We propose a proof-producing symbolic execution for verification of machine-level programs. The analysis is based on a set of core inference rules that are designed to give control over the tradeoff between preservation of precision and the introduction of overapproximation to make the application to real world code useful and tractable. We integrate our symbolic execution in a binary analysis platform that features a low-level intermediate language enabling the application of analyses to many different processor architectures. The overall framework is implemented in the theorem prover HOL4 to be able to obtain highly trustworthy verification results. We demonstrate our approach to establish sound execution time bounds for a control loop program implemented for an ARM Cortex-M0 processor.