An error of this magnitude would hint more at single-precision accuracy than double-precision accuracy. Please note that the math functions are overloaded, and you will get results accurate to double precision only if you pass double-precision data. E.g.
float xf = 0.5f;
double xd = xf;
res1 = sqrt(xf); // square root accurate to single precision
res2 = sqrt(xd); // square root accurate to double precision
The double-precision sqrt() is correctly rounded according to IEEE-754 round-to-nearest-or-even. The maximum ulp error in double-precision log() and exp() is very small, and for most inputs their results will match the correctly rounded result.
As cbuchner1 already stated, the error bounds to all math functions are stated in an appendix to the Programming Guide. These have been determined based on extensive testing. If you have specific cases for which you believe these error bounds are being exceeded, I’d be happy to look into it. All arguments should be stated as hexadecimal numbers for ease of reproduction, or if printed in decimal, be printed with 17 decimal places.