Just a curious mathematical result

[BartDB]

(03-06-2018 04:15 PM)jebem Wrote:  

(03-06-2018 01:59 PM)DA74254 Wrote:  Works on SM DM42 but gives "1" in Prime "home" rpn and "1." in Prime CAS

Yes, HP Prime on CAS mode gives me 1. for approx(SIN(9*(SIN(1)+COS(40))))
However doing 1-Ans gives me 3.5527136788 E-15

So, not exactly the same answer of absolute 1 as got on Home mode, where 1-Ans gives exactly 0.

Further quick searching on google shows a few answers for the above CAS result of 3.5527136788 E-15 for instance here.
Apparently this value corresponds to 8 ^ -16 or 16 ^ -12 or -64 ^ -8 (i didn't take the time to check it).

Tim and Cyrille have been posting some information on the numbers internal representation being different on Home and on CAS modes, and that can explain the different results when trying to get the hidden guard digits on each mode.

1 - sin(9*sin(1)+cos(40))) should yield 1.69173...E-16, so the Prime is quite wrong.

CAS approx. is double precision floating point which gives 15 digit accuracy (17 at most, but for Prime CAS I have found it to be seldom better than 15). However, as you have demonstrated, more digits can be found by subtracting the more significant digits - but I have found they are usually wrong. So I would not rely on it.
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