In this paper, we present several methods to improve the evaluation of homomorphic functions in TFHE, both for fully and for leveled homomorphic encryption. We propose two methods to manipulate packed data, in order to decrease the ciphertext expansion and optimize the evaluation of look-up tables and arbitrary functions in RingGSW based homomorphic schemes. We also extend the automata logic, introduced in [12, 19], to the efficient leveled evaluation of weighted automata, and present a new homomorphic counter called TBSR, that supports all the elementary operations that occur in a multiplication. These improvements speed-up the evaluation of most arithmetic functions in a packed leveled mode, with a noise overhead that remains additive. We finally present a new circuit bootstrapping that converts LWE into low-noise RingGSW ciphertexts in just 137 ms, which makes the leveled mode of TFHE composable, and which is fast enough to speed-up arithmetic functions, compared to the gate-by-gate bootstrapping given in [12]. Finally, we propose concrete parameter sets and timing comparison for all our constructions.