Exercise 1.20

With normal-order evalutation,

(gcd 206 40)

40 != 0

(gcd 40 (r 206 40))

[(r 206 40) != 0]
=> 1 time

(gcd (r 206 40)
     (r 40
        (r 206 40)))

[(r 40 (r 206 40)) != 0 ]
=> 2 times

(gcd (r 40
        (r 206 40))
     (r (r 206 40)
        (r 40
           (r 206 40))))

(r (r 206 40) (r 40 (r 206 40))) != 0
=> 4 times

(gcd (r (r 206 40)
        (r 40
           (r 206 40)))
     (r (r 40
           (r 206 40))
        (r (r 206 40)
           (r 40
              (r 206 40)))))

(r (r 40 (r 206 40)) (r (r 206 40) (r 40 (r 206 40)))) == 0
=>  7 times

(r (r 206 40) (r 40 (r 206 40)))
=> 4 times

So remainder is called 18 times

With applicative-order evalutation,

(gcd 206 40)
(gcd 40 6) 1
(gcd 6 4)  1
(gcd 4 2)  1
(gcd 2 0)  1

Remainder is called 4 times