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

Average Error: 0.1 → 0.1

Time: 8.7s

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 r346386 = x;
        double r346387 = 0.5;
        double r346388 = r346386 * r346387;
        double r346389 = y;
        double r346390 = 1.0;
        double r346391 = z;
        double r346392 = r346390 - r346391;
        double r346393 = log(r346391);
        double r346394 = r346392 + r346393;
        double r346395 = r346389 * r346394;
        double r346396 = r346388 + r346395;
        return r346396;
}

↓

double f(double x, double y, double z) {
        double r346397 = x;
        double r346398 = 0.5;
        double r346399 = r346397 * r346398;
        double r346400 = y;
        double r346401 = 1.0;
        double r346402 = z;
        double r346403 = r346401 - r346402;
        double r346404 = log(r346402);
        double r346405 = r346403 + r346404;
        double r346406 = r346400 * r346405;
        double r346407 = r346399 + r346406;
        return r346407;
}

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 2019350 
(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)))))