General Formula
The conversion from spell slots to spell points doesn't use nice numbers for on the fly calculation. That being said, there is a precise mathematical formula for calculating the number of spell points you regain if the game would have you regain a certain number of "spell levels".
$$
\text{Spell Points regained} = \lceil \frac{11}{8} \times \sum_{}^{\text{Spell Slots} \\ \text{ regained}} \text{(Spell Slot Level)} \rceil
$$
Applying this to regaining an individual spell slot the formula tells us that each spell slot level is worth 1.375 spell points, rounded up to the nearest integer.
Arcane Recovery and similar features
So in a situation like Arcane Recovery where you regain up to "half your class level worth of spell slots rounded up", the adjusted calculation is:
$$
\text{Spell Points regained} = \lceil \frac{11}{8} \times \lceil \frac{\text{(Class Level)}}{2} \rceil \rceil
$$
Here you are just skipping the summation of the levels from the more general formula (since your calculation of \$ \lceil \frac{\text{(Class Level)}}{2} \rceil \$ already gives you that total).
But why does this not yield 4 spell points instead of 3 for a caster wishing to make 2 1st level slots instead of 1 2nd level slot?
With Arcane Recovery you are recovering the spell slots simultaneously, not separately.
You apply this formula to the whole operation of regaining spell slots. If each spell slot is worth 1.375 spell points, you convert each spell slot into it's precise value (in the case of two 1st level slots that is 1.375 + 1.375 = 2.75). Rounding is then performed as the last step of the operation. Which yields 3 spell points for 2 levels worth of spell slots.
If on the other hand you were a Sorcerer converting sorcery points into spell points, then each time you convert sorcery points into spell points you perform a distinct operation. However, this is balanced as Sorcery Points use the same conversion progression as Spell Points (for the portion of the Sorcery Points -> Spell Slot conversion table we have in the PHB).
For example, our prospective sorcerer would need to expend 4 Sorcery Points to gain 4 Spell Points, doing two 1st level slot conversions, or they could spend 3 Sorcery Points to gain 3 Spell Points doing a 2nd level slot conversion.
The notation \$ \lceil \text{a} \rceil \$ indicates you are taking the integer ceiling of the value contained within the symbols. That is, you are rounding the value up to the nearest integer.
If we break down the general formula for one spell slot of each level we get this table:
\begin{array} {|r|r|r|r|}
\hline
\text{Spell Slot} & \frac{11}{8} \times \text{(Spell Slot} & \lceil \frac{11}{8} \times \text{(Spell Slot} & \text{Spell Points} \\
\text{Level} & \text{Level)} & \text{Level)} \rceil &\text{ from the DMG} \\
\hline
1 & 1.375 & 2 & 2 \\
\hline
2 & 2.75 & 3 & 3 \\
\hline
3 & 4.125 & 5 & 5 \\
\hline
4 & 5.5 & 6 & 6 \\
\hline
5 & 6.875 & 7 & 7 \\
\hline
6 & 8.25 & 9 & 9 \\
\hline
7 & 9.625 & 10 & 10 \\
\hline
8 & 11 & 11 & 11 \\
\hline
9 & 12.375 & 13 & 13 \\
\hline
\end{array}
so we can see our formula matches the progression precisely.