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Description
Accidentally noticed when checking solutions for #2300 -- just looking quickly (and not exhaustively yet) for possible impacts on my booklet SILE and the Hydra of Maths -- but the problem was already in the original edition.
It's just slightly more visible here (with the last "attempt" on #2300, resulting in slightly scaled parentheses also raising the overline bar...), but it was still present and I just failed to notice it earlier...

... And that overline bar is actually misplaced -- it should have been as MathJax renders it with the exact same formula (\textstyle
added to switch to inline mode):

Minimal reproduction
Inline $`\mathcal{L}_\phi=\overline{\left(\partial_\mu\phi\right)}\partial^\mu\phi-\frac{\mu\phi-m_h^2\left[\bar{\phi}\phi-\frac{\nu^2}{2}\right]^2}{2\nu^2}`
$`\mathcal{L}_\phi=\overline{(\partial_\mu\phi)}\partial^\mu\phi-\frac{\mu\phi-m_h^2[\bar{\phi}\phi-\frac{\nu^2}{2}]^2}{2\nu^2}`
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
$`\mathcal{L}_\phi=\overline{\left(\partial_\mu\phi\right)}\partial^\mu\phi-\frac{\mu\phi-m_h^2\left[\bar{\phi}\phi-\frac{\nu^2}{2}\right]^2}{2\nu^2}`
Sedeiusmod tempor incididunt.
Lorem ipsum dolor sit amet, consectetur adipiscing elit.
$`\mathcal{L}_\phi=\overline{(\partial_\mu\phi)}\partial^\mu\phi-\frac{\mu\phi-m_h^2[\bar{\phi}\phi-\frac{\nu^2}{2}]^2}{2\nu^2}`
Sedeiusmod tempor incididunt.

Analysis
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It's correct when the line is short.
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It's independent from
\left...\right
constructs being explicitly used or not -
It occurs when the line is stretched or shrunk due to justification. The formula is also stretched or shrunk, everything seems at its intended place, except the accents.
Solution
It turns out there's just a missing scaling for the x position in the call to scaleFn() in method elements.text:output
SILE.outputter:scaleFn(x, y, xratio, yratio, function ()
Should have been:
SILE.outputter:scaleFn(scaleWidth(x, line), y, xratio, yratio, function ()
(Well, this scaleWidth(x, line)
is invoked a few lines earlier, so could be stored in a variable of course, and just reused)
And hurray! This does fix too in my booklet some slightly offset accents on p. 5 (formula above the table of contents), which I had noticed but did not understood at the time.
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