Floating point is notorious for the rounding errors, which could propagate and accumulate to unacceptable results. Detecting inputs that can trigger large floating-point errors is crucial for improving the reliability of numerical programs. Existing error-inducing input generation approaches either heavily depend on the expensive shadow executions with high precision computations or suffer from false positives. This paper introduces chain conditions to capture the propagation and accumulation of floating-point errors and utilize them to guide the search for error-inducing inputs. We implement a tool named FPCC and evaluate it on 88 functions from the GNU Scientific Library and 21 multiple inputs functions from previous researches. The experimental results demonstrate the effectiveness and efficiency of our approach: (1) FPCC achieves 100% accuracy in detecting significant errors for the reported rank-1 inputs, while 72.69% rank-1 inputs of the state-of-the-art tool ATOMU can trigger significant errors. Overall, 99.64% (1049/1053) of the inputs reported by FPCC can trigger significant errors, whereas only 19.45% (141/723) of the inputs reported by ATOMU can trigger significant errors; (2) FPCC exhibits a 2.17x speedup over ATOMU in detecting significant errors; (3) FPCC also excels in supporting multiple inputs functions, outperforming the state-of-the-art technique. To facilitate follow-up research in the community, we make FPCC available on GitHub at \url{https://github.com/DataReportRe/FPCC}.