grammar

expr = eq_expr ;

eq_expr = add_expr, { "=", add_expr } ;
add_expr = mul_expr, { ("+" | "-"), mul_expr } ;
mul_expr = pow_expr, { ("*" | "/" | "%"), pow_expr } ;
pow_expr = parentheses_mul_expr, { "^", factor } ;

parentheses_mul_expr = func_or_var_mul_expr | ( factorial_expr, { "(", expr, ")" } ) ;
func_or_var_mul_expr = identifier, "(", [ expr { ",", expr } ], ")" ; (* need lookahead 2 *)

factorial_expr = factor, { "!" } ;
factor = "(", expr, ")"
       | "|", expr, "|"
       | "-", expr
       | number
       | identifier ;

identifier = alpha, { alpha | digit } ;
alpha = "A".."Z" | "a".."z" ;

digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;
(* number = 52 or .14 or -65535 or -.256 or -340.430 etc *)
number = [ "-" ], ( digit, { digit }, [ ".", { digit } ] ) | ( ".", digit, { digit } ) ;