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The phrase "automatically by the system" is correct and usable in written English.
It can be used to describe actions or processes that occur without human intervention, typically in the context of technology or software.
Example: "The updates will be installed automatically by the system during the scheduled maintenance window."
Alternatives: "instantly by the system" or "systematically by the system.".
Exact(27)
The programmed instructions determine the set of actions that is to be accomplished automatically by the system.
This is a very interesting result, as these lyrics were retrieved automatically by the system.
The knowledge base may be retrieved automatically by the system or upon request.
Dynamic parameters are those that are calculated automatically by the system and are updated according to the user's selection.
In the proposed work, the retrieval of the required information is done automatically by the system thereby the degree of automation is also increased subsequently.
Assessment is performed by examining the temporal coincidence of the manually (by the expert) and automatically (by the system) detected spikes [6].
Similar(32)
Every change is automatically saved by the system.
The experiment was conducted using 120 question items automatically generated by the system and 88 non-native English learners.
This is due to a few overcrowded cells that are quickly and automatically uncrowded by the system itself.
All other question formats, of which the differences are automatically summarized by the system, cost around 10s for each task.
For quantitative evaluation, velocity curves are available: the maximum velocity vector point curve, automatically detected by the system, and the user-defined vector point curve.
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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