This paper presents evidence-based dynamic analysis, an approach that enables lightweight analyses--under 5% overhead for these bugs--making it practical for the first time to perform these analyses in deployed settings. The key insight of evidence-based dynamic analysis is that for a class of errors, it is possible to ensure that evidence that they happened at some point in the past remains for later detection. Evidence-based dynamic analysis allows execution to proceed at nearly full speed until the end of an epoch (e.g., a heavyweight system call). It then examines program state to check for evidence that an error occurred at some time during that epoch. If so, it rolls back execution and re-executes the code with instrumentation activated to pinpoint the error. We present DoubleTake, a prototype evidence-based dynamic analysis framework. DoubleTake is practical and easy to deploy, requiring neither custom hardware, compiler, nor operating system support. We demonstrate DoubleTake's generality and efficiency by building dynamic analyses that find buffer overflows, memory use-after-free errors, and memory leaks. Our evaluation shows that DoubleTake is efficient, imposing just 4% overhead on average, making it the fastest such system to date. It is also precise: DoubleTake pinpoints the location of these errors to the exact line and memory addresses where they occur, providing valuable debugging information to programmers.