Travelers dream of the perfect trick to find the cheapest airfare every time, every trip.

There are theories, some of them backed up by real number-crunching — shop on a Tuesday, 57 days before your flight. But using a tidy formula to find the cheapest fare may be as futile as trying to time the stock market.

"There isn't a golden rule anymore," says Patrick Scurry, chief data scientist for Hopper, a travel-information firm that archives ticket prices. "There are these 'average' rules, but they're not that useful necessarily for a specific trip."

Airlines Reporting Corp., which handles tickets sold through travel agents, pinpointed Day 57 as when you'll find the cheapest average domestic fares. But in a nod to the inexactness of the science, it also said that the lowest domestic prices are relatively unchanged about 50 to 100 days before a flight.

For international trips, ARC says shop 171 days out. CheapAir.com, a fare-search website, says the magic moment is, on average, 47 days before a U.S. trip.

As for the best day to shop for travel, the accepted answer for many years was Tuesday because that is when airlines often announced advertised sales. Expedia Inc. says for tickets bought at least 21 days in advance, Tuesday is still cheapest by a thin margin over Wednesday, but Sunday is better for tickets bought within 21 days of travel — an average savings of $12, or 2.2 percent, over buying on Saturday or Tuesday, according to Expedia.

George Hobica, founder of airfarewatchdog.com, says you should keep checking fares every day because unadvertised sales can pop up any time during the week.

"Sometimes we'll see amazing sales on Saturday mornings, especially to international destinations," he says. "A lot of people don't search on weekends because they've been brainwashed to think that Tuesday is the day to book."

Conventional airline sales often run three days, but some airlines are now using flash sales that further erode old rules about when to buy. For example, Virgin America alerts its customers about a half-dozen times a year about a sale that usually ends within a few hours.

"They certainly work as long as you don't do too many of them," says Virgin's CEO, David Cush. "It does create urgency in the consumer's mind."

Virgin's flash sales are generally advance purchase for travel in a few weeks, so they are not practical for last-minute business trips.

Waiting until the last minute for a bargain fare doesn't work as well anymore. Many flights are full, and prices usually rise as departure time gets close.

If you're flying around the holidays, booking early is unlikely to save you much money. The experts say airlines know flights will be full, they know which days people want to travel — the Sunday after Thanksgiving, for example — so prices start high and stay there.

Buying too soon — booking that 2016 trip to Italy now because you had such a great time there last month — is a mistake because airlines usually aim high when they list flights 11 months or so before departure. But the experts say it's less costly than buying too late when seats are sparse.

Even if you can't always score the lowest possible fare, there are other things you can do to save money:

Most obviously, compare prices from different airlines, and factor in extra services that might involve a fee, such as checking a bag.

There are plenty of websites, apps and Twitter accounts that tell consumers about bargains on specific routes or sales.

Consider alternate airports or days of travel — flying on Tuesday, Wednesday and Saturday tends to be cheaper.

Connecting flights are often cheaper than nonstop, but you'll spend more hours traveling and increase your odds of getting stranded.

There's another little trick while booking, according to CheapAir's Klee. If you're buying several tickets, it can be cheaper to book them one or two at a time rather than all together because of the way airlines price and sell seats.

If you buy a ticket and see the same flight for less the next day, call the airline. 

Federal rules require that airlines give consumers a refund if they cancel a ticket within 24 hours and the flight is at least a week away. American Airlines lets customers reserve a seat for 24 hours before paying, while most airlines meet the requirement simply by offering refunds.