Machine error in computer arithmetic
Yes! Various languages and APIs often specify the precision you are guaranteed.  If the underlying hardware doesn't offer that precision, they must emulate it with extra work.  For instance, some machine instructions that compute transcendental function (sin, cos, exp, log, ...) only offer a limited accuracy. Library implementations that guarantee a certain accuracy must execute extra instructions to accomplish that by correcting the error and improving the approximation.

As a concrete example, consider the native_sin function in OpenCL.  The error is "implementation defined." On the other hand, the regular sin function promises a certain accuracy and implementation of OpenCL must make that happen regardless of the extra work.