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

Average Error: 0.1 → 0.1

Time: 5.7s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

↓

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

C

double f(double x, double y, double z) {
        double r233606 = x;
        double r233607 = 0.5;
        double r233608 = r233606 * r233607;
        double r233609 = y;
        double r233610 = 1.0;
        double r233611 = z;
        double r233612 = r233610 - r233611;
        double r233613 = log(r233611);
        double r233614 = r233612 + r233613;
        double r233615 = r233609 * r233614;
        double r233616 = r233608 + r233615;
        return r233616;
}

↓

double f(double x, double y, double z) {
        double r233617 = x;
        double r233618 = 0.5;
        double r233619 = r233617 * r233618;
        double r233620 = y;
        double r233621 = 1.0;
        double r233622 = z;
        double r233623 = r233621 - r233622;
        double r233624 = log(r233622);
        double r233625 = r233623 + r233624;
        double r233626 = r233620 * r233625;
        double r233627 = r233619 + r233626;
        return r233627;
}

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. Final simplification 0.1

   \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

Reproduce

herbie shell --seed 2020020 +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)))))