, especially when 
is very small, illustrates that a robust computational model does not suffice to ensure good numerical results. The expression 
arises when formulas involving 
are rewritten in exponential form, 
. The problem is not just computing an accurate logarithm; after all, when 
is tiny, 
to within a rounding error. The problem is that merely adding a tiny value 
to 1 will cause significant bits of 
to be rounded off before computing the logarithm. The sum is correctly rounded and the logarithm may be nearly so, but the error suffered by Log(1 + r) can be disastrous in a larger context.
Because this calculation arises so often in financial and engineering applications, the system provides an alternative,
Log1Plus(r), which computes 
without necessarily adding its argument to 1.
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