A method for reducing operations in a processing environment is provided that includes generating one or more binary representations, one or more of the binary representations being included in one or more linear equations that include one or more operations. The method also includes converting one or more of the linear equations to one or more polynomials and then performing kernel extraction and optimization on one or more of the polynomials. One or more common subexpressions associated with the polynomials are identified in order to reduce one or more of the operations.