Mathematica: using simplify to do common sub-expression elimination and reduction in strength
There are also some routines here implemented here by this author: http://stoney.sb.org/wordpress/2009/06/converting-symbolic-mathematica-expressions-to-c-code/
I packaged it into a *.M file and have fixed a bug (if the expression has no repeated subexpressions the it dies), and I am trying to find the author's contact info to see if I can upload his modified code to pastebin or wherever.
EDIT: I have received permission from the author to upload it and have pasted it here: http://pastebin.com/fjYiR0B3
To identify repeating subexpressions, you could use something like this
(*helper functions to add Dictionary-like functionality*)
index[downvalue_,
dict_] := (downvalue[[1]] /. HoldPattern[dict[x_]] -> x) //
ReleaseHold;
value[downvalue_] := downvalue[[-1]];
indices[dict_] :=
Map[#[[1]] /. {HoldPattern[dict[x_]] -> x} &, DownValues[dict]] //
ReleaseHold;
values[dict_] := Map[#[[-1]] &, DownValues[dict]];
items[dict_] := Map[{index[#, dict], value[#]} &, DownValues[dict]];
indexQ[dict_, index_] :=
If[MatchQ[dict[index], HoldPattern[dict[index]]], False, True];
(*count number of times each sub-expressions occurs *)
expr = Cos[x + Cos[Cos[x] + Sin[x]]] + Cos[Cos[x] + Sin[x]];
Map[(counts[#] = If[indexQ[counts, #], counts[#] + 1, 1]; #) &, expr,
Infinity];
items[counts] // Column