> What's the reasoning behind your assertion ?
Exponentiation laws.
E.g. x^10 = x^8 * x^2 and x^8 = ((x^2)^2)^2
Just because 10 is 1010 binary, hence < 4*2 multiplications.
6e7 should have a 26 bit representation so <52 multiplications needed.
Of course there are even faster implementations which are less exact.
I think that's what you are observing.
edit
Of course a binary calculation should be done with integer x=1000001 without fraction, dividing later thru 10^(6*60) should be easy enough.
update
proof of concept -> here
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