Regular Expressions 101

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/
^(?=^[^_\n]+_?[^_\n]+$)\w{3,20}$
/
gm
^ asserts position at start of a line
Positive Lookahead
(?=^[^_\n]+_?[^_\n]+$)
Assert that the Regex below matches
^ asserts position at start of a line
Match a single character not present in the list below
[^_\n]
+ matches the previous token between one and unlimited times, as many times as possible, giving back as needed (greedy)
_ matches the character _ with index 9510 (5F16 or 1378) literally (case sensitive)
\n matches a line-feed (newline) character (ASCII 10)
_
matches the character _ with index 9510 (5F16 or 1378) literally (case sensitive)
Match a single character not present in the list below
[^_\n]
+ matches the previous token between one and unlimited times, as many times as possible, giving back as needed (greedy)
_ matches the character _ with index 9510 (5F16 or 1378) literally (case sensitive)
\n matches a line-feed (newline) character (ASCII 10)
$ asserts position at the end of a line
\w
matches any word character (equivalent to [a-zA-Z0-9_])
{3,20} matches the previous token between 3 and 20 times, as many times as possible, giving back as needed (greedy)
$ asserts position at the end of a line
Global pattern flags
g modifier: global. All matches (don't return after first match)
m modifier: multi line. Causes ^ and $ to match the begin/end of each line (not only begin/end of string)
Your regular expression does not match the subject string.

Regular Expression
No Match

/
/
gm

Test String