Posts: 2,761
Threads: 100
Joined: Jul 2005
ALL 00 RAD
f LBL 01
3
ENTER
2
Roll up
COS

/
x^2
RTN
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0 pi g  01 > 9.19705925621 (after 25 minutes)
/
V3.2r3371 here. The exact result is 2*pi*sqrt(3) = 10.8827961854. I wonder what I'm doing wrong.
Posts: 3,229
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Joined: Jul 2006
Quote:
When I replace build 3363 with v2.2 build 2738, it runs significantly faster (<2s). Seems the price for having a lot of free space in flash memory.
This is not the reason at all. The algorithms used by the two different integration routines are completely different. Version 2.2 firmware uses a nonadaptive GaussKronrod quadrature. Version 3 uses an adaptive Romberg method. The former makes exactly 21 function evaluations and returns its result. The latter can do hundreds or thousands of function evaluations.
For well behaved, relatively smooth functions the GaussKronrod method is better  it is exact for polynomials of degree 20 or less (forget the precise order). For less well behaved functions, Romberg is better. As usual things are a trade off.
The space saving changes essential to version 3 firmware have not created orders of magnitude of performance loss. Sure, they slow things down but not nearly by as much as you see here.
 Pauli
Edited: 7 Mar 2013, 5:09 a.m.