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-37 bytes.

edited Jul 25, 2017 at 8:18

Haskell, 100100 63 bytes

For inputs that don't converge (eg. -2) this won't terminate:

import Data.Complex f x|l<-iterate(x**)x=fst$dropWhile(\x=until(a,b)\a->magnitude(a-bx**a)>1e<1e-6)(zip l$tail lx**)!!0x

Try it online! Thanks a lot @ØrjanJohansen for teaching me about until and saving me 37 bytes!

For inputs that don't converge (eg. -2) this won't terminate:

import Data.Complex f x|l<-iterate(x**)x=fst$dropWhile(\(a,b)->magnitude(a-b)>1e-6)(zip l$tail l)!!0

For inputs that don't converge (eg. -2) this won't terminate:

import Data.Complex f x=until(\a->magnitude(a-x**a)<1e-6)(x**)x

Thanks a lot @ØrjanJohansen for teaching me about until and saving me 37 bytes!

answered Jul 25, 2017 at 7:57

For inputs that don't converge (eg. -2) this won't terminate:

import Data.Complex f x|l<-iterate(x**)x=fst$dropWhile(\(a,b)->magnitude(a-b)>1e-6)(zip l$tail l)!!0