High performance approximate adders typically comprise of multIPle smaller sub-adders, carry prediction units and error correction units. In this paper, we present a low-latency generic accuracy configurable adder to support variable approximation modes. It provides a higher number of potential configurations compared to state-of-the-art, thus enabling a high degree of design flexibility and trade-off between performance and output quality. An error correction unit is integrated to provide accurate results for cases where high accuracy is required. Furthermore, an associated scheme for error probability estimation allows convenient comparison of different approximate adder configurations without requiring the need to numerically simulate the adder. Our experimental results validate the developed error model and also the lower latency of our generic accuracy configurable adder over state-of-the-art approximate adders. For functional verification and prototyping, we have used a Xilinx Virtex-6 FPGA. Our adder model and synthesizable RTL are made open-source.