The gamma-ray burst ( GRB ) rate is essential for revealing the connection between GRBs , supernovae and stellar evolution .
Additionally , the GRB rate at high redshift provides a strong probe of star formation history in the early universe .
While hundreds of GRBs are observed by Swift , it remains difficult to determine the intrinsic GRB rate due to the complex trigger algorithm of Swift .
Current studies of the GRB rate usually approximate the Swift trigger algorithm by a single detection threshold .
However , unlike the previously flown GRB instruments , Swift has over 500 trigger criteria based on photon count rate and additional image threshold for localization .
To investigate possible systematic biases and explore the intrinsic GRB properties , we develop a program that is capable of simulating all the rate trigger criteria and mimicking the image threshold .
Our simulations show that adopting the complex trigger algorithm of Swift increases the detection rate of dim bursts .
As a result , our simulations suggest bursts need to be dimmer than previously expected to avoid over-producing the number of detections and to match with Swift observations .
Moreover , our results indicate that these dim bursts are more likely to be high redshift events than low-luminosity GRBs .
This would imply an even higher cosmic GRB rate at large redshifts than previous expectations based on star-formation rate measurements , unless other factors , such as the luminosity evolution , are taken into account .
The GRB rate from our best result gives a total number of 4571 ^ { +829 } _ { -1584 } GRBs per year that are beamed toward us in the whole universe .

Special note ( 2015.05.16 ) : This new version incorporates an erratum .
All the GRB rate normalizations ( R _ { GRB } ( z = 0 ) ) should be a factor of 2 smaller than previously reported .
Please refer to the Appendix for more details .
All the values are corrected in this version .
We sincerely apologize for the mistake , and for not noticing it earlier .