Regular expression to enforce complex passwords, matching 3 out of 4 rules

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Don’t use one regex to check it then. 

if (password.length < 8)
  alert("bad password");
var hasUpperCase = /[A-Z]/.test(password);
var hasLowerCase = /[a-z]/.test(password);
var hasNumbers = /\d/.test(password);
var hasNonalphas = /\W/.test(password);
if (hasUpperCase + hasLowerCase + hasNumbers + hasNonalphas < 3)
  alert("bad password");

If you must use a single regex:

^(?:(?=.*[a-z])(?:(?=.*[A-Z])(?=.*[\d\W])|(?=.*\W)(?=.*\d))|(?=.*\W)(?=.*[A-Z])(?=.*\d)).{8,}$

This regex is not optimized for efficiency. It is constructed by A·B·C + A·B·D + A·C·D + B·C·D with some factorization. Breakdown:

^
(?:
    (?=.*[a-z])       # 1. there is a lower-case letter ahead,
    (?:               #    and
        (?=.*[A-Z])   #     1.a.i) there is also an upper-case letter, and
        (?=.*[\d\W])  #     1.a.ii) a number (\d) or symbol (\W),
    |                 #    or
        (?=.*\W)      #     1.b.i) there is a symbol, and
        (?=.*\d)      #     1.b.ii) a number ahead
    )
|                     # OR
    (?=.*\W)          # 2.a) there is a symbol, and
    (?=.*[A-Z])       # 2.b) an upper-case letter, and
    (?=.*\d)          # 2.c) a number ahead.
)
.{8,}                 # the password must be at least 8 characters long.
$

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