> I 've done a little playground-style OCaml coding and the feeling you get with OCaml is that once your program compiles, it most likely also runs correctly.

This is only a feeling. Without carefully testing the code to exercise its cases, all you know is that they are properly typed.

For instance, suppose we write a complicated function (or group of functions) which goes through a block of intermediate code (output of a compiler) and assigns registers to all the temporaries, introducing memory spills in situations where more variables are live than the available registers.

We might have a feeling that because this code compiles, it must be free of problems such as accidentally assigning the same register to two variables which have overlapping lifetimes.

That feeling is poorly supported by reality; it is the "safyness" of static typing.

Untested code is garbage. And thorough testing is difficult to impossible, so there is a bit of garbage in almost all software, unfortunately.

Statically type checked code has all of its code paths effectively tested by the compiler, but those tests have only the limited point of view of trying to show that the program contains a trivial type mismatch, a close cousin of the syntax error. These "tests" are not actually feeding values into the code and trying to make it fail or behave incorrectly with respect to its specification.