Найти максимум числового выражения

REM
REM (sin1 + ... + SIN(k)) * (SIN(k+1) + ... + SIN(n))
REM
REM   max = 0.9577862
REM
 
CLS
CONST n = 100
 
FOR m = 2 TO n
FOR k = 1 TO m - 1
   s1 = 0
   FOR i = 1 TO k
      s1 = s1 + SIN(i)
   NEXT
 
   s2 = 0
   FOR i = k + 1 TO m
      s2 = s2 + SIN(i)
   NEXT
 
   IF max < s1 * s2 THEN
      max = s1 * s2
   END IF
NEXT k, m
 
PRINT "MAX ="; max
END

CLS
max = -100
FOR i = 1 TO 100
s = s + SIN(i)
NEXT
FOR i = 1 TO 100
s = s - SIN(i)
s2 = s2 + SIN(i)
IF s * s2 > max THEN max = s * s2: t = i
NEXT
PRINT max, t

max = -100
FOR k = 1 TO 100
s = 0
s2 = 0
FOR i = 1 TO k
s = s + SIN(i)
NEXT
FOR i = 1 TO k
s = s - SIN(i)
s2 = s2 + SIN(i)
IF s * s2 > max THEN max = s * s2: t = i
NEXT
NEXT
PRINT max, t

DIM i AS LONG, j AS LONG, n AS LONG, s(1 TO 100) AS DOUBLE, mx AS DOUBLE, p AS DOUBLE
n = 100
s(1) = SIN(1)
FOR i = 2 TO n
    s(i) = s(i - 1) + SIN(i)
NEXT i
mx = s(1) * (s(2) - s(1))
FOR j = 2 TO n
FOR i = 1 TO j - 1
    p = s(i) * (s(j) - s(i))
    IF p > mx THEN mx = p
NEXT i, j
PRINT mx

max = -100
s = 0
FOR k = 1 TO 100
s = s + SIN(k)
s2 = 0
v = s
FOR i = 1 TO k
v = v - SIN(i)
s2 = s2 + SIN(i)
IF v * s2 > max THEN max = v * s2
NEXT
NEXT
PRINT max

t = TIMER
max = -100
s = 0
FOR k = 1 TO 5000
s = s + SIN(k)
s2 = 0
v = s
FOR i = 1 TO k
v = v - SIN(i)
s2 = s2 + SIN(i)
IF v * s2 > max THEN max = v * s2
NEXT
NEXT
PRINT max, TIMER - t

DIM mx AS DOUBLE, i AS LONG, j AS LONG, s1 AS DOUBLE, s2 AS DOUBLE, t AS SINGLE
t = TIMER
mx = SIN(1) * SIN(2)
FOR i = 1 TO 5000
    s1 = s1 + SIN(i)
    s2 = 0
    FOR j = 1 TO i - 1
        s2 = s2 + SIN(j)
        IF s2 * (s1 - s2) > mx THEN mx = s2 * (s1 - s2)
NEXT j, i
PRINT mx, TIMER - t

DIM i AS LONG, j AS LONG, s(1 TO 5000) AS DOUBLE, mx AS DOUBLE, t AS SINGLE
t = TIMER
s(1) = SIN(1)
mx = SIN(1) * SIN(2)
FOR j = 2 TO 5000
s(j) = s(j-1) + SIN(j)
FOR i = 1 TO j - 1
    IF s(i) * (s(j) - s(i)) > mx THEN mx = s(i) * (s(j) - s(i))
NEXT i, j
PRINT mx, TIMER - t