NEW YORK (AP) — U.S. stocks rallied Tuesday as a late surge helped them regain almost half their losses from the day before, when they had their biggest plunge in 6 ½ years. That came at the end of a day of heavy trading and huge swings for the market.

Major indexes in Asia and Europe took steep losses and U.S. markets started sharply lower, only to repeatedly change direction. After its 1,175-point nosedive Monday, the Dow Jones industrial average lost 567 points right after trading began. After numerous turns higher and lower, it wound up with a gain, coincidentally, of 567.

Despite the turb...