In his sixth year Harry managed to generate a glowing reputation at Potions in the eyes of Slughorn by following Severus Snape's hints and tips as recorded in Snape's old Potions textbook.
For the rest of the week's Potions lessons Harry continued to follow the Half-Blood Prince's instructions wherever they deviated from Libatius Borage's, with the result that by their fourth lesson Slughorn was raving about Harry's abilities, saying that he had rarely taught anyone so talented.
(Half-Blood Prince, Chapter 10, The House of Gaunt).
Snape was an old student of Slughorn's and so Slughorn could easily compare the two Potions prodigies. At the Christmas party Slughorn states that Harry was not only Snape's equal but his better.
"I don't think I've ever known such a natural at Potions!" said Slughorn, regarding Harry with a fond, if bloodshot eye. "Instinctive, you know - like his mother!"
(Half-Blood Prince, Chapter 15, The Unbreakable Vow).
Slughorn even boasts about Harry to Snape.
"Stop sulking and come and join us, Severus!" hiccoughed Slughorn happily. "I was just talking about Harry's exceptional potion-making! Some credit must go to you, of course, you taught him for five years!"
Trapped, with Slughorn's arm around his shoulders, Snape looked down his hooked nose at Harry, his black eyes narrowed.
"Funny, I never had the impression I managed to teach Potter anything at all."
"Well, then, it's natural ability!" shouted Slughorn. "You should have seen what he gave me, first lesson, the Draught of Living Death - never had a student produce finer on a first attempt, I don't think even you, Severus -
(Half-Blood Prince, Chapter 15, The Unbreakable Vow).
Even Snape is surpassed by Harry in Slughorn's opinion. Yet how could this be when Harry was copying Snape's instructions? Harry wasn't all that good at Potions. He only managed to impress Slughorn because he had Snape's book of cheat codes.
Was Harry able to actually perform better in Potions than Snape? How could he recreate Snape's 'recipes' better than Snape could?