One of the goals of a High Level Synthesis process is to minimize the circuit implementation cost. Since the minimization problem associated with those transformations is NP complete, in this work we present an evolutionary algorithm that optimize circuit specifications by means of a special type of genetic operator. We have named this operator algebraic mutation, carried out with the help of algebraic equations. This work can be classified within the algebraic optimization of equational specifications of circuits by using genetic techniques. We have applied this technique to a simple circuit equational specification and to a much more complex algebraic equation. In the first case our algorithm simplifies the equation until the optimum specification is found and in the second a solution improving the former is always obtained, and when we increase the population size, the optimum solution is also found.