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The phrase "to demonstrate the performance" is correct and usable in written English.
It can be used when explaining the purpose of an action or experiment, particularly in contexts related to testing or showcasing capabilities.
Example: "The purpose of this study is to demonstrate the performance of the new software under various conditions."
Alternatives: "to showcase the performance" or "to illustrate the performance."
Exact(60)
Simulation results are provided to demonstrate the performance of DINS.
Numerical simulations are presented to demonstrate the performance.
Finally, experimental results are provided to demonstrate the performance.
Experimental results are given to demonstrate the performance in practice.
Examples are used to demonstrate the performance of the algorithms.
A real-world case study is employed to demonstrate the performance of this method.
Several numerical examples are presented to demonstrate the performance and efficiency of the proposed approach.
Several examples are taken from various contexts to demonstrate the performance of such a program.
A measurement system is developed to demonstrate the performance of the proposed method.
Several examples of curve and surface fitting are given to demonstrate the performance of IMTLS method.
Numerical results are presented with gas water Riemann problems to demonstrate the performance of the scheme.
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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