Solve f(x) = x³ -3x +1

We start at a = 0, b = 1.

f(1/2) < 0, b = 1/2 x =.0u

in binary notation;

u means unknown.

f(1/4) > 0, a = 1/4 x = .01u

f(3/8) < 0, b = 3/8 x = .010u

f(5/16) > 0, a = 5/16 x= .0101u

Notice that each evaluation determines one binary bit in the binary expression for the solution;

Thus, ten decimal place accuracy in this case requires thirty evaluations; since 2^-30 is near 10 ^{- 10} and b - a started at 1.