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The growing market of multimedia applications has required the development of complex application-specified integrated circuits with significant data-path portions. Unfortunately, most high-level synthesis tools and methods cannot automatically synthesize data paths such that complex arithmetic library blocks are intelligently used. Namely, most arithmetic-level optimizations are not supported and they are left to the designer's ingenuity. In this paper, we show how symbolic algebra can be used to construct arithmetic-level decomposition algorithms. We introduce our tool, SymSyn, that optimizes and maps data flow descriptions into data paths using complex arithmetic components. SymSyn uses two new algorithms to find either minimal component mapping or minimal critical path delay (CPD) mapping of the data flow. In this paper, we give an overview of the proposed algorithms. We also show how symbolic manipulations such as tree-height-reduction, factorization, expansion, and Horner transformation are incorporated in the preprocessing step. Such manipulations are used as guidelines in initial library element selection to accelerate the proposed algorithms. Furthermore, we demonstrate how substitution can be used for multiexpression component sharing and CPD optimization.