Every command that uses the minibuffer at least once is recorded on a special history list, together with the values of its arguments, so that you can repeat the entire command. In particular, every use of M-x is recorded there, since M-x uses the minibuffer to read the command name.
repeat-complex-command).
C-x ESC ESC is used to re-execute a recent minibuffer-using command. With no argument, it repeats the last such command. A numeric argument specifies which command to repeat; one means the last one, and larger numbers specify earlier ones.
C-x ESC ESC works by turning the previous command into a Lisp expression and then entering a minibuffer initialized with the text for that expression. If you type just RET, the command is repeated as before. You can also change the command by editing the Lisp expression. Whatever expression you finally submit is what will be executed. The repeated command is added to the front of the command history unless it is identical to the most recently executed command already there.
Even if you don't understand Lisp syntax, it will probably be obvious which command is displayed for repetition. If you do not change the text, it will repeat exactly as before.
Once inside the minibuffer for C-x ESC ESC, you can use the minibuffer history commands (M-p, M-n, M-r, M-s; see section Minibuffer History) to move through the history list of saved entire commands. After finding the desired previous command, you can edit its expression as usual and then resubmit it by typing RET as usual.
The list of previous minibuffer-using commands is stored as a Lisp
list in the variable command-history. Each element is a Lisp
expression which describes one command and its arguments. Lisp programs
can re-execute a command by calling eval with the
command-history element.
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