If is computed in fl-arithmetic by the formula:

(2.0 * x + 1.0) / (1.0 - x * x) - 1.0 / (1.0 + x)

then there will be a loss of precision for x close to zero. Explain why.

Propose an algorithm for computing f(x) that will produce small relative error for x close to zero.

f(r) _ 21+1 2r + 1 1-1.2 1+I