The rapid evolution of compute-intensive programs from bio-signal to image-, and video processing has motivated moving toward coarse grained reconfigurable architectures (CGRAs), having high-parallelism capability with post-fabrication datapath versatility. To enhance energy efficiency of such error-resilient applications, state-of-the-art (SoA) CGRAs exploit approximation techniques, while maintaining an acceptable accuracy for the final quality of result (QoR). However, such CGRAs suffer from overheads of utilizing separate Add/Mul/Div units. We propose GREEN as an energy-efficient CGRA, which enables synergistic effects of a chain of approximation and optimization techniques in various levels of abstraction, from application-, to architecture-, to circuit-level, in a cross-layer hierarchy. Enabling this, GREEN offers different levels of energy-accuracy tradeoffs through the flexibility of its small processing elements (PEs), each of which can support various functionalities and precision-adaptability in a single instruction, multiple data (SIMD) or multiple instruction, multiple data (MIMD) manner. Experimental results obtained with Synopsys Design Compiler and Cadence Innovus at 45-nm CMOS technology node demonstrate the efficiency of the proposed SISD/SIMD/MIMD CGRA over the accurate and SoA counterparts. In particular, the MIMD mode of GREEN enables up to $6.6\times$ higher throughput while dissipating 21% less energy than the accurate counterpart. Moreover, the end-to-end evaluation of GREEN variants on eight single- and multikernel applications from classification, bio-signal (ECG/EEG), and image/video processing domains demonstrates significant performance improvement, compared to the accurate CGRA. In particular, GREEN-MIMD not only speed-ups the ECG QRS detection by 49% and consumes 43% less area and 66% less energy than the accurate CGRA, but also maintains the heartbeat detection accuracy at 100%. GREEN implementations is available at https://cfaed.t...