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The phrase "determined by formula" is correct and can be used in written English.
It means that something is calculated or figured out using a specific set of instructions or equations. Here is an example: "The amount of interest you'll pay on your loan is determined by formula, based on your credit score and the current interest rate."
Exact(16)
(u(t)) is determined by formula (51).
The modulus and orientation are determined by Formula (8).
(5) (u(t)) is determined by formula (51).
ICAR functions had been studied for the set which is determined by formula (2.45).
Averaged values of weighting coefficients are determined by formula (1): w t r ¯ = ∑ p = 1 N w t p N, t = 1, k − 1 ¯, r = 1, R ¯, (1).
Figure 3 demonstrates the transformation of the number of years since a disaster into the resulting single factor time as determined by formula 2.
Similar(44)
But even those supplies are determined by formulas based on the spot prices.
It's true that increased spending also contributes to the deficit, and that there has been a substantial increase in discretionary spending -- spending that, unlike such items as Social Security payments, isn't automatically determined by formulas.
The amount given to each state is determined by formulas involving current energy prices, the number of low-income families in a state and how cold a particular region has been.
An outgrowth of the study was a consensus to eliminate parole for many offenders and to mandate long sentences determined by formulas rather than rely on the discretion of judges and parole boards.
Relative expression was determined by the formula 2− ΔΔCt.
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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