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To generate circuits respecting both limits, a promising opportunity is exploiting u<\/mml:mi>n<\/mml:mi>c<\/mml:mi>o<\/mml:mi>m<\/mml:mi>p<\/mml:mi>u<\/mml:mi>t<\/mml:mi>a<\/mml:mi>t<\/mml:mi>i<\/mml:mi>o<\/mml:mi>n<\/mml:mi><\/mml:math> to trade qubits for gates. We present Reqomp, a method to automatically synthesize correct and efficient uncomputation of ancillae while respecting hardware constraints. For a given circuit, Reqomp can offer a wide range of trade-offs between tightly constraining qubit count or gate count. Our evaluation demonstrates that Reqomp can significantly reduce the number of required ancilla qubits by up to 96%. 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