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The phrase "the same function as" is correct and usable in written English.
You can use it when comparing two things or ideas and when you want to show that they both have a similar purpose. For example, "The brain and the heart both have the same function as they are both essential to keeping the body alive."
Exact(56)
However, both authors report striking differences in the structures that realize one and the same function, as well as striking differences in the function of identical structures.
The internal feedback generated by these easy trials serves the same function as would external feedback [2], [8], [30], [31].
"We serve the same function as the broadsheets," he added.
In her project, the grid of steel mullions performs the same function as Johnson's period windows.
Sociologically, "I think papal trips perform the same function as gay pride parades," Mr. Allen said.
In China, glass served the same function as jade, which was associated with perfectibility and immortality.
Meals serve the same function as the on-board movie, Mr. Mann, the consultant, said.
In the dark era in which it began, it served much the same function as I Love Lucy.
During daylight hours it performs the same function as any other cigar store on a busy corner.
These breaks may be labeled differently, but they serve the same function as government spending.
A contemplative woman lodged in the craggy landscape of "Low Tide" serves the same function as the doppelg?er figures in Friedrich paintings.
More suggestions(17)
the same operation as
the same work as
the same business as
the same responsibility as
the same job as
the same assignment as
the same position as
the same authority as
the same functionality as
the same performance as
the same capability as
the same capabilities as
the same manner as
the same theme as
the same garbage as
the same drill as
the same color as
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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