Performance of reciprocal calculation in C++

Is there any way to improve the performance of calculating the reciprocal of a number without losing precision? Currently I'm simply doing:

1 / (1 + a * b)

Where a and b are double. Value of a is constant. I need to do millions of such calculations.

Let's separate when a == 0, a != 0,

• if a == 0, then answer is 1 (crystal clear)
• if a ==!0, let c = 1/a

(c is also constant) then entire expression becomes

    c / (b + c)

This will save one of multiplication calculation.