On Monday 07 February 2005 02:22, I wrote:
> I imagine (but did not prove) that the maximum error is quite similar
> over all the intervals between .5 and 1, because the curvature of 1/x
> doesn't change much in that interval...

This turned out to be wrong.  The result for the left end of the 
interval is:

>>> ((1/.501 + 2)/2 - 1/.5005)
1.9940139697194326e-06

or about one part in 500,000, i.e., 19 bits of accuracy.  Just enough.

It's kind of surprising that the maximum error varies by a factor of 8 
over the interval [.5, 1].  Could somebody please double check my 
reasoning?

Regards,

Daniel
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