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

[download]

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

[download]

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.
"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

In reply to Re^2: Boolean math: Fill in the blanks. by BrowserUk
in thread Boolean math: Fill in the blanks. by BrowserUk

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