Guided fuzzing has, in recent years, been able to uncover many new vulnerabilities in real-world software due to its fast input mutation strategies guided by path-coverage. However, most fuzzers are unable to achieve high coverage in deeper parts of programs. Moreover, fuzzers heavily rely on the diversity of the seed inputs, often manually provided, to be able to produce meaningful results. In this paper, we present Wildfire, a novel open-source compositional fuzzing framework. Wildfire finds vulnerabilities by fuzzing isolated functions in a C-program and, then, using targeted symbolic execution it determines the feasibility of exploitation for these vulnerabilities. Based on our evaluation of 23 open-source programs (nearly 1 million LOC), we show that Wildfire, as a result of the increased coverage, finds more true-positives than baseline symbolic execution and fuzzing tools, as well as state-of-the-art coverage-guided tools, in only 10% of the analysis time taken by them. Additionally, Wildfire finds many other potential vulnerabilities whose feasibility can be determined compositionally to confirm if they are false-positives. Wildfire could also reproduce all of the known vulnerabilities and found several previously-unknown vulnerabilities in three open-source libraries.