Performance analysis of a distributed system is typically achieved by collecting profiles whose underlying events are timestamped with unsynchronized clocks of multiple machines in the system. To allow comparison of timestamps taken at different machines, several timestamp synchronization algorithms have been developed. However, the inaccuracies associated with these algorithms can lead to inaccuracies in the final results of performance analysis. To address this problem, in this paper, we develop a system for constructing distributed performance profiles called DProf. At the core of DProf is a new timestamp synchronization algorithm, FreeZer, that tightly bounds the inaccuracy in a converted timestamp to a time interval. This not only allows timestamps from different machines to be compared, it also enables maintaining strong guarantees throughout the comparison which can be carefully transformed into guarantees for analysis results. To demonstrate the utility of DProf, we use it to implement dCSP and dCOZ that are accuracy bounded distributed versions of Context Sensitive Profiles and Causal Profiles developed for shared memory systems. While dCSP enables user to ascertain existence of a performance bottleneck, dCOZ estimates the expected performance benefit from eliminating that bottleneck. Experiments with three distributed applications on a cluster of heterogeneous machines validate that inferences via dCSP and dCOZ are highly accurate. Moreover, if FreeZer is replaced by two existing timestamp algorithms (linear regression & convex hull), the inferences provided by dCSP and dCOZ are severely degraded.