Re: Just why is the HP35s 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 
Quote:
.. but when I compare (the HP35s) 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 HP32SII and the HP33s/35s in the meaning of the display setting for specifying the "uncertainty" of the user's integrand function.
On the HP35SII, "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 HP33s and HP35s, "FIX 5" sets a relative uncertainty of 0.00001  i.e., the uncertainty is the absolute value of the function multiplied by 1E05.
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 HP35s than on the HP32SII. 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 HP35s, er, might be faster for a "FIX n" setting.
That difference having been acknowledged, the HP35s does seem to be substantially slower for integration than the HP33s. My favorite example is that of integrating
f(x) = sqrt(x)/(x1)  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 HP34C. The example was later presented in the HP15C Advanced Functions Handbook, the HP71B Math ROM manual, and probably others.)
With a "FIX 6" setting, the HP33s and HP35s return the same results (0.0364899763890 with estimated error 3.648998E08). Representing f(x) as a keystroke program (not an equation), the HP35s takes 4:05 minutes; the HP33s takes 2:15 minutes.
Neither the HP33s nor the HP35s manuals explain the details of the integrand accuracy setting. I inferred it from comparisons with the HP48G, for which the methods are explained and the results are identical. Please see the following article and thread:
HP SOLVEINTEG on all RPNbased models
Uncertainty and accuracy for numerical integration
 KS
Edited: 4 Sept 2007, 11:38 p.m. after one or more responses were posted
