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An oracle for a software program might be a second program that uses a different [[algorithm]] to evaluate the same mathematical expression as the product under test. This is an example of a pseudo-oracle, which is a derived test oracle.<ref name="pseudo-oracle"/>{{rp|466}}
During [[Google]] search, we do not have a complete oracle to verify whether the number of returned results is correct. We may define a metamorphic relation<ref>{{cite journal |first1=Z.Q. |last1=Zhou |first2=S. |last2=Zhang |first3=M. |last3=Hagenbuchner |first4=T.H. |last4=Tse |first5=F.-C. | last5=Kuo |first6=T.Y. |last6=Chen |date=2012 |title=Automated functional testing of online search services |journal=Software Testing, Verification and Reliability |volume=22 |issue=4 |pages=221–243 |doi=10.1002/stvr.437 |hdl=10722/123864 |hdl-access=free }}</ref> such that a follow-up narrowed-down search will produce fewer results. This is an example of a partial oracle, which is a hybrid between specified test oracle and derived test oracle.
A statistical oracle uses probabilistic characteristics,<ref>{{cite conference |url=http://www.mathematik.uni-ulm.de/sai/mayer/publications/oracles.pdf |title=Test Oracles Using Statistical Methods |last1=Mayer |first1=Johannes |last2=Guderlei |first2=Ralph |date=2004 |publisher=Springer |book-title=Proceedings of the First International Workshop on Software Quality, Lecture Notes in Informatics |pages=179–189 |conference=First International Workshop on Software Quality}}</ref> for example with image analysis where a range of certainty and uncertainty is defined for the test oracle to pronounce a match or otherwise. This would be an example of a quantitative approach in human test oracle.
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