036;
        double r271038 = log(r271036);
        double r271039 = r271037 + r271038;
        double r271040 = r271034 * r271039;
        double r271041 = fma(r271032, r271033, r271040);
        return r271041;
}

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 2020046 +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)))))