I still don't get it. How do you know that 1/x = 0.abc... without performing the division? I mean in general case, not in something matching binary tricks. Such as 1/3 for example. Unless you mean you somehow know the value of 1/x ahead of time. But where does it come from?
If you know the divisor x ahead of time you can pre-compute 1/x at compile time, so that your actual compiled code never does the division--only your compiler does. Your actual compiled code just does the multiplication by a pre-computed constant (and the compiled code doesn't have to know that that constant was pre-computed as the reciprocal of x).
Often, you can amortize a division or reciprocal by calculating it once and then reusing it. Frequently the divisor is dynamic, but reused locally.
For example, if you want to normalize a 3D vector you could do:
mag = sqrt(x*x + y*y + z*z)
x /= mag
y /= mag
z /= mag
That's three divisions with the same divisor. But you could instead do:
invMag = 1.0 / sqrt(x*x + y*y + z*z)
x *= invMag
y *= invMag
z *= invMag
There's still a single division (or reciprocal) done here. But you've eliminated at least the other two. (And it's even better if you have an rsqrt function.)
