# arithmetic formula simplication

Consider a function $f : \mathbb R^m \rightarrow \mathbb R^n$.

Function $f$ can be written down as a simple arithmetic program. It uses addition, subtraction, multiplication and division - however, we condition the input to be such that no division by zero occurs.

Which algorithms do exist to simplify such a program, i.e., that produce an equivalent program of shorter (or shortest) length?

• Does your program include controle structures, such as loops, or is it just one large arithmetic formula. Does it have variables and assignment? This kind of question requires some precision regarding the language considered. Also, are you interested in the length of the program (how is it measured) or in te number of arithmetic operations executed when it runs, or any othr size measure? – babou May 26 '14 at 21:45
• When you say "Which algorithms do exist" do you mean "exist" in the theoretical sense, or an actual implementation that you want to use? – Joshua Grochow May 27 '14 at 2:46