I think this program must have been accepted by CVX due to a bug in CVX 3.0beta. CVX 3.0beta does extend he DCP rules and allow some programs which CVX 2,1 does not, but this program should not be accepted. I have no idea what problem CVX 3.0beta actually is submitting to the solver, but youy should consider any answer provided to be wrong.
I recommend you switch to CVX 2.,1 and not use CVX 3.0beta. Given your interest in problems involving log, rel_entr , etc. I suggest you install CVXQUAD and follow the instructions at CVXQUAD: How to use CVXQUAD's Pade Approximant instead of CVX's unreliable Successive Approximation for GP mode, log, exp, entr, rel_entr, kl_div, log_det, det_rootn, exponential cone. CVXQUAD's Quantum (Matrix) Entropy & Matrix Log related functions
Edit: I see you used CvX 3.0beta Build 1175, which is not the most recent build of 3.0beta. I still recommend that you not use CVX 3.0beta, but if you do, at least change to 3.0beta Build 1183, which is the most recent 3.0beta vuild.
Edit2: I ran this program under CVX 30beta Build 1183, and duplicated your results. I then specified
cvx_solver scs, which utilized scs’ native exponential cone capability, and got the same result (to several decimal places). So apparently CVX 3.0beta is formulating the same wrong problem both for its successive approximation method and for utilization of the native exponential cone capability of scs.