There are exceptions. But the type of barycentric interpolation formula that leads to Inf/Inf at an interpolation point isn't one of those exceptions - it's an

There are exceptions. But the type of barycentric interpolation formula that leads to Inf/Inf at an interpolation point isn't one of those exceptions - it's an example which shows why the rule should be borne in mind. When the input is very close to one of the interpolation points, the calculation becomes ill-conditioned, unsurprisingly as two values are diverging towards Inf, so the result can become incorrect as the input approaches the interpolation point, until it becomes Inf/Inf = Nan at some even closer, but non-zero, distance. Before reaching Nan it can also have an interval where the result is +/-Inf. It depends on the interpolation points. But under some circumstances, it is necessary to recognise when the input is close to an interpolation point, and adjust the formula appropriately.