Should-Read: The answer is: not precise at all. Nobody should imagine that they know what the NAIRU is right now, or make policy that does not take account of the fact that there is great uncertainty about what the NAIRU is right now:
Douglas O. Staiger, James H. Stock, and Mark W. Watson (1997): How Precise Are Estimates of the Natural Rate of Unemployment?: "Uncertainty arising from not knowing the parameters of the model at hand...
...A second source of uncertainty.... [It is] plausible... that the NAIRU switches stochastically among several regimes... the additional uncertainty of not knowing the current regime.... A third source of uncertainty arises from the choice of specification.... None of the confidence intervals presented in this paper formally incorporate this uncertainty.... Informally incorporating this additional source further increases the uncertainty surrounding the actual value of the NAIRU.
A central conclusion... is that a wide range of values of the NAIRU are consistent with the empirical evidence. However, the unemployment rate and changes in the unemployment rate are useful predictors of future changes in inflation.... The value of unemployment corresponding to a stable rate of inflation is imprecisely measured, even though an increase in unemployment will on average be associated with a decline in future rates of inflation.