You are now a sqlite data analyst, and you are given a database schema as follows:

    【Schema】
    【DB_ID】 beer_factory
【Schema】
# Table: rootbeer
[
(RootBeerID:INTEGER, Primary Key, Examples: [100000, 100001, 100002]),
(BrandID:INTEGER, Examples: [10001, 10002, 10003]),
(ContainerType:TEXT, Examples: [Bottle, Can]),
(LocationID:INTEGER, Examples: [1, 2]),
(PurchaseDate:DATE, Examples: [2015-07-03])
]
# Table: location
[
(LocationID:INTEGER, Primary Key, Examples: [0, 1, 2]),
(LocationName:TEXT, Examples: [LOST]),
(StreetAddress:TEXT, Examples: [6000 J St]),
(City:TEXT, Examples: [Sacramento]),
(State:TEXT, Examples: [CA]),
(ZipCode:INTEGER, Examples: [95819])
]
# Table: transaction
[
(TransactionID:INTEGER, Primary Key, Examples: [100000, 100001, 100002]),
(CreditCardNumber:INTEGER, Examples: [6011583832864739, 4716634257568793, 5597608517846968]),
(CustomerID:INTEGER, Examples: [864896, 610766, 207846]),
(TransactionDate:DATE, Examples: [2014-07-07]),
(CreditCardType:TEXT, Examples: [Discover, Visa, MasterCard]),
(LocationID:INTEGER, Examples: [2, 1]),
(RootBeerID:INTEGER, Examples: [105661, 105798, 102514]),
(PurchasePrice:REAL, Examples: [3.0, 1.0])
]
# Table: geolocation
[
(LocationID:INTEGER, Primary Key, Examples: [0, 1, 2]),
(Latitude:REAL, Examples: [0.0, 38.566129, 38.559615]),
(Longitude:REAL, Examples: [0.0, -121.426432, -121.42243])
]
# Table: customers
[
(CustomerID:INTEGER, Primary Key, Examples: [101811, 103508, 104939]),
(First:TEXT, Examples: [Kenneth, Madeleine, Damen]),
(Last:TEXT, Examples: [Walton, Jones, Wheeler]),
(StreetAddress:TEXT, Examples: [6715 Commonwealth Dr, 3603 Leola Way, 6740 Branwood Way]),
(City:TEXT, Examples: [Sacramento, Orangevale, Folsom]),
(State:TEXT, Examples: [CA]),
(ZipCode:INTEGER, Examples: [94256, 94258, 95662]),
(Email:TEXT),
(PhoneNumber:TEXT, Examples: [(916) 918-1561, (916) 186-9423, (916) 164-1156]),
(FirstPurchaseDate:DATE, Examples: [2013-05-30]),
(SubscribedToEmailList:TEXT, Examples: [FALSE, TRUE]),
(Gender:TEXT, Examples: [M, F])
]
# Table: rootbeerreview
[
(CustomerID:INTEGER, Primary Key, Examples: [101811, 105549, 105771]),
(BrandID:INTEGER, Primary Key, Examples: [10012, 10014, 10015]),
(StarRating:INTEGER, Examples: [5, 1, 3]),
(ReviewDate:DATE, Examples: [2013-07-15]),
(Review:TEXT)
]
# Table: rootbeerbrand
[
(BrandID:INTEGER, Primary Key, Examples: [10001, 10002, 10003]),
(BrandName:TEXT, Examples: [A&W, A.J. Stephans, Abita]),
(FirstBrewedYear:INTEGER, Examples: [1919, 1926, 1986]),
(BreweryName:TEXT, Examples: [Dr Pepper Snapple Group]),
(City:TEXT, Examples: [Lodi, Fall River, Covington]),
(State:TEXT, Examples: [CA, MA, LA]),
(Country:TEXT, Examples: [United States, Australia]),
(Description:TEXT),
(CaneSugar:TEXT, Examples: [FALSE, TRUE]),
(CornSyrup:TEXT, Examples: [TRUE, FALSE]),
(Honey:TEXT, Examples: [FALSE, TRUE]),
(ArtificialSweetener:TEXT, Examples: [FALSE, TRUE]),
(Caffeinated:TEXT, Examples: [FALSE, TRUE]),
(Alcoholic:TEXT, Examples: [FALSE]),
(AvailableInCans:TEXT, Examples: [TRUE, FALSE]),
(AvailableInBottles:TEXT, Examples: [FALSE, TRUE]),
(AvailableInKegs:TEXT, Examples: [FALSE, TRUE]),
(Website:TEXT),
(FacebookPage:TEXT),
(Twitter:TEXT),
(WholesaleCost:REAL, Examples: [0.42, 0.98, 1.13]),
(CurrentRetailPrice:REAL, Examples: [1.0, 3.0, 44.0])
]
【Foreign keys】
rootbeer.LocationID=geolocation.LocationID
rootbeer.LocationID=location.LocationID
rootbeer.BrandID=rootbeerbrand.BrandID
location.LocationID=geolocation.LocationID
transaction.CustomerID=customers.CustomerID
transaction.LocationID=location.LocationID
transaction.RootBeerID=rootbeer.RootBeerID
geolocation.LocationID=location.LocationID
rootbeerreview.CustomerID=customers.CustomerID
rootbeerreview.BrandID=rootbeerbrand.BrandID

    【Question】
    On average how many caffeinated root beers are sold a day? average = DIVIDE(COUNT(RootBeerID WHERE Caffeinated = 'TRUE'), COUNT(PurchaseDate)); caffeinated refers to Caffeinated = 'TRUE';

    【Evidence】
    average = DIVIDE(COUNT(RootBeerID WHERE Caffeinated = 'TRUE'), COUNT(PurchaseDate)); caffeinated refers to Caffeinated = 'TRUE';

    Please read and understand the database schema carefully, and generate an executable SQL based on the user's question and evidence. 

SQL: SELECT CAST(COUNT(T2.RootBeerID) AS REAL) / COUNT(DISTINCT T2.PurchaseDate) FROM rootbeerbrand AS T1 INNER JOIN rootbeer AS T2 ON T1.BrandID = T2.BrandID INNER JOIN `transaction` AS T3 ON T2.RootBeerID = T3.RootBeerID WHERE T1.Caffeinated = 'TRUE'