Conformance checking compares a process model to its corresponding execution log, to detect inconsistencies and improve compliance with business processes. Nowadays, driven by trends such as big data and process automation, business processes are becoming more complex and integrated. Unfortunately, a major downside of the current standard-de-facto technique of alignment is that alignment suffers from poor performance (worst-case exponential time complexity) on an unstructured event log or a spaghetti-like process model. Therefore, the main purpose of this paper is to provide an approach to estimating the fitness. Since the fitness of different traces could be extremely close, we first propose that an event log contains a tiny number of traces with new information in the context of token-based replay. Then, we can estimate the fitness through a sub-event log composed of at most 6 % traces. Experiments on real-life event logs demonstrate that the fitness of the complete log can be estimated using only 1% traces.