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

Average Error: 0.1 → 0.1

Time: 5.1s

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 r363715 = x;
        double r363716 = 0.5;
        double r363717 = r363715 * r363716;
        double r363718 = y;
        double r363719 = 1.0;
        double r363720 = z;
        double r363721 = r363719 - r363720;
        double r363722 = log(r363720);
        double r363723 = r363721 + r363722;
        double r363724 = r363718 * r363723;
        double r363725 = r363717 + r363724;
        return r363725;
}

↓

double f(double x, double y, double z) {
        double r363726 = x;
        double r363727 = 0.5;
        double r363728 = r363726 * r363727;
        double r363729 = y;
        double r363730 = 1.0;
        double r363731 = z;
        double r363732 = r363730 - r363731;
        double r363733 = log(r363731);
        double r363734 = r363732 + r363733;
        double r363735 = r363729 * r363734;
        double r363736 = r363728 + r363735;
        return r363736;
}

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 2020065 
(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)))))