We present RustSmith, the first Rust randomised program generator for end-to-end testing of Rust compilers. RustSmith generates programs that conform to the advanced type system of Rust, respecting rules related to borrowing and lifetimes, and that are guaranteed to terminate normally yielding a well-defined result. This makes Rust suitable for differential testing between compilers or across optimisation levels. We report on our experience applying RustSmith to a series of historic versions of the official Rust compiler, rustc, showing that RustSmith can detect historical insidious compiler bugs that evaded detection for some time, and to an alternative Rust compiler implementation, mrustc. We also present the results of a controlled experiment assessing statement and mutation coverage in comparison to that achieved by the rustc optimisation test suite.