ACURACY
06-22-2016, 05:33 PM (This post was last modified: 06-22-2016 06:15 PM by RPL Calcs.)
Post: #1
 RPL Calcs Junior Member Posts: 22 Joined: May 2016
ACURACY
The result from the evaluation of this equation

ARCSIN(ARCCOS(ARCTAN(TAN(COS(SIN(9)))))) is 8.99999864267
in the Saturn models:

HP-19BII
HP-20S
HP-22S
HP-27S
HP-28C/S
HP-32S/SII
HP-38G
HP-39G
HP-42S
HP-48SX/S/G/GX/G+/GII
HP-49G/G+
HP-50G
HP-71B

Look other results:
http://www.rskey.org/~mwsebastian/miscprj/models.htm

Best regards,
06-22-2016, 05:51 PM
Post: #2
 dalupus Junior Member Posts: 41 Joined: Oct 2014
RE: ACURACY
HP35S 8.99999986001
HPPrime 8.99999864267 In rpn mode
HPPrime 9 in CAS mode

Did we actually find a case where the 35s is actually more accurate at a trig function?
06-22-2016, 06:18 PM (This post was last modified: 06-22-2016 06:24 PM by RPL Calcs.)
Post: #3
 RPL Calcs Junior Member Posts: 22 Joined: May 2016
RE: ACURACY
:0 My HP 15C LE, in DEG mode, evaluates to
9.000417403
the same value of the table.

The HP 42S emulator evaluates to 9.

Quote:HPPrime 8.99999864267 In rpn mode
Question: HP Prime also emulates Saturn? :-)
06-22-2016, 07:08 PM
Post: #4
 Jake Schwartz Senior Member Posts: 320 Joined: Dec 2013
RE: ACURACY
(06-22-2016 06:18 PM)RPL Calcs Wrote:  :0 My HP 15C LE, in DEG mode, evaluates to
9.000417403
the same value of the table.

The HP 42S emulator evaluates to 9.

Quote:HPPrime 8.99999864267 In rpn mode
Question: HP Prime also emulates Saturn? :-)

FWIW, in double-precision mode, on the WP-34S I get:
8.999 999 999 999 999 999 999 999 999 937 535

Jake
06-22-2016, 10:35 PM (This post was last modified: 06-22-2016 10:37 PM by Dieter.)
Post: #5
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: ACURACY
(06-22-2016 06:18 PM)RPL Calcs Wrote:  My HP 15C LE, in DEG mode, evaluates to
9.000417403

That's the perfect result for a 10-digit calculator. If it would return anything closer to 9 or even a plain 9 it would run faulty software.

BTW the other mentioned value 8,99999864267 is the perfect result for a correctly operating 12-digit calculator.

(06-22-2016 06:18 PM)RPL Calcs Wrote:  The HP 42S emulator evaluates to 9.

I don't think that e.g. Free42 returns 9. Maybe that's what you see, but this is not the calculated result. Subtract 9 from this and see what you get. ;-)

Dieter
06-22-2016, 11:18 PM
Post: #6
 Gerson W. Barbosa Senior Member Posts: 1,452 Joined: Dec 2013
RE: ACURACY
(06-22-2016 10:35 PM)Dieter Wrote:
(06-22-2016 06:18 PM)RPL Calcs Wrote:  My HP 15C LE, in DEG mode, evaluates to
9.000417403

That's the perfect result for a 10-digit calculator. If it would return anything closer to 9 or even a plain 9 it would run faulty software.

That's exactly what I get on my HP-12C Prestige running this 399-step program :-)

Gerson.
06-22-2016, 11:44 PM
Post: #7
 RPL Calcs Junior Member Posts: 22 Joined: May 2016
RE: ACURACY
Quote:I don't think that e.g. Free42 returns 9. Maybe that's what you see, but this is not the calculated result. Subtract 9 from this and see what you get. ;-)

The emulator is Free42. You´re RIGHT. 9 9 - returns -6.2466E-29
06-23-2016, 07:49 AM (This post was last modified: 06-23-2016 07:53 AM by Dieter.)
Post: #8
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: ACURACY
(06-22-2016 11:44 PM)RPL Calcs Wrote:  The emulator is Free42. You´re RIGHT. 9 9 - returns -6.2466E-29

Sure. A little bit of calculus shows that about six digits are lost. So this is the expected result.

BTW the WP34s returns virtually the same result, here the difference is 6,2465 E–29. You obviously use Free42 Decimal which AFAIK is based on the same 34-digit floating point library.

Dieter
06-23-2016, 08:05 AM
Post: #9
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: ACURACY
(06-22-2016 05:51 PM)dalupus Wrote:  HP35S 8.99999986001
HPPrime 8.99999864267 In rpn mode
HPPrime 9 in CAS mode

Did we actually find a case where the 35s is actually more accurate at a trig function?

No, we didn't. The correct result for a 12-digit calculator is 8,99999864267.

The 35s rounds down the arctan although it should round up: the exact value is 0,999996272743 534... which is rounded to ...43 on the 35s and to ...44 on other calculators. Once this is adjusted the 35s yields the same correct result as the Saturn calculators. On the other hand this is a close case, and the trig functions may have an error of 0,6 ULP, so this still is within the allowed tolerance.

Dieter
06-25-2016, 06:44 PM
Post: #10
 ijabbott Senior Member Posts: 1,088 Joined: Jul 2015
RE: ACURACY
(06-22-2016 05:51 PM)dalupus Wrote:  HP35S 8.99999986001
HPPrime 8.99999864267 In rpn mode
HPPrime 9 in CAS mode

Did we actually find a case where the 35s is actually more accurate at a trig function?
FWIW:
TI Nspire CX CAS 8.99999998177 in approximate mode
TI Nspire CX CAS 9 in exact mode
06-25-2016, 11:09 PM
Post: #11
 Paul Dale Senior Member Posts: 1,748 Joined: Dec 2013
RE: ACURACY
(06-23-2016 07:49 AM)Dieter Wrote:  BTW the WP34s returns virtually the same result, here the difference is 6,2465 E–29. You obviously use Free42 Decimal which AFAIK is based on the same 34-digit floating point library.

The floating point library only provides basic arithmetic, square root and natural logarithm and exponential. The trigonometric functions are implemented differently on each.

I believe that Free42 Decimal has moved to the Intel decimal library which is different again. It is much faster than the 34S's code but it is also much larger -- there are quite a few large lookup tables and it uses binary arithmetic and transcendental functions to get initial approximations for decimal results. In effect, you end up with two mathematics libraries.

Pauli
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