How about this case:
(%i3) exp(-1000.0) * exp(1000);
(%o3) 0.0
Barton
-----"Robert Dodier" <robert.dodier at gmail.com> wrote: -----
>To: "Barton Willis" <willisb at unk.edu>
>From: "Robert Dodier" <robert.dodier at gmail.com>
>Date: 06/07/2007 07:26PM
>cc: "Detlef Schmicker" , maxima-help
><maxima at math.utexas.edu>
>Subject: Re: [Maxima] Possible bugs in integrate?
>
>On 6/7/07, Barton Willis <willisb at unk.edu> wrote:
>
>> (%i65) ff:exp(-x^2/50^2)*sin(x)^2*cos(2*x)$
>> (%i66) gg : integrate(ff,x,-4*%pi,4*%pi)$
>> (%i67) float(gg);
>> (%o67) 0.0
>> (%i68) float(expand(gg));
>> (%o68) -6.153361529128077
>>
>> Look at both gg and expand(gg). You should see why (%o67) = 0.0, but
>> (%o68) isn't 0.0.
>
>%o67 = 0.0 looks to me like a bug in GCL's floating point math.
>There is one term exp(10000) and another one exp(-10000).
>The first yields a floating point inf and the second, 0.0.
>The product should be NaN (not-a-number).
>
>SBCL could probably be coaxed into yielding NaN for %o67.
>(Clisp cannot, to the best of my knowledge.)
>
>About this stuff,
>
>>(%i164) integrate(ff,x,-4*%pi,4*%pi);
>>(%o164) -(%e^(-36)*sqrt(%pi)*(3*erf((4*%pi+18*%i)/3)-6*%e^27*erf((4*%pi
>>+9*%i)/3)-6*%e^27*erf((4*%pi-9*%i)/3)+3*erf((4*%pi-18*%i)/3)+6*%
>>e^36*erf((4*%pi)/3)))/8
>>
>>(%i165) float(%);
>>(%o165) -5.1390589659105944*10^-17*(3.0*erf(0.33333333333333*(18.0*%i
>>+12.56637061435917))-3.192289443610792*10^+12*
>>erf(0.33333333333333*(9.0*%i+12.56637061435917))-3.192289443610792*10^
>>+12*erf(0.33333333333333*(12.56637061435917-9.0*%i))+3.0*
>>erf(0.33333333333333*(12.56637061435917-18.0*%i))+2.5867389201337716*10^
>>+16)
>
>I wonder if Maxima could output something nicer here.
>(1) Could erf applied to a complex float (i.e. float + %i * float)
>yield a float or complex float?
>(2) I tried abs(%o165) and realpart(%o165) and imagpart(%o165)
>to try to get real floats from the %o165 but abs and friends didn't
>seem to know how to do something useful with it. I wonder what
>we could do to change that. Maybe (2) is moot if (1) is implemented.
>
>FWIW
>Robert Dodier