From Halopedia, the Halo wiki
On September 22, 2489, as the ship was preparing to jump to slipspace, Lorelei shut herself down for routine maintenance, which resulted in Lieutenant Commander Nevel ordering Ensign Otto Seinmann to do slipspace calculations by hand.
Seinmann had Crewman Apprentice Preston Cole do most of the work for him instead. When Lorelei reappeared, she found Seinmann's initial calculations to be very rough. However, when she and Nevel saw Cole's work, they were surprised to find that he had actually come up a new method for calculating input parameters. Thoroughly impressed, Lorelei and Nevel recommended Cole for Luna Officer Candidate School later that year.
Lorelei is referred to as a new "smarter" AI, suggesting that she was from a generation of "smart" AI that had been recently developed at the time.
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