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

Average Error: 0.1 → 0.1

Time: 5.2s

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 r302560 = x;
        double r302561 = 0.5;
        double r302562 = r302560 * r302561;
        double r302563 = y;
        double r302564 = 1.0;
        double r302565 = z;
        double r302566 = r302564 - r302565;
        double r302567 = log(r302565);
        double r302568 = r302566 + r302567;
        double r302569 = r302563 * r302568;
        double r302570 = r302562 + r302569;
        return r302570;
}

↓

double f(double x, double y, double z) {
        double r302571 = x;
        double r302572 = 0.5;
        double r302573 = r302571 * r302572;
        double r302574 = y;
        double r302575 = 1.0;
        double r302576 = z;
        double r302577 = r302575 - r302576;
        double r302578 = log(r302576);
        double r302579 = r302577 + r302578;
        double r302580 = r302574 * r302579;
        double r302581 = r302573 + r302580;
        return r302581;
}

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 2020100 
(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)))))