At 20th level of Alchemist, one of the class feats you can take is Craft Philosopher's Stone, which gives you the formula for the aforementioned stone, an uncommon formula. One of the things the stone can be used to do is create an Elixir of Rejuvenation, which is also an uncommon formula.
But does my knowing the formula for the Philosopher's Stone automatically grant me the formula for the Elixir of Rejuvenation, as well? Or do I have to find it separately?
That usage of the Stone bypasses the need for the elixir of rejuvenation's formula.
• You can apply the stone’s quicksilver to an infused true elixir of life using an Operate Activation action to create an infused elixir of rejuvenation. This is instantaneous and does not require any crafting time or additional materials.
So, you just need to be able to create a true elixir of life, which is a common formula.