Dear rodion15,
First off, I'm really happy that you found my initial answer helpful. In response to your follow up question: It appears that Apple Service Diagnostic is an application designed very differently from Memtest86. As far as I'm aware, there is no option to perform a memory test (on its own), however ASD includes a memory scan in its overall diagnostic scan. This appears to be a program specifically designed for the singular purpose of performing a full diagnostic scan and only providing information to the user in the form of an error code (if one is found), and that is the extent of this program's capabilities.
Although comparing ASD's memory testing capabilities to Memtest86 is something I know nothing about. I do know that the best way to do a proper memory test using The Apple Service Diagnostic application is to perform an "extended test". I'd especially recommend performing an extended test if you've received the "No trouble found" message from the standard test yet you still suspect an error. Although though the extended test may take more time, it is better at detecting memory and graphics problems than the standard test. Also, seeing as this was an application designed by Apple for Apple for as a stand alone OS to serve a singular purpose, I personally feel pretty confident in my assumption that ASD is likely, at the very least, comparable to any other diagnostic tool on apple hardware. I hope this helps, and answers your question!
P.S. Incase you're having issues understanding ASD's output here are the Apple Hardware Test Error Codes:
Error Code Description
4AIR AirPort wireless card
4ETH Ethernet
4HDD Hard disk (includes SSD)
4IRP Logic board
4MEM Memory module (RAM)
4MHD External disk
4MLB Logic board controller
4MOT Fans
4PRC Processor
4SNS Failed sensor
4YDC Video/Graphics card