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

Average Error: 0.1 → 0.1

Time: 11.8s

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 r238288 = x;
        double r238289 = 0.5;
        double r238290 = r238288 * r238289;
        double r238291 = y;
        double r238292 = 1.0;
        double r238293 = z;
        double r238294 = r238292 - r238293;
        double r238295 = log(r238293);
        double r238296 = r238294 + r238295;
        double r238297 = r238291 * r238296;
        double r238298 = r238290 + r238297;
        return r238298;
}

↓

double f(double x, double y, double z) {
        double r238299 = x;
        double r238300 = 0.5;
        double r238301 = r238299 * r238300;
        double r238302 = y;
        double r238303 = 1.0;
        double r238304 = z;
        double r238305 = r238303 - r238304;
        double r238306 = log(r238304);
        double r238307 = r238305 + r238306;
        double r238308 = r238302 * r238307;
        double r238309 = r238301 + r238308;
        return r238309;
}

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 2020046 +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)))))