Math expression reducing algorithm

I have been searching for a solution to this problem:
I have an expression in infix which can contain *,/,-,+ and I have to find the reduced form
of this expression.

Ex: Input: ((A+45)*16+(B-C)*D/4 )/8+ 55
Output: A*2+B*D/32-C*D/32 +145

All that can be calculated must be calculated and the simplest form must be returned.
A,B,C,D do NOT have numeric values. They are name of variables(strings).
The expressions that have to be calculated can be more complicated.
I have found on the net algorithms that only evaluate expressions that have numerical values in them(or variables that are replaced by numerical values).

What I have done: I have translated the expression into expression tree form and now I'm a bit lost . Maybe I should have gone a different path ?

Can you help?

 

I'm sorry if I'm missing anything but your article was about evaluating an expression.
You give each of the variables a numerical value.
I don't want that.
My program has to output the expression in a simpler form with all possible calculations being made. But I cannot replace the name of a variable with an value.

 

By "first part" do you mean the one that transfoorms infix to postfix ?
Or what ? Can you copy here please exactly the part of code that you mean, cause I can't find it.

Thanks

 

I think you don't understand what I need. I already have the expression converted into postfix and then into expression tree.
Your code seems to be just the algo for converting to postfix and then evaluating that.

I have found a solution that seemms to be what I need which involves a polynomial class with all the operations.