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Casio fx-991EX vs Hp 50g speed difference
07-13-2018, 08:50 PM (This post was last modified: 07-13-2018 08:52 PM by Tugdual.)
Post: #1
Casio fx-991EX vs Hp 50g speed difference
Found something weird.
Was speed testing the fx991ex vs 50g on \(\int_0^{500}e^{-x} dx \)
Results:
fx-991EX: result:1 time:6.64s
50g using ->NUM : result:1 time:46.69s

Huge difference...

Pressing EVAL on the 50g returns instantly \( - \frac {1-e^{500}}{e^{500}} \) which seems to indicate that CAS was used since this is the exact result.

I'm a bit surprised the 50g performs so poorly since I doubt the fx991ex uses any smart CAS behind the scene. Any thoughts on that?
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07-13-2018, 10:36 PM (This post was last modified: 07-13-2018 10:44 PM by StephenG1CMZ.)
Post: #2
RE: Casio fx-991EX vs Hp 50g speed difference
On HP Prime I get result 1-(1/e^500), in 20 ms (Android), using CAS.

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07-13-2018, 11:13 PM
Post: #3
RE: Casio fx-991EX vs Hp 50g speed difference
(07-13-2018 08:50 PM)Tugdual Wrote:  I'm a bit surprised the 50g performs so poorly since I doubt the fx991ex uses any smart CAS behind the scene. Any thoughts on that?

I can't really say why the HP 50g takes awhile to get an approximate answer for the given integral. I do know that if you take it out of Standard format and put it into a smaller number format like Fix 4, it would get a numeric answer quicker with an accuracy up to the given number format. But you probably knew that already.

(07-13-2018 08:50 PM)Tugdual Wrote:  Pressing EVAL on the 50g returns instantly \( - \frac {1-e^{500}}{e^{500}} \) which seems to indicate that CAS was used since this is the exact result.

Weird right? The difference between Exact and Approx. speeds in this case is very interesting and I don't know why that is. I get the answer in 0.70 milliseconds if I want an exact result. And when I press ->NUM on the exact result, it solves the exact answer in .06 milliseconds. This means I can get the approximate result of the integral in .76 milliseconds, beating the Casio. But every attempt to solve the integral approximately, I get a 47 second wait. I'm sorry, I don't have a guess on why it does this.

(07-13-2018 10:36 PM)StephenG1CMZ Wrote:  On HP Prime I get result 1-(1/e^500), in 20 ms (Android), using CAS.

The Prime is great isn't it? But the 50g getting the same answer in .70 milliseconds is also impressive to me.

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07-14-2018, 01:45 AM
Post: #4
RE: Casio fx-991EX vs Hp 50g speed difference
(07-13-2018 08:50 PM)Tugdual Wrote:  Found something weird.
Was speed testing the fx991ex vs 50g on \(\int_0^{500}e^{-x} dx \)
Results:
fx-991EX: result:1 time:6.64s
50g using ->NUM : result:1 time:46.69s

Huge difference...

The function e^-x is not very well-behaved for integration over the interval [0, 500], being close to zero for most of it. Everything happens in a small interval near 0, and that kind of thing makes some numerical integrators converge rather slowly. On my HP-42S, which I'm guessing uses the same Romberg integration algorithm as the RPL numerical integrator, the integral in question takes 2047 evaluations of the function (with ACC=0, which is full accuracy), taking 4 minutes and 4 seconds.
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07-14-2018, 03:17 AM (This post was last modified: 07-14-2018 03:18 AM by Albert Chan.)
Post: #5
RE: Casio fx-991EX vs Hp 50g speed difference
I wonder if Casio flush values below 1e-99 to zero, which might save time
for integration (flush-to-zero section "converge" to zero area right the way)

For a fair test, try limit of 0 to 200

Just curious, is the final result same for both calculator ?
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07-14-2018, 10:27 AM
Post: #6
RE: Casio fx-991EX vs Hp 50g speed difference
another result that may be interesting.

http://www.hpmuseum.org/forum/thread-9750.html (sum, trig, power/root , exp/log)

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07-14-2018, 03:10 PM (This post was last modified: 07-14-2018 03:11 PM by ijabbott.)
Post: #7
RE: Casio fx-991EX vs Hp 50g speed difference
(07-14-2018 10:27 AM)pier4r Wrote:  another result that may be interesting.

http://www.hpmuseum.org/forum/thread-9750.html (sum, trig, power/root , exp/log)

I appear to have one of the "fast" batch. The diagnostics show "CY-235 VerB".

To enter diagnostics mode, while holding "SHIFT" and "7" together, press "ON", then release all buttons. You should see:
Quote:DIAGNOSTIC

Press AC

(If it doesn't work, press and release "ON" first, then try again.)

Pressing "9" in diagnostic mode shows:
Quote:8888888888888888

8.888888889x10^15

Then pressing "SHIFT" repeatedly goes through some display tests, ending with:
Quote:CY-235 VerB

Press AC

(The version may be different on the "slow" batch.)

Pressing "AC" shows "00" in the top corner of the display. If you press the keys in the correct order, it increments to "01", "02" etc.

On the initial diagnostic screen, pressing "8" goes into a more brief keyboard test where various labels get highlighted when you press the corresponding key (although the \(x\) key is labelled as "[logab]" for some reason!). After pressing all the keys, the display changes to:
Quote:Solar MODEL OK!

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07-16-2018, 07:07 AM (This post was last modified: 07-16-2018 07:08 AM by Tugdual.)
Post: #8
RE: Casio fx-991EX vs Hp 50g speed difference
Just for the records mine says
CY-235 VerF
And seems to belong to the fast batch
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Yesterday, 04:28 AM (This post was last modified: Yesterday 05:50 AM by brickviking.)
Post: #9
RE: Casio fx-991EX vs Hp 50g speed difference
(07-13-2018 08:50 PM)Tugdual Wrote:  Found something weird.
Was speed testing the fx991ex vs 50g on \(\int_0^{500}e^{-x} dx \)
Results:
fx-991EX: result:1 time:6.64s
50g using ->NUM : result:1 time:46.69s

Huge difference...

My upgraded 9750GII gave me 1 for that formula: \( \int \)(e^-X,0,500), almost immediately. If I add a tolerance value: \( \int \)(e^-X,0,500,0.01) I get 1.000000014 in about 0.5 seconds
for tolerance values of 0.009 to 0.1724, and 1.000050478 (for a tolerance value of >0.1724 to 0.66558). Larger tolerance values affect the result more. It'd be interesting to see whether the 991EX has this tolerance value in the formula it uses.

(07-13-2018 08:50 PM)Tugdual Wrote:  Pressing EVAL on the 50g returns instantly \( - \frac {1-e^{500}}{e^{500}} \) which seems to indicate that CAS was used since this is the exact result.

My HP50G gave me \(\frac {e^{500}-1}{e^{500}} \) instantly instead of \( - \frac {1-e^{500}}{e^{500}} \) when I hit EVAL from the equation writer. I presume those two are equivalent. I also observed the Approx/Exact discrepancy.

(Post 258)

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