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Out of curiosity, I conducted a number of integrations on the HP 35S and the HP 42S. I discovered that the two calculators produce identical results, and in identical times if I have the HP 35S in fix 4, and the HP 42S with an accuracy of 1e-05. I was surprised that HP 42S accuracy of 1e-05 was identical in speed, results when shown to full display of digits, and reported accuracy.

I was also expecting that the HP 35S would be slower than the HP 42S as my impression was that the HP 35S was a bit slow!
…I was surprised that fix 4 on the HP 35S was the equivalent of accuracy setting of 1e-05 on the HP 42S.
For integral from 0 to 4 of 1/SQRT(4*X-X^2), fix 3 on the HP 35S and ACC of .001 on the HP 42S are doable, higher accuracy requests result in an integration time that I ran out of patience on both calculators. The HP 35S produced 3.140, the HP 42S produced 3.133. Actual answer is PI.
If you look in the forum archive I believe you’ll find the 35S is one of the fastest HP calcs.
(07-14-2022 02:28 PM)Sukiari Wrote: [ -> ]If you look in the forum archive I believe you’ll find the 35S is one of the fastest HP calcs.

True. Note that the 33s is even faster. In this particular example of taking the integral of 1/sqrt(4x-x^2) from 0 to 4 in FIX 3 mode, the 35s take 149 seconds, but the 33s takes 119 seconds. Saving 30 seconds is nice.
The CASIO 991 EX CLASSWIZ using an interval from 1e-12 to 4-1e-11 came up with a much better answer of 3.14158849 in just 48 seconds (error results from 1/0 division using 0 to 4). The TI-30X Pro MathPrint is fine using 0 to 4, comes up with 3.141587206 after 134 seconds.
Integral take a long time because u-transformed integral, end-points still not zero.

∫(1/√(4x-x^2), x, 0, 4) = ∫(1/√(1-y^2), y, -1, 1) = ∫(3/√(4-u^2), u, -1, 1)

Here, u-transformation only turned infinite end-points to finite (both ends √3), not 0.
If you integrate u-version instead (i.e. u-transformed once more), problem goes away.

https://www.hpmuseum.org/forum/thread-14...#pid127621
An WP34S will give you 8 correct digits, integrating from 0 to 4, in less than 4 seconds.
(07-14-2022 05:08 PM)Joe Horn Wrote: [ -> ]... Note that the 33s is even faster. In this particular example of taking the integral of 1/sqrt(4x-x^2) from 0 to 4 in FIX 3 mode, the 35s take 149 seconds, but the 33s takes 119 seconds. Saving 30 seconds is nice.

The 50g isn't that much better. In FIX 3 mode, it returns 3.13952... in 28.6 seconds. However, in exact mode it returns symbolic PI in 3.8 seconds.
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