Integration Accuracy

Discussion around the Swiss Micros DM42 calculator.
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lrdheat
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Joined: Tue May 02, 2017 4:17 pm

Integration Accuracy

Post by lrdheat » Sun Feb 24, 2019 5:28 pm

I am curious...I notice that the DM42 and Free42 both produce better indicated accuracies for the same epsilon for integrals than on the 42S.

What (in simple terms) is the reason that the accuracy is improved over the 42S?

rprosperi
Posts: 410
Joined: Mon Apr 24, 2017 5:48 pm
Location: New York

Re: Integration Accuracy

Post by rprosperi » Sun Feb 24, 2019 7:36 pm

lrdheat wrote:
Sun Feb 24, 2019 5:28 pm
What (in simple terms) is the reason that the accuracy is improved over the 42S?
The DM42 (built using Free42) use 34 internal digits, while the 42S uses 15 internal digits (12 visible).
--bob p

DM42: β00071 & 00282

Thomas Okken
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Re: Integration Accuracy

Post by Thomas Okken » Sun Feb 24, 2019 8:14 pm

lrdheat wrote:
Sun Feb 24, 2019 5:28 pm
the DM42 and Free42 both produce better indicated accuracies for the same epsilon for integrals than on the 42S.
You tend to get better accuracy for the same epsilon (or rather, ACC) because the error estimate used by Free42 is not very sharp, so it will often iterate for one more step than the HP-42S, giving an end result that is more accurate than it needs to be.

This is computationally wasteful, because every extra iteration doubles the amount of work, but since the hardware that Free42 runs on, including the DM42, is a lot faster than the HP-42S, it can get away with that.

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