How need help to specify a grammar for arithmetic expressions

Question

I am trying to come up with a grammar for arithmetic expressions with the following order of operations:

1. Parentheses
2. Factorials
3. Exponents
4. Functions / unary plus and minus
5. Juxtaposition (implied multiplication)
6. Multiplication and division
7. Addition and subtraction
8. Comma separated expressions

Functions should not require parenthesis, i.e. both sqrt 2 and sqrt(2) are valid. Valid juxtapositions should be <number> (<parenthesis> | <constant> | <function_expression>).

I can find plenty of examples of people who have created grammar for simple arithmetic that only includes binary operators and parenthesis. This is trivial, but when I try to expand it to included the previously stated items, it never works. I am not sure if the grammar I want is even specifiable in a non-ambiguous way, or if I am simply failing.

    <expression> ::= <add> ("," <add>)*
    <add> ::= <multiply> (("+" | "-") <multiply>)*
    <multiply> ::= <juxtapose> (("*" | "/") <juxtapose>)*
    
    ... no idea how to handle unary ops, functions, and juxtaposition
    as they seem to interact with each other ...

    <exponent> ::= <factorial> ("^" <exponent>)*
    <factorial> ::= <primary> ("!" | "!!")*
    <primary> ::= <number> | <constant> | <parenthesis>
    <parenthesis> ::= "(" <expression> ")"

Also, if you are unfamiliar with it, I found this useful site https://bnfplayground.pauliankline.com/

Edit: Here are some examples sentences:

• -2^2 = -(2 ^ 2) Exp > Unary
• 2pi^2 = 2 * (pi ^ 2) Exp > Juxtapose
• 2/2pi = 2 / (2 * pi) Juxtapose > Divide
• 2(3) = 2 * 3
• 2 sqrt 2 = 2 * sqrt(2)
• sqrt -2 = sqrt(-2)
• sin 2pi = sin(2 * pi)
• atan pi, pi = (atan(pi), pi)
• atan(pi, pi) = atan(pi, pi)