You might find this helpful.
Evaluate Expressions. This is one of my favorite things I've ever written. It parses expressions and evaluates them. It's the basis for a mini language that got put on hold for some time.

In the evaulate sub, right after  @$ops = grep { defined $_ } @$ops; You basically have a parse tree.

For your example, you'd have

(foo*2) + (foo*3)
$ops = [
          [
            'foo',
            '*',
            '2'
          ],
          '+',
          [
            'foo',
            '*',
            '3'
          ]
        ];
[download]

You could modify it there to optimize the tree the way you w ant.