quickly, fast, swiftly, speedily, at (full) speed, at the speed of light, post-haste, hotfoot, at full tilt, as fast as one's legs can carry one, at a gallop, expeditiously, briskly, promptly;

hurriedly, in a hurry, fast and furious, hastily, in haste, in a rush, precipitately, abruptly

informal like a shot, double quick, p.d.q. (pretty damn quick), before one can say Jack Robinson, in a flash, hell for leather, at warp speed, pronto, at the double, like a bat out of hell, like (greased) lightning, like a madman/madwoman, like mad, like crazy, like blazes, like a streak, like the wind, like a bomb, like nobody's business, like a scalded cat, like the deuce, a mile a minute, before the ink is dry on the page, before one can say knife

British informal like the clappers, at a rate of knots, like billy-o

North American informal lickety-split

literary apace