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

Average Error: 0.1 → 0.1

Time: 7.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

↓

\[x \cdot 0.5 + \left(\left(1 - z\right) + \log z\right) \cdot y\]

C

double f(double x, double y, double z) {
        double r347796 = x;
        double r347797 = 0.5;
        double r347798 = r347796 * r347797;
        double r347799 = y;
        double r347800 = 1.0;
        double r347801 = z;
        double r347802 = r347800 - r347801;
        double r347803 = log(r347801);
        double r347804 = r347802 + r347803;
        double r347805 = r347799 * r347804;
        double r347806 = r347798 + r347805;
        return r347806;
}

↓

double f(double x, double y, double z) {
        double r347807 = x;
        double r347808 = 0.5;
        double r347809 = r347807 * r347808;
        double r347810 = 1.0;
        double r347811 = z;
        double r347812 = r347810 - r347811;
        double r347813 = log(r347811);
        double r347814 = r347812 + r347813;
        double r347815 = y;
        double r347816 = r347814 * r347815;
        double r347817 = r347809 + r347816;
        return r347817;
}

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. Using strategy rm

3. Applied *-commutative 0.1

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(1 - z\right) + \log z\right) \cdot y}\]

4. Final simplification 0.1

   \[\leadsto x \cdot 0.5 + \left(\left(1 - z\right) + \log z\right) \cdot y\]

Reproduce

herbie shell --seed 2020047 
(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)))))