(define (smooth s)
  (define (avpt x y)
    (/ (+ x y) 2))
  (cons-stream (avpt (stream-car s)
                     (stream-car (stream-cdr s)))
               (smooth (stream-cdr s))))

(define (make-zero-crossings input-stream last-value)
  (let ((new-stream (smooth (cons-stream last-value input-stream))))
    (define (make-zero-crossings-temp stream)
      (cons-stream
       (sign-change-detector (stream-car stream)
                             (stream-car (stream-cdr stream)))
       (make-zero-crossings-temp (stream-cdr stream))))
    (make-zero-crossings-temp new-stream)))

(define (smooth s)
  (stream-map (lambda (x y) (/ (+ x y) 2))
              s
              (stream-cdr s)))

(define (make-zero-crossings input-stream last-value)
  (let ((new-stream (smooth (cons-stream last-value input-stream))))
    (stream-map sign-change-detector new-stream
                (cons-stream 0 new-stream))))