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The phrase "add by" is not correct in written English
You would not usually use this phrase in any context.
Exact(47)
He compounded the error, they add, by failing to cut rates last fall, hobbling the economy.
BRITAIN and America: two nations divided by a common language and, you could add, by their taste in fiction.
Followed, it might add, by nearly half a century of what Richter has many times (supposedly jokingly) called "Capitalist Realism" in the west.
He does not need to move tall buildings; he just needs to deal with any inaccuracies they add by blocking the signals used to locate the people.
Overstretched in part, I should add, by Labour's lax immigration stance towards east European migrants, since Jack Straw and David Blunkett are this week finally admitting it.
Moody's Economy.com nearly halved its estimate of how many jobs the region would add by June to 9,500, from 18,700.
Similar(11)
You should have added: "by Babbage".
Later details were added by Norwegian sealers.
Another 17 restrictions were added by May 15th.
Nothign is added by "outing".
More can be added by adding a Sony Memory Stick Duo.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com