Approximate Computing (AxC) paradigm aims at designing computing systems that can satisfy the rising performance demands and improve the energy efficiency. AxC exploits the gap between the level of accuracy required by the users, and the actual precision provided by the computing system, for achieving diverse optimizations. Various AxC techniques have been proposed so far in the literature at different abstraction levels from hardware to software. These techniques have been successfully utilized and combined to realize approximate implementations of applications in various domains (e.g. data analytic, scientific computing, multimedia and signal processing, and machine learning). Unfortunately, state-ofthe-art approximation methodologies focus on a single abstraction level, such as combining elementary components (e.g., arithmetic operations) which are firstly approximated using component-level metrics and then combined to provide a good trade-off between efficiency and accuracy at the application level. This hinders the possibility for designers to explore different approximation opportunities, optimized for different applications and implementation targets. Therefore, we designed and implemented E-IDEA, an automatic framework that provides an application-driven pproximation approach to find the best approximate versions of a given application targeting different implementations (i.e., hardware and software). E-IDEA compounds 1) a source-to-source manipulation tool and 2) an evolutionary search engine to automatically realize approximate application variants and perform a Design-Space Exploration (DSE). The latter results in a set of non-dominate approximate solutions in terms of trade-off between accuracy and efficiency. Experimental results validate the effectiveness and the flexibility of the approach in generating optimized approximate implementations of different applications, by using different approximation techniques and different accuracy/error metrics and for different implementation targets.