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Or wait also tanh(x) is good. I think is perfect for your case
Yes I quote him! You can use arctan(x) by creating your own function
kdria posted that meaning to reply to this topic, but accidentally starting a new one instead.
arctan(x) also has two horizontal asymptotes.
The tanh(x) function has two horizontal asymptotes, it could be adapted possibly.
Here is a silly answer that uses operators that are probably disallowed in algebra in this fashion for some reason or other.