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

Average Error: 0.1 → 0.1

Time: 26.5s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

↓

\[\left(\log z + \left(1.0 - z\right)\right) \cdot y + x \cdot 0.5\]

C

double f(double x, double y, double z) {
        double r14953583 = x;
        double r14953584 = 0.5;
        double r14953585 = r14953583 * r14953584;
        double r14953586 = y;
        double r14953587 = 1.0;
        double r14953588 = z;
        double r14953589 = r14953587 - r14953588;
        double r14953590 = log(r14953588);
        double r14953591 = r14953589 + r14953590;
        double r14953592 = r14953586 * r14953591;
        double r14953593 = r14953585 + r14953592;
        return r14953593;
}

↓

double f(double x, double y, double z) {
        double r14953594 = z;
        double r14953595 = log(r14953594);
        double r14953596 = 1.0;
        double r14953597 = r14953596 - r14953594;
        double r14953598 = r14953595 + r14953597;
        double r14953599 = y;
        double r14953600 = r14953598 * r14953599;
        double r14953601 = x;
        double r14953602 = 0.5;
        double r14953603 = r14953601 * r14953602;
        double r14953604 = r14953600 + r14953603;
        return r14953604;
}

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

   \[x \cdot 0.5 + y \cdot \left(\left(1.0 - z\right) + \log z\right)\]

2. Final simplification 0.1

   \[\leadsto \left(\log z + \left(1.0 - z\right)\right) \cdot y + x \cdot 0.5\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))