Abstract: Computers represent real numbers using finite-precision binary formats,where inherent rounding errors may accumulate during computation and,in certain scenarios,lead to severe or even catastrophic failures.Floating-point error detection is cri-tical for ensuring the correctness of program outputs.Theoretically,the most accurate method for detecting floating-point errors is exhaustive search over all possible floating-point inputs.However,due to the enormous search space,this approach is practically infeasible.Given the sparsity of floating-point errors-where only a limited number of input values trigger significant errors－efficiently detecting these inputs and selecting appropriate search techniques poses a substantial challenge for maximum floating-point error detection.To address this challenge,a tool called HSIBA for error detection in floating-point expressions has been designed and implemented,based on hierarchical search and interval partitioning analysis.HSIBA employs hierarchical search by manipulating the mantissa of double-precision floating-point numbers to simulate varying precisions,combined with interval partitioning analysis.This approach detects potential maxima of floating-point errors and their corresponding inputs,which are then reported.Evaluation uses 28 expressions from the FPBench standard benchmark suite as test cases,and HSIBA is compared with the advanceddetection tools PSOED and ATOMU.Experimental results demonstrate that HSIBA outperforms PSOED on 16 test cases and ATOMU on 20 test cases.Furthermore,PSOED requires 3.15 times longer on average than HSIBA,while HSIBA exhibits inferior performance compared to ATOMU.

Key words: Floating-point operations, Rounding errors, Error detection, Hierarchical search, Interval partitioning analysis