Synthetic data generation has become a cornerstone for advancing large language models. However, the lack of the quantitative analysis for error tolerance became a critical bottleneck. Consequently, current filtering strategies fluctuate between two extremes: they are either overly aggressive, risking the exclusion of potentially valuable samples, or overly permissive, failing to eliminate erroneous samples effectively. To bridge this gap, this paper introduces **A**tomic **T**ree **O**peration **M**odeling (**ATOM**), a framework that decomposes data into functional units (f(x)→ y). ATOM distinguishes *benign Operand* x *perturbations* from *fatal Operator* f *perturbations*. The former are needlessly discarded by aggressive filtering, while the latter slip through permissive filtering. Our experiments reveal a **double dissociation**: models are robust to operand perturbations but collapse under operator perturbations. By prioritizing operator over aggressive operand precision, our ATOM-synthesized data outperforms rigorous baselines (e.g., +3.1% gain over LIMA), suggesting that operator diversity matters more than operand precision. Our code is available at [GitHub](https://github.com/Lut-hub/ATOM).