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The capability of performing semi-automated design space exploration is the main advantage of high-level synthesis with respect to RTL design. However, design space exploration performed during; high-level synthesis is limited in scope, since it provides promising solutions that represent good starting points for subsequent optimizations, but it provides no insight about the overall structure of the design space. In this work we propose unsupervised Monte-Carlo design exploration and statistical characterization to capture the key features of the design space. Our analysis provides insight on how various solutions are distributed over the entire design space. In addition, we apply extreme value theory (1997) to extrapolate achievable bounds from the sampling points.