Text under Semantics reads:
"Implementations should be wary of actually calculating PEARSON this way, due to numerical instability issues."
"...be wary..."? Perhaps a note, if it says what those "issues" may be.
BTW, in researching this function I found: http://www.statemaster.com/encyclopedia/Correlational-research
It may just be a presentation issue but does the square root on the denominator extend across both of the summation signs?
Oh, the resource I cite above alleges a better way to calculate this function with numeric stability.