Depending on what exactly your f1 etc. are, you may be able to use various
symbolic techniques to reorganize the expression so that it is more
numerically tractable.
For example, you might want to exponentialize then factor or expand. You
may want to expand in a series (try taylor(..., x, inf, 3), etc.
-s
On Fri, Aug 6, 2010 at 11:57, Bastiaan Bergman <Bastiaan.Bergman at wdc.com>wrote:
>
> Exactly! And that "re-arranging by hand" I would like to have some tips
> for,
> or preferably some handy CAS routines. My expr is a very big and
> complicated
> structure of mainly cosh and sinh, I know its right because it gives the
> right answer for small x. Just larger x cannot be evaluated, very
> frustrating...
>
> Anyway, thanks for the B-float tips, for sure nice to play with too.
> Bastiaan.
>
>
>
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:
> maxima-bounces at math.utexas.edu]
> On Behalf Of Dan
> Sent: Friday, August 06, 2010 4:06 AM
> To: Maxima mailing list
> Subject: Re: [Maxima] Expressions with exploding factors
>
> On Thu, 5 Aug 2010, Jeffrey Hankins wrote:
>
> > What's numerical hygiene? I searched for it, but didn't find it.
>
> Imagine you have some number a, and you ask a computer to calculate,
> in floating point,
>
> a-(1.0-1.0e-50)*a
>
> The computer will first work out (1.0-1.0e-50)*a with limited
> precision, introducing an error that is some very small but non-zero
> percentage of (1.0-1.0e-50)*a.
>
> The trouble is, when the computer takes the small difference
> a-(1.0-1.0e-50)*a, that same "small" error becomes a very large
> percentage of the small difference, and the computer gives you an
> answer that is wildly wrong.
>
> What you should do, before passing the expression to the computer, is
> rearrange it by hand (or perhaps by CAS) to
>
> 1.0e-50*a
>
> which doesn't involve taking a small difference between two large
> numbers. Then the computer gets it right. That by-hand rearrangement
> is an example of "numerical hygiene". It can also refer to more
> general rearrangments that reduce the number of individual
> floating-point opeartions the computer has to do, to avoid
> accumulating rounding errors. Unfortunately, the only detailed
> documentation of the use of the term I can find right now is in
> unpublished lecture handouts (Dr. Frank H. King's "Computing
> Techniques and Applications") from the mid-1990s ;-(.
>
> I mentioned it because Bastiaan's original problem involved taking a
> near-unity quotient of two numbers whose logarithms are large, which
> is equivalent to taking a small difference between two large numbers.
>
> --
>
> HTH,
>
> Dan
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