Alchemist

The Alchemist is an Artificer subclass from TCoE. It functions as printed, except as noted below.

Unstable Compound

After a long rest, you can freely create a number of unstable compounds equal to your Intelligence modifier + your proficiency bonus, provided you have flasks, clay pots, or other such vessels. These are alchemical items like acid, alchemist's fire, etc. They last until the earlier of 1 day, after your next long rest, or when used, and if not used become inert. You can "hold" one or more of these free compounds you would get after a long rest, and create them later on a short rest instead. 
As you rise in level and understanding of your craft, your compounds become more potent. You multiply any flat or dice of damage by the highest artificer spell level to which you have access. You use your spell save DC in place of the inherent save DC of the item if it is better. If the item has a duration measured in a unit of time (e.g., "rounds" or "minutes"), you increase that duration by a number of units equal to the highest spell level to which you have access.
For example, when you create alchemist's fire as a 5th level artificer with access to 2nd level spells, it deals double damage, uses your spell save DC for the check to extinguish it if higher than the default DC 10, and would burn for 2 rounds even on the surface of water where its duration would otherwise be 0. 

Experimental Elixir

You can "hold" one or more of the free elixirs you would get after a long rest, and create them later on a short rest instead. Each elixir now improves in effect with the spell level of the spell slot used to create it, and your free elixirs that you get after a long rest are created at your highest spell level.

1. Healing: The drinker regains a number of hit points equal to your Intelligence modifier, plus 2d4 as a first level elixir, plus 4d4 per level above that.
2. Swiftness: The drinker's walking speed increases for 1 hour, by 10 feet as a first level elixir, 20 feet as a third level elixir, or 30 feet as a fifth level elixir, and you count as having a running start when you jump. At second level you can move up and along vertical surfaces and upside down, at fourth level you can cross liquid and fragile surfaces like water or a bed of leaves without falling in, and at sixth level you can walk on air; in all these cases, you fall at the end of your turn unless you are on a solid surface again.
3. Resilience: The drinker gains a bonus to AC for 10 minutes, equal to +1 per level of the elixir. Any trivial attack or effect whose total damage does not exceed this AC bonus, such as one dealing 1-3 damage when you have a +3 bonus, is negated entirely.
4. Boldness: The drinker gains a bonus to attack rolls for 10 minutes, equal to +1 per level of the elixir, and to their saving throw DCs, equal to +1 per two levels rounded down.
5. Effusion: The drinker gains resistance to one damage type of their choice for 10 minutes, chosen from acid, cold, electricity, fire, poison, and thunder, but emits bright light in a 20 foot radius and dim light in a 60 foot radius for 1 round for every point of damage prevented in this way - the duration of which can continue past the end of the protection. At second level, force, necrotic, psychic, and radiant damage are added to the list. At third level, two damage types may be chosen. At fourth level, bludgeoning, piercing, and slashing damage are added to the list. At fifth level, three damage types may be chosen. At sixth level, duration increases to 1 hour.
6. Puissance: The drinker gains a bonus to all Strength and Constitution ability checks and saving throws for 1 hour, equal to +1 per level of the elixir.
7. Prowess: The drinker gains a bonus to all Dexterity and Intelligence ability checks and saving throws for 1 hour, equal to +1 per level of the elixir.
8. Presence: The drinker gains a bonus to all Wisdom and Charisma ability checks and saving throws for 1 hour, equal to +1 per level of the elixir.
9. Flight: The drinker gains a flying speed of 20 feet for 10 minutes, but does not have hover and so must move at least half their speed each turn while in the air or they fall. As a first level elixir, the flyer can only move up and down. As a first or second level elixir, the flyer has disadvantage on all attack rolls and all Strength and Dexterity based skill checks and saving throws while in the air. At third level these restrictions are removed, at fourth level speed increases to 30 feet, at fifth level you gain hover and if your flight is dispelled you feather fall, and at sixth level duration increases to 1 hour.
10. Transformation: The drinker's body is transformed as if by the Change Self spell as a first level elixir, or by the Alter Self spell at second or third level, or by the Polymorph spell at fourth or fifth level, or by the True Polymorph spell at sixth level. The drinker determines the transformation caused by the spell, the effects of which last for 1 day, and always keeps their mental ability scores regardless of the spell being simulated. Unlike some versions of the spells in question, the drinker cannot keep changing their form during this duration; the form chosen is set until the elixir expires or is dispelled.

Additionally, you now are allowed to select the effects of the free elixirs you create after a rest. However, any time you make an elixir, including after a rest or when you expend spell slots to make a new one, you can choose to roll randomly instead of choosing; if you do so, your elixir is treated as one spell level higher in effect than if you chose the effect, and this is the only way to create the sixth level elixirs!

Alchemical Savant

This feature is rewritten, because all spellcasters now add their ability modifier to the damage or healing rolls of their spells and cantrips. 
At 5th level, add your Intelligence modifier to the damage or healing of any potion or alchemical item you use, whether you created it or not. This also applies to the splash damage of alchemist's fire and other grenade-like weapons. 
Further, when using a grenade-like weapon with splash damage or another area of effect, you may remove and/or add a total number of 5 foot spaces to the effect up to the highest spell level of alchemist spell you can cast, so long as every space of the modified effect is left touching another space of the effect. 
Finally, when you randomly create an elixir, roll twice and pick which of the two results is actually created.