There is a growing interest in numeric-algebraic techniques in the computer algebra community as such techniques can speed up many applications. This paper is concerned with one such approach called Exact Numeric Computation (ENC). The ENC approach to algebraic number computation is based on iterative verified approximations, combined with constructive zero bounds. This paper describes CORE 2, the latest version of the CORE, a package designed for applications such as non-linear computational geometry. The adaptive complexity of ENC combined with filters makes such libraries practical. CORE 2 smoothly integrates our algebraic ENC subsystem with transcendental functions with epsilon-accurate comparisons. This paper describes how the design of CORE 2 addresses key software issues such as modularity, extensibility, efficiency in the a setting that combines algebraic and transcendental elements. Our redesign preserves the original goals of the CORE, namely, to provide a simple and natural interface for ENC computation to support rapid prototyping and exploration. We present examples, experimental results, and timings for our new system, released as CORE 2.0.