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 systems that include one or more operations and a plurality of different distinct variables; converting one or more of the linear systems to one or more polynomials including the plurality of different distinct variables; generating a plurality of kernels from the one or more polynomials; generating a matrix of the plurality of kernels; performing kernel extraction on the matrix for optimization of the one or more polynomials; and identifying one or more common subexpressions associated with the polynomials by extracting common bit patterns among constants multiplying two or more variables of the plurality of different distinct variables in order to reduce one or more of the operations, wherein the identifying is facilitated by rectangle covering.