|Re: Just why is the HP-35s so slooow?|
Message #5 Posted by Karl Schneider on 3 Sept 2007, 4:33 p.m.,
in response to message #1 by Jeff Kearns
Welcome, Jeff --
.. but when I compare (the HP-35s) to the trusty 32sii, it just doesn't measure up, especially for definite integral evaluation and I do not understand why. One example is the evaluation of Vardi's integral ... to 5 decimal places;
There's an unobvious, but important difference between the HP-32SII and the HP-33s/35s in the meaning of the display setting for specifying the "uncertainty" of the user's integrand function.
On the HP-35SII, "FIX 5" sets an absolute uncertainty of 0.000005 -- i.e., the fifth decimal digit is assumed to show the correct rounded function value. On the HP-33s and HP-35s, "FIX 5" sets a relative uncertainty of 0.00001 -- i.e., the uncertainty is the absolute value of the function multiplied by 1E-05.
So, if the magnitude of the integrand function is small (say, less than 0.1), "FIX n" specifies a tighter tolerance for the integrand on the HP-35s than on the HP-32SII. This will prompt more evalutations of the functions, and longer execution time for integration. Conversely, if the magnitude of the integrand function is large (say, greater than 10), the HP-35s, er, might be faster for a "FIX n" setting.
That difference having been acknowledged, the HP-35s does seem to be substantially slower for integration than the HP-33s. My favorite example is that of integrating
f(x) = sqrt(x)/(x-1) - 1/ln(x)
for x between 0 and 1.
(This problem was originally presented in the HP Journal article from 1980 describing the INTEG function on the HP-34C. The example was later presented in the HP-15C Advanced Functions Handbook, the HP-71B Math ROM manual, and probably others.)
With a "FIX 6" setting, the HP-33s and HP-35s return the same results (0.0364899763890 with estimated error 3.648998E-08). Representing f(x) as a keystroke program (not an equation), the HP-35s takes 4:05 minutes; the HP-33s takes 2:15 minutes.
Neither the HP-33s nor the HP-35s manuals explain the details of the integrand accuracy setting. I inferred it from comparisons with the HP-48G, for which the methods are explained and the results are identical. Please see the following article and thread:
HP SOLVE-INTEG on all RPN-based models
Uncertainty and accuracy for numerical integration
Edited: 4 Sept 2007, 11:38 p.m. after one or more responses were posted