The following expresses the tautology that
((x^2)-y^2) = (x+y)*(x-y) :

   diffsq=: -&*: = + * -
   x=: 0.001 * _1e9 + 10 ?...@$ 2e9
   y=: 0.001 * _1e9 + 10 ?...@$ 2e9
   x diffsq y
1 1 1 1 1 1 1 1 1 1

Your question brings to mind events in the early days of J.  
For a time Ken wondered, are there many examples of fork?  
After a while, it seemed that _everything_ was a fork.
http://keiapl.org/rhui/remember.htm#fork3



----- Original Message -----
From: John Randall <[email protected]>
Date: Sunday, February 1, 2009 15:21
Subject: [Jprogramming] Examples of dyadic forks
To: JProgramming <[email protected]>

> Does anyone have a good example of a dyadic fork?  By this 
> I mean one
> of the form fgh where f and g both use x and y, there are no [ 
> or ],
> no constant functions, and no @ or @: .  I am having 
> trouble coming up
> with nontrivial examples.
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