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The IBM ACRITH package of numerical software is advertised as reliable and easy to use; but sometimes its results must astonish or confuse a naive user. This report exhibits a few of the surprises. For instance, a finite continued fraction, easy to evaluate in two dozen keystrokes on a handheld calculator, causes ACRITH to overflow either exponent range or 15 Megabytes of virtual memory. Lacking access to source code, we must speculate to explain the anomalies. Some seem attributable to small bugs in the code; some to optimistic claims or oversimplifications in the code's documentation; some to flaws in the doctrine underlying the code. We conclude that different techniques than used by ACRITH might have been about as accurate and yet more economical, robust and perspicuous.