## Integration Accuracy

Discussion around the Swiss Micros DM42 calculator.
lrdheat
Posts: 2
Joined: Tue May 02, 2017 6:17 pm

### Integration Accuracy

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: 888
Joined: Mon Apr 24, 2017 7:48 pm
Location: New York

### Re: Integration Accuracy

lrdheat wrote:
Sun Feb 24, 2019 6:28 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, DM41X: β00071, DM10L: 071/100

Thomas Okken
Posts: 716
Joined: Tue May 02, 2017 5:48 pm
Location: United States
Contact:

### Re: Integration Accuracy

lrdheat wrote:
Sun Feb 24, 2019 6:28 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.