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The paper deals with an improved algorithm for estimating errors during approximate symbolic analysis. A linear system can be solved symbolically. However, the size of the resulting formula grows exponentially with the matrix size. The approximate symbolic analysis omits insignificant terms of the exact formula to decrease its size, which, on the other hand, limits the validity of the approximate result. The proposed algorithm estimates, in a computationally feasible way, the approximation error over a region of system parameters. This makes it possible to maintain the validity of the results even if the tolerances of the system parameters are defined. The method is based on the first-order approximation of error functions. The algorithm is demonstrated using the SNAP symbolic analyzer, which has been developed by the authors.