A stream of tuples are processed by a plurality of processing elements, each including one or more stream operators, operating on computer processors. A method determines whether a first stream operator includes a first operation that is deterministic and whether a second stream operator includes a second operation that is equivalent to the first operation. In response to determining that the first operation is deterministic and the second operation is equivalent to the first operation, the first stream operator is configured to include in a tuple output from the first stream operator a result of performing the first operation using a first input. The second stream operator, which uses a second input when performing the second operation, determines whether the second input is the same as the first input, and uses the result in lieu of performing the second operation when the first and second inputs are the same.