All pure mathematicians know that the goal is to produce insight, rather than to simply obtain results. However, it might sometimes be of value to disseminate largely empirical work. In the same spirit as this question, which journals publish experimental and computational work in pure maths? Experimental Mathematics is one obvious answer, but what others exist?
I think one suitable journal is "Mathematics of Computation", an AMS journal. http://www.ams.org/publications/journals/journalsframework/mcom
Also, specific to algebra, the Journal of Algebra has a computational section: http://www.journals.elsevier.com/journal-of-algebra/
There is LMS Journal of Mathematics and Computation, which is currently in an unclear position, as the LMS Council (the governing body of LMS) wants to shut it down as unprofitable (sic!), but due to objections by a considerable number of members (IMHO Council is just dead wrong on this, and lives in the past, as far as publishing matters go) a special meeting of LMS will take place in February 2016 to discuss and (hopefully) reverse this.
For some reason this meeting cannot be found in LMS agenda.
Electronic Journal of Combinatorics does publish experimental things, provided they are sufficiently related to discrete mathematics.
Arnold Mathematical Journal has this option. See the Journal Description, AMJ, Vol 1, pp 1 - 3:
Following Arnold, we will try to unhide this process and made it public by encouraging the authors to include informal discussion of their motivation, possibly unsuccessful lines of attack, experimental data and close by research directions.
Computational Methods in Science and Technology is a Polish physics-oriented journal, but also lists experimental mathematics as a field of interest in its ''Aims and Scope'' section.