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

Average Error: 0.1 → 0.1

Time: 5.3s

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 r277551 = x;
        double r277552 = 0.5;
        double r277553 = r277551 * r277552;
        double r277554 = y;
        double r277555 = 1.0;
        double r277556 = z;
        double r277557 = r277555 - r277556;
        double r277558 = log(r277556);
        double r277559 = r277557 + r277558;
        double r277560 = r277554 * r277559;
        double r277561 = r277553 + r277560;
        return r277561;
}

↓

double f(double x, double y, double z) {
        double r277562 = x;
        double r277563 = 0.5;
        double r277564 = y;
        double r277565 = 1.0;
        double r277566 = z;
        double r277567 = r277565 - r277566;
        double r277568 = log(r277566);
        double r277569 = r277567 + r277568;
        double r277570 = r277564 * r277569;
        double r277571 = fma(r277562, r277563, r277570);
        return r277571;
}

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 2020100 +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)))))