1 (define (search f neg-point pos-point)
2   (let ((midpoint (average neg-point pos-point)))
3     (if (close-enough? neg-point pos-point)
4 	midpoint
5 	(let ((test-value (f midpoint)))
6 	  (cond ((positive? test-value)
7 		 (search f neg-point midpoint))
8 		((negative? test-value)
9 		 (search f midpoint pos-point))
10 		(else midpoint))))))
11 (define (close-enough? x y)
12   (< (abs (- x y)) 0.001))
13 
14 (define (half-interval-method f a b)
15   (let ((a-value (f a))
16 	(b-value (f b)))
17     (cond ((and (negative? a-value) (positive? b-value))
18 	   (search f a b))
19 	  ((and (negative? b-value) (positive? a-value))
20 	   (search f b a))
21 	  (else
22 	   (error "Values are not of opposite sign" a b)))))
23 (define tolerance 0.00001)
24 (define (fixed-point f first-guess)
25   (define (close-enough? v1 v2)
26     (< (abs (- v1 v2)) tolerance))
27   (define (try guess)
28     (let ((next (f guess)))
29       (if (close-enough? guess next)
30 	  next
31 	  (try next))))
32   (try first-guess))
33 
34 (fixed-point (lambda (y) (+ (sin y) (cos y))) 
35 	     1.0)
36 
37 (define (sqrt x)
38   (fixed-point (lambda (y) (average y (/ x y)))
39 	       1.0))
40 
41 (define (average x y)
42   (/ (+ x y) 2))
43 
44 (define golden-ratio (fixed-point (lambda (x) (+ 1 (/ 1 x)))
45 				  1.0))
46 
47 (define (test-case actual expected)
48   (load-option 'format)
49   (newline)
50   (format #t "Actual: ~A Expected: ~A" actual expected))
51 
52 (test-case golden-ratio (/ (+ 1.0 (sqrt 5.0)) 2.0))