The paper deals with a procedure for approximate symbolic analysis of linear circuits based on simplifying the circuit model. The procedure consists of two main steps. First, network elements whose influence on the circuit function is negligible are completely removed, i.e. their parameters are removed from the resulting symbolic formula. The second step consists in modifying the voltage and current graphs in order to decrease the number of common spanning trees. The influence of each modification of the circuit model is ranked numerically. A fast method based on the use of cofactors is presented. It allows evaluating all the prospective simplifications using at most two matrix inversions per one frequency point.