I highly recommend you use Parse::RecDescent. It has an <autotree> directive which, although it doesn't work exactly as you describe, builds a tree that's probably better for your purposes:

      +
     / \
    /   \
   /     \
 tan     *
  |     / \
  ^    2 sin
 / \      |
x   4     x
[download]

The advantage of this tree is that you can just do a postorder traversal with a number stack to run it. Of course, if you really like the tree design you describe above, you can also just provide the tree-building actions yourself instead of using <autotree>.

=cut
--Brent Dax
There is no sig.