Also note that the if the stream exponents is Euler's continued fraction, the stream bases (RLRLRLRLRLRLR...) is nothing else than the golden ratio in our Stern-Brocot tree number system. So, if you want a rational approximation of Φ instead, just do this
> (define (Φ ref)
(mat->rat (stream-ref (stream-scan mat-mul I bases) ref)))
> (time (Φ 10000))
cpu time: 33 real time: 34 gc time: 15
'(/
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