unexplained space in math mode (left/right brackets, vphantom)

Question

I'm currently writing a small tool which automatically generates latex code for equations. I stumbled over the following problem, which in extremely boiled-down form looks like this:

\begin{align*}
a
&=
\left( \left[ \left\{ \left( b
\vphantom{x} \right.
\vphantom{x} \right.
\vphantom{x} \right.
\vphantom{x} \right. 
\\&\quad\;
%--------
c
\\&\quad\;
%--------
\left. \vphantom{x}
\left. \vphantom{x}
\left. \vphantom{x}
\left. \vphantom{x}
d
\right) \right\} \right] \right)
\\&\quad\;
%--------
\left. \left. \left. \left.
e
\right) \right\} \right] \right)
\end{align*}

The output contains some space for which I have no explanation:

Please let me guide you through this.

In the align environment, I have a left side (a) only in the first line, and right sides in all lines. I insert a \quad\; at the beginning of each line (except for the first) to jump over the space of the = character.

In the first line (a, b), I have four opening brackets with auto-scaling (\left). The \vphantom are required in my code to keep the vertical size of the brackets over the line breaks; they contain more complex text, but here I simply pass x. I compensate the four opening brackets with for virtual closing brackets (\right.).

In the second line (c), I just have c which nicely aligns below the right side of the first line. This is what I want for the third line as well.

In the third line (d) (which is actually of the form that my code generates), I have four virtual opening brackets (\left.) and four closing brackets. Now this line generates a lot of space before the d.

In the fourth line (e) I deleted all the \vphantom commands. Surprisingly, this reduces the space. The remaining space seems to be generated by the \left. commands. I could understand if this would be the space occupied by the closing brackets, but it is smaller (please compare with the first line).

So, my problem is that I want to compensate for the unwanted space in the third line by inserting a negative space (e.g. \!), but I have no clue how and why latex generates the space in the first place. Since the code is automatically generated and has an arbitrary number of brackets, I can't just use a negative space of fixed size.

I there anyone deeply familiar with the internal latex code to tell me what latex is doing in this case, such that I can compensate for the unwanted space? Thanks a lot!

---

Edit in response to campa: I included \setlength{\nulldelimiterspace}{0pt} which seems to reduce the spacing, but doesn't eliminate it completely (second example):

Answer 1

I think you need to run \setlength\nulldelimiterspace{0pt}, load the mleftright package, and replace all instances of \left and \right with \mleft and \mright, respectively.

Separately, I'd replace all instances of &\quad\; with &\phantom{{}={}} in order to guarantee correct alignment.

In the following screenshot, I employ | merely to indicate the start and end of material on the right hand side of the (visible or hidden) = symbols. Observe that I've also dropped all \vphantom{x} directives since they don't do anything.

\documentclass{article}
\usepackage{amsmath}    % for 'align*' environment
\usepackage{mleftright} % for '\mleft' and '\mright' macros
\begin{document}
\setlength\nulldelimiterspace{0pt}
\begin{align*}
a
&=
|\mleft( \mleft[ \mleft\{ \mleft( 
b
\mright. \mright. \mright. \mright. | \\
&\phantom{{}={}}
|b| \\
&\phantom{{}={}}
|\mleft. \mleft. \mleft. \mleft. 
b
\mright) \mright\} \mright] \mright) | 
\end{align*}
\end{document}