How much does a square root cost?

An interesting diversion: how much (time) does calling the square root function sqrt() cost, and is it even worth trying alternative less-accurate implementations?

Some Assembly Required provides some answers: 

SQUARE ROOT

Method	Total time	Time per float	Avg Error
Compiler sqrt(x) / x87 FPU FSQRT	404.029ms	24ns	0.0000%
SSE intrinsic ssqrts	200.395ms	11.9ns	0.0000%
Carmack’s Magic Number rsqrt * x	72.682ms	4.33ns	0.0990%
SSE rsqrtss * x	20.495ms	1.22ns	0.0094%
SSE rsqrtss * x with one NR step	53.401ms	3.18ns	0.0000%
SSE rsqrtss * x with one NR step, unrolled by four	48.701ms	2.90ns	0.0000%

RECIPROCAL SQRT

Method	Total time	Time per float	Avg Error
Carmack’s Magic Number rsqrt	59.378ms	3.54ns	0.0990%
SSE rsqrtss	14.202ms	0.85ns	0.0094%
SSE rsqrtss with one NR step	45.952ms	2.74ns	0.0000%