The disclosed embodiments relate to a system that gathers telemetry data while testing a computer system. During operation, the system obtains a test script that generates a load profile to exercise the computer system, wherein a running time of the test script is designed to be relatively prime in comparison to a sampling interval for telemetry data in the computer system. Next, the system gathers telemetry data during multiple successive executions of the test script on the computer system. The system merges the telemetry data gathered during the multiple successive executions of the test script, wherein the relatively prime relationship between the running time of the test script and the sampling interval for the telemetry data causes a sampling point for the telemetry data to precess through different points in the test script during the multiple successive executions of the test script, thereby densifying sampled telemetry data points gathered for the test script. Finally, the system outputs the densified telemetry data.