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AFAIK (and wikipedia tells), this is not how IQ works. For measuring intelligence, we get an "ordinal scale", i.e. a ranking between test-subjects. An honest reporting would be "you are in the top such-and-so percent". For example, testing someone as "one-in-a-billion performant" is not even wrong; it is meaningless, since we have not administered one billion IQ tests over the course of human history, and have no idea what one-in-a-billion performance on an IQ test would look like.
Because the IQ is designed by people who would try to parse HTML by regex (I cannot think of a worse insult here), it is normalized to a normal distribution. This means that one applies the inverse error-function with SD of 15 points to the percentile data. Hence, IQ is Gaussian-by-definition. In order to compare, use e.g. python as a handy pocket calculator:
4.442300208692339e-10
So we see that claims of any human being having an IQ of 165+ is statistically meaningless. If you extrapolated to all of human history, an IQ of 180+ is meaningless:
2.3057198811629745e-14
Yep, by current definition you would need to test 10^14 humans to get one that manages an IQ of 180. If you test 10^12 humans and one god-like super-intelligence, then the super-intelligence gets an IQ of maybe 175 -- because you should not apply the inverse error-function to an ordinal scale, because ordinal scales cannot capture bimodals. Trying to do so invites eldritch horrors on our plane who will parse HTML with a regex.
The 15 should be (15.*sqrt(2)) actually, resulting in iqtopercentile(115) = 0.16 as it should be rather than 0.079 as your expression gives, iqtopercentile(165) = 7.3e-6 (i.e. 7 such people in a city with 1 million inhabitants in average), and iqtopercentile(180) = 4.8e-8 (i.e. several hundred such people in the world).
(Note also that in python (x-100)/15 returns an integer whenever x is an integer.)