# [racket] Style and Performance question

I was working through a problem at Programming
Praxis<http://programmingpraxis.com/2009/12/18/calculating-logarithms/>,
and was happy to find that my solution closely matched the "approved"
solution, but I noted a fairly big difference in our styles, and I thought
I'd seek the community's feedback...
To illustrate, I present part of the problem, that solves for square roots
by recursion using Newton's method:
x <- x - (y - x^2)/2x
I now show the "approved" solution, and my own, both edited a bit to cleanly
present my questions.
(define epsilon 1e-7)
; The "approved" solution
(define (approved-sqrt y)
(let loop [(x (/ y 2))]
(if (< (abs (- (* x x) y)) epsilon) x
(loop (- x (/ (- (* x x) y) (+ x x)))))))
; My solution
(define (my-sqrt y)
(let loop [(x (/ y 2))]
(let [(error (- y (* x x)))]
(if (< (abs error) epsilon) x
(loop (+ x (/ error 2 x)))))))
I haven't timed the two, as I'm more interested in the "big picture" than
this particular function.
Question 1: Is my use of the temporary "error" worth it in terms of
performance (the approved solution calculates (* x x) twice)? If it's not
worth it, how big does the calculation have to become before it does? Can
the compiler make such a temporary live only in a register?
Question 1a: How creeped are you by my changing the meaning of error for
these few lines? I find myself doing stuff like this, in the name of my idea
of readability, a lot.
Question 2: The approved solution favored (/ ... (+ x x)) over my (/ ... 2
x). Cost of division versus readability. Wasn't a conscious decision of mine
at the time, but now I'm curious. How smart is the compiler when presented
with a division by 2? With multiple recalls of the same value?
Thanks for any comments.
Pat
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