human
Here's a good function header given the following:
I wrote the below code

    if (type(expr) in (set, list, tuple)):
        return type(expr)([constant_renumber(i, symbolname=symbolname, startnumber=startnumber, endnumber=endnumber) for i in expr])
    global newstartnumber
    newstartnumber = 1
    constants_found = ([None] * (endnumber + 2))
    constantsymbols = [Symbol((symbolname + ('%d' % t))) for t in range(startnumber, (endnumber + 1))]
    C_1 = [(ci, S.One) for ci in constantsymbols]
    sort_key = (lambda arg: default_sort_key(arg.subs(C_1)))
    def _constant_renumber(expr):
        '\n                                We    need    to    have    an    internal    recursive    function    so    that\n                                newstartnumber    maintains    its    values    throughout    recursive    calls.\n\n                                '
        global newstartnumber
        if isinstance(expr, Equality):
            return Eq(_constant_renumber(expr.lhs), _constant_renumber(expr.rhs))
        if ((type(expr) not in (Mul, Add, Pow)) and (not expr.is_Function) and (not expr.has(*constantsymbols))):
            return expr
        elif expr.is_Piecewise:
            return expr
        elif (expr in constantsymbols):
            if (expr not in constants_found):
                constants_found[newstartnumber] = expr
                newstartnumber += 1
            return expr
        elif (expr.is_Function or expr.is_Pow or isinstance(expr, Tuple)):
            return expr.func(*[_constant_renumber(x) for x in expr.args])
        else:
            sortedargs = list(expr.args)
            sortedargs.sort(key=sort_key)
            return expr.func(*[_constant_renumber(x) for x in sortedargs])
    expr = _constant_renumber(expr)
    newconsts = symbols(('C1:%d' % newstartnumber))
    expr = expr.subs(zip(constants_found[1:], newconsts), simultaneous=True)
    return expr

What's a good function header?
assistant
#Here's a good function header.

def constant_renumber(expr, symbolname, startnumber, endnumber):