The process generated using the normal-order evaluation is the following. It performs 18 remainder operations: 14 when evaluating the condition and 4 in the final reduction phase.
(gcd 206 40) (if (= 40 0) ...) (gcd 40 (remainder 206 40)) (if (= (remainder 206 40) 0) ...) (if (= 6 0) ...) (gcd (remainder 206 40) (remainder 40 (remainder 206 40))) (if (= (remainder 40 (remainder 206 40)) 0) ...) (if (= 4 0) ...) (gcd (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40)))) (if (= (remainder (remainder 206 40) (remainder 40 (remainder 206 40))) 0) ...) (if (= 2 0) ...) (gcd (remainder (remainder 206 40) (remainder 40 (remainder 206 40))) (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))) (if (= (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40)))) 0) ...) (if (= 0 0) ...) (remainder (remainder 206 40) (remainder 40 (remainder 206 40)))
The process generated using the applicative-order evaluation is the following. It performs 4 remainder operations.
(gcd 206 40) (gcd 40 (remainder 206 40)) (gcd 40 6) (gcd 6 (remainder 40 6)) (gcd 6 4) (gcd 4 (remainder 6 4)) (gcd 4 2) (gcd 2 (remainder 4 2)) (gcd 2 0) 2
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