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

Average Error: 0.1 → 0.1

Time: 12.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r349566 = x;
        double r349567 = 0.5;
        double r349568 = r349566 * r349567;
        double r349569 = y;
        double r349570 = 1.0;
        double r349571 = z;
        double r349572 = r349570 - r349571;
        double r349573 = log(r349571);
        double r349574 = r349572 + r349573;
        double r349575 = r349569 * r349574;
        double r349576 = r349568 + r349575;
        return r349576;
}

↓

double f(double x, double y, double z) {
        double r349577 = x;
        double r349578 = 0.5;
        double r349579 = r349577 * r349578;
        double r349580 = y;
        double r349581 = 1.0;
        double r349582 = z;
        double r349583 = r349581 - r349582;
        double r349584 = log(r349582);
        double r349585 = r349583 + r349584;
        double r349586 = r349580 * r349585;
        double r349587 = r349579 + r349586;
        return r349587;
}

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 2019350 +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)))))