Question: Which cocktails has more nicknames, "Jack and Coke" or "Derby"?

full_context: Document 1: Jack and Coke: Jack and Coke (also referred to as JD and Coke, Jack Coke, or a Lemmy) is a cocktail made with Jack Daniel's whiskey and Coca-Cola. The drink is usually served with ice in an old-fashioned glass or a Collins glass.
Document 2: Dark 'n' Stormy: A Dark 'n' Stormy is a highball cocktail made with dark rum (the "dark") and ginger beer (the "stormy") served over ice and garnished with a slice of lime. Lime juice is also frequently added.
Document 3: Tom Collins: The Tom Collins is a Collins cocktail made from gin, lemon juice, sugar, and carbonated water. First memorialized in writing in 1876 by Jerry Thomas, "the father of American mixology", this "gin and sparkling lemonade" drink is typically served in a Collins glass over ice.
Document 4: Lynchburg Lemonade: A Lynchburg Lemonade is a cocktail and long drink made with, among other ingredients, Jack Daniel's Tennessee whiskey. It is named after Lynchburg, Tennessee, home of the Jack Daniel's distillery. A typical recipe is:
Document 5: Gimlet (cocktail): The gimlet (pronounced with a hard 'g') is a cocktail made of gin and lime juice. A 1928 description of the drink was: "gin, a spot of lime, and soda". The description in the 1953 Raymond Chandler novel "The Long Goodbye" stated that "a real gimlet is half gin and half Rose's lime juice and nothing else". This is in line with the proportions suggested by "The Savoy Cocktail Book" (1930) which specifies one half Plymouth Gin and one half Rose's Lime Juice Cordial. However, modern tastes are less sweet, and generally provide for at least two parts gin to one part of the lime and other non alcoholic elements (see recipes below).
Document 6: Old Fashioned: The Old Fashioned is a cocktail made by muddling sugar with bitters, then adding alcohol, such as whiskey or brandy, and a twist of citrus rind. It is traditionally served in a short, round, tumbler-like glass, which is called an Old Fashioned glass, named after the drink.
Document 7: Farnell (cocktail): A Farnell is a cocktail made with Jack Daniel's whiskey or often with whiskey from the High West Distillery mixed with lemonade. The drink is usually served in an old-fashioned glass or a Collins glass with ice, and it is considered a lighter, less sweet alternative to a lynchburg lemonade.
Document 8: Derby (cocktail): The Derby is an IBA Official Cocktail composed of gin, peach bitters and mint leaves.
Document 9: Clover Club Cocktail: The Clover Club Cocktail is a cocktail consisting of Gin, Lemon Juice, Raspberry Syrup, and an egg white. The egg white is not added for the purpose of giving the drink flavor, but rather acts as an emulsifier. Thus when the drink is shaken a characteristic foamy head is formed.
Document 10: Pink Gin: Pink Gin or Pink Plymouth is a cocktail made fashionable in England in the mid-19th century, consisting of Plymouth gin and a dash of Angostura bitters, a dark red bitters that makes the whole drink pinkish. Lemon rind is also commonly used as a garnish, with the citrus oils subtly complementing the flavour.
Document 11: American Trilogy Cocktail: The American Trilogy cocktail is a variation of the classic Old Fashioned. Barmen Richard Boccato and Michael McIlroy, created the American Trilogy in 2007 while bartending together at New York’s Little Branch. This Old Fashioned-style cocktail follows the same bitters, sugar, whiskey and orange peel profile as the classic, but uses orange bitters, a brown sugar cube and one part Applejack and one part rye whiskey to change it up. As the name implies, each ingredient of this three-part cocktail represents one pillar of the Trilogy. Laird’s Bonded Applejack Brandy is the first and oldest distilled spirit in America with American rye whiskey following soon after in the late 1700s. The third pillar of this cocktail is somewhat of a mystery according to creator Richard Boccato, but is often thought to be the orange bitters because of its American Origins.
Document 12: Gin and tonic: A gin and tonic is a highball cocktail made with gin and tonic water poured over ice. It is usually garnished with a slice or wedge of lime. The amount of gin varies according to taste. Suggested ratios of gin to tonic are between 1:1 and 1:3.
Document 13: Old Fashioned glass: The Old Fashioned glass or rocks glass is a short tumbler used for serving tan spirits, such as whisky, with ice cubes ("on the rocks"). It is also normally used to serve certain cocktails, such as the Old Fashioned, from which it receives its name.
Document 14: Planter's Punch: Planter's Punch is an IBA Official Cocktail made of dark rum, several juices, grenadine syrup, sugar syrup, and Angostura bitters.
Document 15: Jack Daniel's: Jack Daniel's is a brand of Tennessee whiskey and the top selling American whiskey in the world. It is produced in Lynchburg, Tennessee, by the Jack Daniel Distillery, which has been owned by the Brown-Forman Corporation since 1956. Despite being the location of a major operational distillery, Jack Daniel's home county of Moore is a dry county, so the product is not available for purchase at stores or restaurants within the county.
ground_truth: Jack and Coke