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Exploiting the benefits afforded by runtime partial reconfiguration (PR) on modern field-programmable gate arrays (FPGAs)requires PR-capable applications and associated PR-architectures, both of which are challenging tasks due to competing implementation metrics(e.g., area, power, operating frequency, etc.) and results in unmanageable design spaces. PR design space exploration (DSE) techniques and tools assist designers in efficiently and effectively exploring this design space. This paper presents the first, to the best of our knowledge, formulation-level PR DSE tool - FoRSE. FoRSE leverages the application's PR-architecture and mathematical FPGA device models and vendor-specified PR technology to generate Pareto-optimal sets of PR-floorplans and devices based on designer-designated implementation metrics. FoRSE can prune an application's implementation design space by three to four orders of magnitude in approximately 15 seconds.