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

Average Error: 0.1 → 0.1

Time: 6.2s

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 r296948 = x;
        double r296949 = 0.5;
        double r296950 = r296948 * r296949;
        double r296951 = y;
        double r296952 = 1.0;
        double r296953 = z;
        double r296954 = r296952 - r296953;
        double r296955 = log(r296953);
        double r296956 = r296954 + r296955;
        double r296957 = r296951 * r296956;
        double r296958 = r296950 + r296957;
        return r296958;
}

↓

double f(double x, double y, double z) {
        double r296959 = x;
        double r296960 = 0.5;
        double r296961 = y;
        double r296962 = 1.0;
        double r296963 = z;
        double r296964 = r296962 - r296963;
        double r296965 = log(r296963);
        double r296966 = r296964 + r296965;
        double r296967 = r296961 * r296966;
        double r296968 = fma(r296959, r296960, r296967);
        return r296968;
}

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 2019353 +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)))))