Re: Locating common subexpressions
- To: mathgroup at smc.vnet.net
- Subject: [mg69523] Re: Locating common subexpressions
- From: carlos at colorado.edu
- Date: Thu, 14 Sep 2006 06:57:08 -0400 (EDT)
- References: <200609121052.GAA04126@smc.vnet.net><ee8h38$j1h$1@smc.vnet.net>
Daniel Lichtblau wrote: > carlos at colorado.edu wrote: > > The strangest thing about the behvior of Simplify in my > > previous post can be seen at a glance: > > > > R = (3 + 3*a^2 + Sqrt[5 + 6*a + 5*a^2] + a*(4 + Sqrt[5 + 6*a + > > 5*a^2]))/6 > > R = Simplify[R,a>=0] > > (3 + 3*a^2 + Sqrt[5 + 6*a + 5*a^2] + a*(4 + Sqrt[5 + 6*a + 5*a^2]))/6 > > > > The subexpression Sqrt[5 + 6*a + 5*a^2] is not located. Ideally > > Simplify should right away replace that by a temp, say t$, and > > get to work on > > > > (3 + 3*a^2 + t$ + a*(4 + t$))/6 > > > > where from the assumptions, t$>0 and real. Of course the leaf count > > of t$ should influence subsequent transformations. > > This initial pass is useful in complicated expressions that come, eg, > > from an equation solver since messy subexpressions like the > > discriminant may appear in several places. I had some of those > > with leaf counts in the tens of thousands. > > > > Locating common subs is of course an key task of optimizing > > compilers. Simplification and compilation share some objectives, > > although compilers have to deal with timing and side effects. In fact > > I wouldnt mind at all if Simplify would return a compound expression: > > > > Block [{t$}, t$=Sqrt[5 + 6*a + 5*a^2]; (3 + 4*a + 3*a^2 + (1 + > > a)*t$)/6 ] > > > > since this is perfect for documentation, or conversion to low-level > > code. > > If you want CSE you can use OptimizeExpression in Experimental` context. > > In[8]:= InputForm[Experimental`OptimizeExpression[(3 + 3*a^2 + Sqrt[5 + > 6*a + 5*a^2] + a*(4 + Sqrt[5 + 6*a + 5*a^2]))/6]] > > Out[8]//InputForm= > Experimental`OptimizedExpression[Block[{$$25, $$27, $$28, $$29, $$30}, > $$25 = a^2; $$27 = 6*a; $$28 = 5*$$25; $$29 = 5 + $$27 + $$28; > $$30 = Sqrt[$$29]; (3 + 3*$$25 + $$30 + a*(4 + $$30))/6]] > > This sort of thing is not a part of the Simplify "charter", but is very > much the intent of OptimizeExpression. As you might suspect, this is > meant for reforming expressions prior to conversion to lower level > languages such as C or the byte code of Mathematica's Compile virtual > machine. > > > Daniel Lichtblau > Wolfram Research Is this facility available in 5.0? I havent upgraded to 5.2. Would be interesting to combine this and Simplify, and eventually extend to Modules. I believe that would be unique to Mathematica.
- References:
- Locating common subexpressions
- From: carlos@colorado.edu
- Locating common subexpressions