I managed to make up the workaround and get highly desirable zero.

I try to answer all your posts concerning the problem in a fcfs
manner.

The original formula was:

=IF(BH3=0;"N";IF(BK3-AE$12<=0;"P";BK3-AE$12))
repeated 1499 times in BM3:BM1502

The part of the formula which should return 0 but returned 2.22045E-16
is BK3-AE$12.
Referenced value in column BK3:BK1502 is the increasing amount of
sent messages
of analyzed billing calculated with =IF(BH3=1;SUM($BJ$3:BJ3);0).
AE$12 is a place where a user puts the value of the messages pack.
It can be 10 20 or 50. The cost of a single message can be 0.1 0.2 or
0.4.

Definitely it is not a rounding problem then.
The values the formula returns include between -50 and 50 and it is
calculated with adding or subtracting 10 20 50 0.1 0.2 0.4.
All is calculated in a default number format so I can see 2.22045E-16
at once.

After a day of extensive search I have tried all I could think of to
get rid of 2.22045E-16. I have run out of ideas and finally the
approach of that hp calc fan I mentioned in my original post have
worked: Do not use parenthesis – he says (here I can be
extravagant
and put even two ; ).

I changed original formula
=IF(BH3=0;"N";IF(BK3-AE$12<=0;"P";BK3-AE$12))
to
=IF(BH3=0;"N";IF(BI3<=0;"P";BI3))
and put
BK3-AE$12
in
BI3:BI1502

It works. Discrepancy reduced to zero.
And definitely I have learnt how much the zero is.

Bug found? Maybe.

So remember no parenthesis and keep calm.