Weird spacing around large brackets in Plain TeX

Question

I use Plain TeX on a daily basis and a frequent annoyance when typesetting large displays is weird spacing that occurs around bigger parentheses/braces/etc. For example, here is \exp(-x) with the five sizes of braces. In all but the first one, there seems to be extra spacing around the opening parenthesis.

I replaced \exp with {\rm exp} and now the space before the opening parenthesis is gone, but the space after it remains. (I guess it is not really extra space, since the roundedness of the parenthesis makes it take more horizontal space above and below the vertical axis of the minus sign.) There is also random space between the minus sign and the x, which is not there in the first case. I normally fix this by adding a \! before the parenthesis, two \!s before the minus sign, and one more after it.

What is going on behind the scenes to cause this? Is TeX treating the larger parenthesis as a different kind of symbol than the normal-sized parenthesis? (It seems as if TeX thinks I want to subtract x from (.) If so, is there something I can add to my macros to save from having to sprinkle \!s everywhere?

Answer 1

You have not shown your input which makes it rather hard to comment on what is wrong with it but I would guess you have done

$\exp(-x)$
$\exp\big(-x\big)$
$\exp\Big(-x\Big)$
$\exp\bigg(-x\bigg)$
$\exp\Bigg(-x\Bigg)$

\bye

That is an input error, \big is the internal helper for \bigl and \bigr and makes a \mathord so losing the left/right nature and as you note forcing - to take on infix \mathbin spacing.

With the intended input you do not get the spacing that you showed.

$\exp(-x)$
$\exp\bigl(-x\bigr)$
$\exp\Bigl(-x\Bigr)$
$\exp\biggl(-x\biggr)$
$\exp\Biggl(-x\Biggr)$

\bye