I did some research but I cannot find analytical IK solutions for CRX type of robot, what I ended up with is IKFast. It returns multiple solutions without configuration information.
During the analytical study, I found that paper  mentioned that CRX robot is cuspidal type of robot. This type of robot can pass through different configurations without going across singularities, quite difficult to imagine.
In another paper , the author proposed a method for Kinova robot inverse kinematics. This Kinova is the same with CRX (Fig. 2 of ). They use polynomial method and provides source code. I haven't got a chance to reimplement to CRX robot.
If you guys got an more elegant solution, I would be very much appreciate it!
 A review of cuspidal serial and parallel manipulators
 Kinova Gen3 Lite manipulator inverse kinematics optimal polynomial solution