Somewhat inspired by somebody's question on Reddit, I thought it might be useful to do a little infodump on what I know of how graphing speed differs between 8x calculator models and OS versions.
  • The baseline TI-83+ is the baseline. I have nothing interesting to say about that.

  • The 83+ SE runs the same OS versions as the baseline 83+ but runs the CPU at 15 MHz rather than the baseline 8 MHz, so should be about twice as fast.

  • The monochrome 84 models (TI-84+ and TI-84+ SE) run the CPU at the same 15 MHz as the 83+ SE, so for most operations they should also be about twice as fast as the baseline 83+.
    However, OS 2.30 added asymptote detection when graphing functions which makes graphing much slower than the baseline. Sadly, versions before 2.30 (2.21, 2.22) are said to have various bugs that make them problematic for various use, and later versions with TestGuard (2.40 and up) or MathPrint (2.53MP and up) might be required for some uses.
    Graphing in Parametric mode doesn't support asymptote detection so should be as fast as would be expected based on the CPU speed.

  • The TI-84 Plus Color Silver Edition (CSE) is very slow all around because its high-resolution color screen is a poor fit for its architecture which is largely unchanged from the monochrome calculators. It does however have an option to disable asymptote detection in the FORMAT (2ND->ZOOM) menu, so disabling that should regain some graphing speed.

  • The TI-84 Plus CE (and all variants such as the TI-83 Premium CE and various Python Editions) has basically the same feature set as the CSE but is generally fast- exactly how much so I'm not sure since I don't own one myself nor have I tried to do any true comparison.

The main conclusion to draw here is that asymptote detection is very slow, so if your graphing performance is not as good as you'd expect you may be able to turn it off and make graphing much faster (at the cost of vertical asymptotes being drawn as vertical lines rather than discontinuities).



Rather annoyingly, the Internet Archive doesn't seem to have a copy of the threads on the Detached Solutions forum linked from the OS 2.30 discussion on calcg, and the DS forum seems to have been removed at some point (rather reasonably, since it was basically dead and probably tedious to handle spam). I'm following up with the DS staff I have contacts for to see if anybody kept a copy.
Approximate time to graph Y=X with default settings (except where noted) on various models:

TI-84 Plus CE, rev. N, OS 5.4.0: 1.5 seconds (asymptote detection on) / 0.5 seconds (asymptote detection off)
TI-81, rev. pre-A, OS 1.0: 2 seconds
TI-81, rev. B, OS 1.8K: 2 seconds
TI-92 Plus, rev. A, OS 2.09: 2 seconds
TI-89 Titanium, rev. R, HW4, OS 3.10: 3 seconds (same with discontinuity detection on or off)
TI-84 Plus CE, rev. C, OS 5.3.0: 3 seconds (asymptote detection on) / 1 second (asymptote detection off)
TI-80 ViewScreen, rev. B, OS 4.0: 3.5 seconds
TI-80, rev. C, OS 4.0: 3.5 seconds
TI-80, rev. A, OS 3.0: 4 seconds
TI-86, rev. E, OS 1.4: 4 seconds
TI-86, rev. K, OS 1.6: 4 seconds

Note that the graphing speed depends not only on the CPU speed but also on the other hardware & the OS. For example, both TI-84 Plus CEs have the same CPU speed, & the TI-81s have the same CPU speed as the TI-86 (& in the case of the rev. B TI-81, even the same ASIC & thus CPU).

EDIT: Not a plain TI-89
On my rev. I CE (OS 5.2.2) graphing Y=X takes... (average of three trials each)

    3.7 seconds with detect asym on
    1.5 seconds with detect asym off
    1 second using dot-thin instead of the default thick and detect asym off


I used my phone's stopwatch, it might be nice to time these without human error using CEmu. I thought the last number was particularly interesting- I used to switch to one of the dot modes if I was feeling impatient because it felt faster. It's nice to see it is actually faster.
  
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