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To produce or create something very hastily. A noun or pronoun can be used between "bat" and "out." A: "I can't believe he batted out three papers in one day." B: "I bet he doesn't get very good grades on them though."
To produce something in a hurried or informal manner: The new store owner batted out thank-you notes to his first customers all morning. I don't have time before the big party to bake hundreds of cookies, but I think I can bat a few dozen out.