One of the most widely studied techniques in software testing researchis mutation testing - a technique for evaluating the quality of testsuites. Despite over four decades of academic advances in thistechnique, mutation testing has not found its way to mainstreamdevelopment. The key issue with mutation testing is its highcomputational cost: It requires running the test suite against notjust the program under test but against typically thousands ofmutants, i.e., syntactic variants, of the program. Our key insight isthat exciting advances in the upcoming, yet unrelated, area ofapproximate computing allow us to define a principled approach thatprovides the benefits of traditional mutation testing at a fraction ofits usually large cost. This paper introduces the idea of a novel approach, named ApproxiMut, that blends the power of mutation testing with the practicality ofapproximate computing. To demonstrate the potential of our approach, we present a concrete instantiation: Rather than executing testsagainst each mutant on the exact program version, ApproxiMut obtainsan approximate test/program version by applying approximatetransformations and runs tests against each mutant on the approximatedversion. Our initial goal is to (1) measure the correlation betweenmutation scores on the exact and approximate program versions, (2)evaluate the relation among mutation operators and approximatetransformations, (3) discover the best way to approximate a test and aprogram, and (4) evaluate the benefits of ApproxiMut. Our preliminaryresults show similar mutation scores on the exact and approximateprogram versions and uncovered a case when an approximated test was, to our surprise, better than the exact test.