Function speculation design with error recovery mechanisms is quite promising due to its high performance and low area overhead. Previous work has focused on two-stage function speculation and thus lacks a systematic way to address the challenge of the multistage function speculation approach. This paper proposes a multistage function speculation with adaptive predictors and applies it in a novel adder. We deduced the analytical performance and area models for the design and validated them in our experiments. Based on those models, a general methodology is presented to guide design optimization. Both analytical proofs and experimental results on the fabricated chips show that the proposed adder's delay and area have a logarithmic and linear relationship with its bit number, respectively. Compared with the DesignWare IP, the proposed adder provides the same performance with 6-17% area reduction under different bit lengths.