How to compare carry-lookahead and ripple-carry adders?

Question

I am a bit stuck with the concept of carry-lookahead adder so I'd like to compare it with another concept I'm more familiar with: the ripple-carry adder. I'm trying to make some basic math comparison between the two ones.

Assuming every gate can accept at most 2 (two) inputs and has a delay of '1', and that, at least for the moment, we're adding two 4-bit numbers.

Let's start with the ripple-carry adder. I've built it putting four full-adder in column. Every carry-out is computed as

$$c_i^{(\text{out})} = a_i \cdot b_i + \left[ a_i + b_i \right] \cdot c_i^{(\text{in})} \qquad \text{where} \; \cdot \equiv \text{AND},\, + \equiv \text{OR}$$

Since

$$\left[ a_i + b_i \right]$$

is computed in parallel for every full-adder, the cost for computing the k-th carry-out is

$$1 + 2k$$

right?

Now say we want to compute carry's at first, then the sum -- bit by bit. Using the formula above, (and omitting the superscript) we write that

$$c_{i+1} = g_i + p_i c_i$$

Hence, we can write recursively the fourth term as a function of the first one, i.e.

$$c_1 = g_0 + p_0 c_0 \\ c_2 = g_1 + p_1 g_0 + p_1 p_0 c_0 \\ \vdots \\ c_4 = g_3 + p_3 g_2 + p_3 p_2 g_1 + p_3 p_2 p_1 g_0 + p_3 p_2 p_1 p_0 c_0$$

Of course it is the last term that costs more. How much? I'd say

$$\lceil \log_2{4} \rceil + \lceil \log_2{4} \rceil $$

where the first term is needed for computing every AND operations, while the second one for computing every OR operation.

Hence for an overview ...

$$1 + \lceil \log_2{k} \rceil + 2$$

where the first term is the gate delay needed for computing every propagator/generator term, the second term is the one needed for computing every carry_in, then the last term is the gate delay of a single full-adder.

That is, the comparison of "time" between a ripple-carry adder and a carry-lookahead's one is the comparison of the following two functions

$$1 + 2k$$ $$3 + \lceil \log_2{k} \rceil$$

I know that carry-lookahead can be improved more, and I've done that by myself...though I'd like you give me some feedback about the stuff above for now.