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

Average Error: 0.1 → 0.1

Time: 6.8s

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 r321510 = x;
        double r321511 = 0.5;
        double r321512 = r321510 * r321511;
        double r321513 = y;
        double r321514 = 1.0;
        double r321515 = z;
        double r321516 = r321514 - r321515;
        double r321517 = log(r321515);
        double r321518 = r321516 + r321517;
        double r321519 = r321513 * r321518;
        double r321520 = r321512 + r321519;
        return r321520;
}

↓

double f(double x, double y, double z) {
        double r321521 = x;
        double r321522 = 0.5;
        double r321523 = r321521 * r321522;
        double r321524 = y;
        double r321525 = 1.0;
        double r321526 = z;
        double r321527 = r321525 - r321526;
        double r321528 = log(r321526);
        double r321529 = r321527 + r321528;
        double r321530 = r321524 * r321529;
        double r321531 = r321523 + r321530;
        return r321531;
}

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 2019354 +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)))))