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I happen to come across the = register. I checked :h @= and :h recording where it is mentioned. I am not able to understand how to use it. It could be helpful to know a valid usecase for the same.

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    You can check in this video from 0:52 sec to 1:09 sec. It is a demo of my homework.
    – klaus
    Mar 14 '19 at 8:28
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So let's begin by quoting the doc :h @=

When typing the '=' after " or CTRL-R the cursor moves to the command-line,
where you can enter any expression (see |expression|).  All normal
command-line editing commands are available, including a special history for
expressions.  When you end the command-line by typing <CR>, Vim computes the
result of the expression.  If you end it with <Esc>, Vim abandons the
expression.

And it is also worth reading :h usr_41.txt about the expressions.

Now how can you use the expression register?

It is important to understand the the expression register is not meant to be used in a macro, it more common usage is to insert the result of an expression while you are in insert mode.

For example you can do simple math. Let's get this in our buffer:

1 + 2 + 3 + 4 = 

If you want to put the result you can do the following:

0               To go the the beginning of the line
yf4             To yank the text from 1 to 4
A               To start inserting at the end of the line
<C-r>           Here the magic begins, this allow to insert the content of a register
=               To start editing the content of the expression register
<C-r>"          To insert your yanked text in the expression register
<CR>            To validate the operation

And voila vim computes the content of the expression register (i.e. 1 + 2 + 3 + 4) and inserts the result (i.e. 10)

1 + 2 + 3 + 4 = 10

Now the actual use cases depends on your usage but evaluating some vimscript while you are in insert mode can sometimes be useful.

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Assume you often need to insert a timestamp in your documents. Then you could define a mapping for that:

:inoremap <C-G>t <C-R>=strftime("%Y-%m-%dT%H:%M:%S%z")<CR>

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