1 (define (test-case actual expected)
2   (newline)
3   (display "Actual:   ")
4   (display actual)
5   (newline)
6   (display "Expected: ")
7   (display expected)
8   (newline))
9 
10 ;; (+ (* 2 1)
11 ;;    0)
12 ;; (+ (* 2 (+ (* 2 1)
13 ;; 	   0))
14 ;;    5)
15 ;; (+ (* 2 (+ (* 2 (+ (* 2 1)
16 ;; 		   0))
17 ;; 	   5))
18 ;;    0)
19 ;; (+ (* 2 (+ (* 2 (+ (* 2 (+ (* 2 1)
20 ;; 			   0))
21 ;; 		   5))
22 ;; 	   0))
23 ;;    3)
24 ;; (+ (* 2 (+ (* 2 (+ (* 2 (+ (* 2 (+ (* 2 1)
25 ;; 				   0))
26 ;; 			   5))
27 ;; 		   0))
28 ;; 	   3))
29 ;;    1)
30 
31 ;; the pattern sort of looks like this in pseudo-code
32 ;; (+ (* 2 (horner-eval 2 (cdr coefficient-sequence)))
33 ;;    (car coefficient-sequence))
34 
35 (define (accumulate op initial sequence)
36   (if (null? sequence)
37       initial
38       (op (car sequence)
39 	  (accumulate op initial (cdr sequence)))))
40 
41 (define (horner-eval x coefficient-sequence)
42   (accumulate (lambda (coefficient remaining-horner) 
43 		(+ coefficient
44 		   (* x remaining-horner)))
45 	      0
46 	      coefficient-sequence))
47 
48 (test-case (horner-eval 0 '()) 0)
49 (test-case (horner-eval 10 '()) 0)
50 (test-case (horner-eval 0 '(1)) 1)
51 (test-case (horner-eval 2 '(1 3 0 5 0 1)) 79)
52 (test-case (horner-eval -1 '(2 4 1 1 8 3)) 3)
53 (test-case (horner-eval 1.23 '(3 5 2 9 4)) 38.079068639999996)
54