Did you know the 2nd bathch of Spice calculators are more accurate?

[J-F Garnier]

(05-18-2023 11:51 AM)Gil Wrote:  'EXP(LN(3)*201)'
7.9684196 7193 E95

This is equivalent to compute the exponentiation without guard digits, as did the early HP handhelds.

Quote:« 3. 1 200
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» 7.96841966622 E95

Here, not only you are calculating without guard digits, but you are cumulating rounding errors.

Quote:ALOG(LOG(3)*201)' 7.9684196 6716 E95

e powers and ln (base e) seen to give worse results than when working with 10^ and log(base 10).

Globally, when calculating without guard digits and results of this magnitude, the last 3 digits are not reliable, and the two results are about equally correct (or wrong).

You may also try the test 3^729, that is better adapted to the 12-digit Saturn machines (see here):
3^729 =                  6.62818605419 E 347
EXP(729*LN(3)) =     6.62818606053 E 347
ALOG(729*LOG(3)) = 6.62818605986 E 347
exact  =                  6.62818605424(187) E 347

J-F