What was found
AT CRUISE FL370, APPOX 3HRS 20 MINUTES INTO FLIGHT, LEFT FMC FAILED. LOST COURSE INTO LEFT NAV DISPLAY. SAW CWS ON PFD, VTK ON LEFT NAV DISPLAYS, LOST FMC PROMPT ON BOTH MCDU'S. FMC RECOVERED BEFORE WE INITIATED QRH PROCEDURE (ABOUT 30 SECONDS). HIGHEST ANP WE SAW WAS .16 NM. UPON RECOVERY RETURNED TO ANP .O2 NM. GROUNDED - YES. LEFT FMC CHECKED GOOD IAW B737-800 AMM 34-61-00-710-801, ETOPS GROUND FUNCTIONAL CHECK GOOD IAW AMM 34-61-00-710-801, NO HISTORY LAST 30 DAYS. ETOPS SIGNIFICANT SYSTEM MAINTENANCE.