When experimenting with new ideas or methods, there are various synonyms for the phrase "by trial and error". "Through experimentation" indicates a process of discovery, often involving a number of attempts before achieving the desired result. "Through trial and experiment" conveys a similar concept. "By experimenting with" suggests a more focused approach, indicating that one is specifically testing different methods or ideas. "By trial and testing" is a straightforward synonym for "by trial and error". Finally, "through iterative attempts" emphasizes the idea of repeating and refining a process until success is achieved. These synonyms provide a range of alternatives for expressing the process of trial and error.