ICE: Reducing Search Space for Error-Inducing Input Detection

Abstract

Floating-point programs play a crucial role in scientific and engineering applications as well as daily life. Due to the inherent inaccuracies of floating-point arithmetic, these programs are susceptible to errors. While only a small subset of possible inputs may lead to significant inaccuracies in the program’s final results, such errors can have serious consequences. Prior approaches have been developed to identify error-inducing inputs using search algorithms. However, the task is challenging due to the sparsity of the search space. Furthermore, these tools frequently depend on high-precision programs as oracles for computing floating-point errors. This reliance introduces additional challenges, including prolonged execution times and instability. To detect these inputs more effectively and efficiently, we propose a simple yet effective method called ICE, designed to generate reduced and erroneous domains for these approaches. ICE first calculates the errors of the target program by taking all half-precision floating-point numbers as inputs. Instead of calculating errors based on high-precision programs, ICE injects small perturbations into each atomic operation of the program and measures the difference between the perturbed and original results to estimate floating-point errors. Subsequently, ICE selects the numbers with errors in the top $\boldsymbol{n\%}$ as the endpoints of the important ranges. These individual ranges, which form domains, can then be used to improve existing tools by reducing the search space. To evaluate ICE, we apply ICE with three state-of-the-art error-inducing input detection approaches, i.e., ATOMU, HSED, and FPCC. Experimental results demonstrate that ICE could improve the performance of existing approaches by effectively reducing the search space, detecting more error-inducing inputs, and significantly shortening the search time.