If you wrote code that failed to compile, you wouldn't impulsively call your compiler incorrect. This title sounds like it puts the blame in the wrong place. You can get error accumulation from even a basic calculation in a loop. We could try to solve these problems but it's not the algorithm's fault you don't know what you're doing.

This has nothing to do with floating point error accumulation or numerical stability in the floating point sense. You can do this with arbitrary sized floating point values and you will still get the same non-convergence result.