I became one of the 15c collecting Crowd

[Valentin Albillo]

.
Hi, Johnh,

Quote:Interesting to hear about the results from different machines.

Good. Here's some other HP results for you, obtained directly from the command line (no programming needed) using the HP-71B:

>INTEGRAL(0,6,1E-4,EXP(IVAR*IVAR*IVAR))


5.96393743820E91 in 0.39" @ 128x (50" physical), ~7 correct digits

>INTEGRAL(0,6,1E-6,EXP(IVAR*IVAR*IVAR))


5.96393809255E91 in 0.78" @ 128x (1' 40" physical), ~10 correct digits

Again, note that no programming was needed, just a very short expression executed directly from the command line and there you are.

Frankly, this isn't a really difficult integral at all, I've seen much, much worse of the same size and furthermore, though the modified Romberg method was surely optimal for the reasons Kahan gives in his HP Journal article re Integral on the HP-34C (mainly because of the serious HP-34C memory limitations,) there are much better, much faster methods (even if coded in user code, let alone in assembler) for machines with no such memory constraints (e.g. the HP-71B and most RPL models,) so I don't quite understand why they weren't used instead.

Just to speculate a little, perhaps to try and achieve some production costs reduction by reusing the old Romberg algorithm instead of implementing a better one and its documentation anew.

V.