1. A method for reducing operations in a processing environment, comprising: generating one or more binary representations, wherein one or more of the binary representations are included in one or more linear equations that include one or more operations; converting one or more of the linear equations to one or more polynomials; performing kernel extraction and optimization on one or more of the polynomials; and identifying one or more common subexpressions associated with the polynomials in order to reduce one or more of the operations, wherein the identifying is facilitated by rectangle covering.