Why does Intelligent math give this strange answer?

02252024, 11:57 PM
Post: #1




Why does Intelligent math give this strange answer?  
02262024, 02:58 AM
(This post was last modified: 02262024 03:02 AM by Steve Simpkin.)
Post: #2




RE: Why does Intelligent math give this strange answer?  
02262024, 06:14 AM
(This post was last modified: 02262024 06:57 AM by nickapos.)
Post: #3




RE: Why does Intelligent math give this strange answer?
(02262024 02:58 AM)Steve Simpkin Wrote: The TI89 gives a slightly different answer of 2.71456748202. I am getting 2.71456748459 on my app which does not have an option for intelligent math at all and this matches the results on my physical device with the latest firmware and with intelligent math enabled. Not sure why intelligent math is missing on my app which is the latest. 

02262024, 01:41 PM
Post: #4




RE: Why does Intelligent math give this strange answer?
(02262024 06:14 AM)nickapos Wrote:(02262024 02:58 AM)Steve Simpkin Wrote: The TI89 gives a slightly different answer of 2.71456748202. Regarding your physical device, please make sure you are not in the CAS mode, Is it still the correct answer? 

02262024, 02:21 PM
(This post was last modified: 02262024 02:22 PM by rawi.)
Post: #5




RE: Why does Intelligent math give this strange answer?
Quote: When I select "Intelligent math" in settings I get a strange result with simple equation (noncas) This is confirmed in nonCASmode with the physical device. I get the same result 9.9999..E499/9.9999...E499. If I compute approx(9.9999..E499/9.9999...E499) I get the result "Undefined". 

02262024, 02:26 PM
Post: #6




RE: Why does Intelligent math give this strange answer?
I tried with (1+1/100)^100 and I got 2,70481..E200/1E200.
So this seems to be an overflow. If you put in (11/365)^365 and use the approx key (blue  enter) you get 2.71456748459. 

02262024, 02:45 PM
Post: #7




RE: Why does Intelligent math give this strange answer?
You’ve typed in an exact expression  no decimal points in any of your numbers  so it tries to evaluate it exactly, as a rational number. Both numerator and denominator overflow, so this fails. (Also, Home mode doesn’t have large integers.)
I think this is acceptable. What I don’t like is that putting a decimal point in one of the numbers (i.e., 1. instead of 1) doesn’t change this behaviour. CAS mode is better here  it gives the exact rational answer with no decimal, and the numerical answer if I put “365.” in the denominator. Nigel (UK) 

02262024, 03:07 PM
Post: #8




RE: Why does Intelligent math give this strange answer?
(02262024 02:45 PM)Nigel (UK) Wrote: You’ve typed in an exact expression  no decimal points in any of your numbers  so it tries to evaluate it exactly, as a rational number. Both numerator and denominator overflow, so this fails. (Also, Home mode doesn’t have large integers.) Excellent! Thank you 

02262024, 06:13 PM
Post: #9




RE: Why does Intelligent math give this strange answer?
(02262024 02:26 PM)rawi Wrote: I tried with (1+1/100)^100 and I got 2,70481..E200/1E200. The HP50 gets the same answer which is notably less accurate than the TI. EVALuating the expression in exact mode returns, after a long calculation, a fraction with 936digit numerator and denominator. Converting to an approximate number also returns 1. However, taking the first 20 digits of the numerator and denominator, dividing and converting to approximate, return the correct value 2.71456748202. Clearly the Prime and the HP50 both have problems with fractions having very large terms. 

02262024, 09:54 PM
(This post was last modified: 02262024 10:41 PM by Steve Simpkin.)
Post: #10




RE: Why does Intelligent math give this strange answer?
Here are answers from some of the calculator models I had handy.
TI57: 2.714567 TI59: 2.714567482 TI86, TI95, TI89, WP 34S: 2.71456748202 TI34 MultiView, TI36X Pro: 2.714567482 Casio fx8000G, fx115ES PLUS, fx991EX, fxCG50: 2.714567482 HP35, HP25: 2.714567463 HP27, HP67, HP34C, HP41C, HP15C, HP12C: 2.714567455 HP48SX, HP48GX, HP42S: 2.71456748459 HP 50g (aprox mode): 2.71456748459 HP 35s: 2.71456748459 Free42 (decimal): 2.714567482021874303193886306685083 WP43: 2.714567482021874303193886306685084 Sharp ELW535X: 2.714567482 

02272024, 06:44 PM
Post: #11




RE: Why does Intelligent math give this strange answer?
Canon F605G, Sharp EL510RT, Sharp EL9950, Casio fx5800, TI74,
2.714567482 Sharp EL501TB, Sharp EL5500II, Sharp PC1403, Casio fx82 Solar II with fraction 2.7145677475 TI57 II 2.7145677 Citizen SRP75 2.714567485 

02282024, 04:31 PM
Post: #12




RE: Why does Intelligent math give this strange answer?
(02262024 02:26 PM)rawi Wrote: So this seems to be an overflow. I don't have a Prime, but I believe the processing in this case is similar to what happens with the 50g. On the 50g, there is a system flag (21) that controls whether an overflow triggers an error (21 is SET), or simply uses the "maximum real" of 9.99999999999E499 and keeps on processing (21 is CLEAR). The default status for the flag is cleared, meaning no error is thrown. Setting system flag 21 on the 50g will cause an overflow error to be thrown when attempting to convert the exact fractional result to an approximate number with >NUM. Clearing system flag 21 essentially tells the 50g to cap any numeric values to 9.99999999999E499 (or the corresponding negated value for negative numbers). Thus, in this case, returning "1." since the fractional result simply becomes 9.99999999999E499/9.99999999999E499. Does the Prime also have a similar "overflow mode" for this? Regarding the accuracy of the approximate results, I believe we're simply seeing the difference that the lack of guard digits makes for this type of expression. The HP calculators giving a result of 2.71456748459 are giving the most accurate result they can given all the numeric values in the calculation are limited to 12 significant digits. In particular for this example, digits are lost when adding 1 to 1/365, a typical scenario for financial calculations and perhaps one of the main reasons that the LNP1 and EXPM functions were included in some of the calculators. Executing this on a 50g: Code: « 365. INV LNP1 365. * EXP » 

02282024, 05:04 PM
Post: #13




RE: Why does Intelligent math give this strange answer?
(02282024 04:31 PM)DavidM Wrote: In particular for this example, digits are lost when adding 1 to 1/365, a typical scenario for financial calculations and perhaps one of the main reasons that the LNP1 and EXPM functions were included in some of the calculators. Exactly ! Also on the 41C: 365 ENTER 1/x LN1+X * EXP > 2.714567481 Or in the other way, calculating with the same 10digit input number (1.002739726)^365 on every machine gives very close results, except the early HP (before the HP22/HP27 improvement): HP41C: 2.714567455 HP42S: 2.71456745495 Free42 : 2.714567454950368... No "errors", all machines are doing their best, the fault entirely to the input value. JF 

03022024, 05:54 PM
Post: #14




RE: Why does Intelligent math give this strange answer?
f:=(1+1/365)^365 in CAS returns a fraction with numerator and denominator having about 900 digits, evalf(f) returns 2.71456748202, seems correct.


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