HP calcs are really not that accurate..

[SlideRule]

"There are four properties of computers that are relevant to their use in the
numerical solution of problems of algebra and analysis. These properties are
causes of many pitfalls:
(i) Computers use not the real number system, but instead a simulation of
it called a "floating-point number system." This introduces the problem of
round-off.
(ii) The speed of computer processing permits the solution of very large
problems. And frequently (but not always) large problems have answers that
are much more sensitive to perturbations of the data than small problems are.
(iii) The speed of computer processing permits many more operations to be
carried out for a reasonable price than were possible in the pre-computer era.
As a result, the instability of many processes is conspicuously revealed.
(iv) Normally the intermediate results of a computer computation are hidden
in the store of the machine, and never known to the programmer. Consequently
the programmer must be able to detect errors in his process without seeing
the warning signals of possible error that occur in desk computation, where
all intermediate results are in front of the problem solver. Or, conversely, he
must be able to prove that his process cannot fail in any way".
Pitfalls in Computation, or Why a Math Book Isn't Enough by George E. Forsythe (Stanford University)