What is another word for by experimentation?
Pronunciation: [ba͡ɪ ɛkspˌɛɹɪməntˈe͡ɪʃən] (IPA) 
When someone wants to highlight that they achieved something through experimentation, there are many synonyms that they can choose from to convey their message effectively. Some alternatives to "by experimentation" include "by trial and error," "based on testing," "through empirical evidence," "via exploration," and "through investigative methods." Each of these phrases emphasizes an aspect of experimentation that makes it a useful and reliable method for discovering new information. Whether you highlight the process of elimination that comes with trial and error or the investigative nature of experimentation, there are numerous ways to express an experimental approach and the results it yields.
