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### Re^2: Boolean math: Fill in the blanks.

by BrowserUk (Pope)
 on Oct 12, 2008 at 08:25 UTC ( #716662=note: print w/replies, xml ) Need Help??

in reply to Re: Boolean math: Fill in the blanks.
in thread Boolean math: Fill in the blanks.

Conclusion: ... I see some inconsistent results ... 7 of ( R & R | R & R ) & R evaluates to 5 bits set on average.

If you plug ( R & R | R & R ) & R into the OP code and run it a few times, you'll see that the average does approximate 7:

```C:\test>booleanBuk -N=1e2
7.02

C:\test>booleanBuk -N=1e2
6.88

C:\test>booleanBuk -N=1e2
7.06

C:\test>booleanBuk -N=1e2
7.06

C:\test>booleanBuk -N=1e2
6.92

C:\test>booleanBuk -N=1e2
7.08

And as you increase the number of iterations, the more closely the observations coincide with the theoretical value:

```C:\test>booleanBuk -N=1e5
7.00138

C:\test>booleanBuk -N=1e5
6.98986

C:\test>booleanBuk -N=1e5
6.99812

C:\test>booleanBuk -N=1e5
7.00729

C:\test>booleanBuk -N=1e6
6.994402

C:\test>booleanBuk -N=1e6
7.002038

That's how I like my proofs. Tangible :)

Sorry if I have misunderstood your hypothesis.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

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Re^3: Boolean math: Fill in the blanks.
by repellent (Priest) on Oct 12, 2008 at 16:54 UTC
But plug in
(( R & R ) | R ) & R & R

into the OP code and it tends towards 5, which was how I was interpreting the expression:
( R & R | R & R ) & R

My mistake. Perl evaluates ( R & R | R & R ) & R as ( (R & R) | (R & R) ) & R and that, according to my hypothesis, results in 7 bits set on average.

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