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"by direct calculation" is a correct and usable phrase in written English.
You can use it whenever you are referring to something that has been determined by calculation, without using any additional information or data as a source. Example: He determined the value of pi to six decimal places by direct calculation.
Exact(57)
Stereology-based calculation of microstructural parameters (other than BV/TV, Eu.N and DA) results in values that are different from those obtained by direct calculation [ 15, 30] but microstructural parameters calculated using one method are highly correlated to those calculated using the other method [ 15].
By direct calculation (3.4).
For, by direct calculation, we can get.
By direct calculation, we obtain that.
By direct calculation, we have (3.3).
We prove this by direct calculation.
By direct calculation we obtain (2.12).
By direct calculation, we have (x^{2}=-vert xvert ^{2}).
Similar(3)
By direct calculations we obtain (e).
By direct calculations, we can obtain that.
that can be verified by direct calculations (see, e.g., [27]).
More suggestions(15)
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by direct counting
by direct determination
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by direct deposit
by direct transmission
by direct contact
by direct translocation
by direct observation
by direct transfer
by directly calculation
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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