Floating-point computation is a core technology in critical domains such as aerospace, artificial intelligence, defense, and financial settlement, where computational accuracy and performance are closely tied to system safety and reliability. However, the inherent representation error of floating-point numbers can propagate and accumulate during computation, potentially leading to severe consequences. In theory, the most accurate way to detect numerical errors is to exhaustively enumerate the entire floating-point input space, but the computational cost of doing so is prohibitive in practice. To address this challenge, this paper proposes a segmented-search-based error detection method for floating-point arithmetic expressions and implements it as an automated tool, SPOT (Segmented Precision Optimized Testing). SPOT adopts a two-stage optimization strategy. First, it leverages exponent-related error characteristics of floating-point numbers to narrow the exponent search space, thereby identifying exponent regions that are more likely to produce significant errors. It then applies the DEPS algorithm to search the mantissa space, while uniformly introducing an error-level-driven budget allocation mechanism across both stages to dynamically adjust search resources. In this way, SPOT ultimately identifies the maximum error and its corresponding input. Experimental results show that SPOT successfully detected errors on all 166 benchmark cases. In terms of maximum-error detection, SPOT outperformed ATOMU, EIFFEL, and FPCC on 95.69%, 89.76%, and 89.16% of the benchmarks, respectively, and achieved average speedups of 135.24× over EIFFEL and 58.11× over FPCC.