C++11 introduced very useful math functions in the standard like erf and erfc. There are mentions about "guaranteed underflow" for inputs greater or smaller than certain values, but I don't know enough about floating point representation to understand clearly what this means in terms of precision.
If this question makes sense; what precision (order of magnitude at least) can I expect from the approximation implemented by the standard library (if it is specified)?
This depends on the quality of the implementation, which is up to the vendor of the compiler (or runtime libraries, if acquired separately). In the best case, the precision will match the precision of the specific type you use (double, long double, and so on).
Notice that the precision of the returned value is not related to the guaranteed underflow. This is just an enforced postcondition that assures the return value is the special underflow FP value if the input is outside the expected domain.
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