The files in the before/after preview slider are exactly the same file size when they're supposed to be showing how their compressed image looks as good as the original. They're also not the same files you get when you click the download button.
Looks like snake oil to me.
That is indeed what the FAQ says, but that being the case, the tool does not actually work very well, and the presentation is incredibly dishonest. The fact is that the JPEGmini versions of these images do lose noticeable quality, but Beamr is hiding this by giving a demo where the images are shown at 25% scale.
Take the dog image, for example. Using the slider, you'd think that JPEGmini nailed it; no visible artifacts whatsoever. But let's look at a section of the image at 100% scale, and see if this tool is really that impressive: http://imgur.com/z12mHnd
...holy block artifacts Batman!
I mean, as far as I know, there aren't even any practically useful algorithms out there for doing lossy compression on PNGs (although there should be).
Excluding of course, the for loop or the while loop; particularly when used in a shell/python/perl/etc script. Matlab is also particularly well suited for this. Then there are visual macro thingamajigs. iMacros for browser based repetitive tasks, which could then be used with an online image editor. Irfanview, I believe has batch image processing, as do many other popular photo/image editors. And last, but not least, Imagej.
You may have added feedback to the loop where many would have had none, but feedback is not a new or novel concept. The only thing I can see that is possibly non-trivial is your method for assessing quality of the output. Given the many high-quality image-processing libraries, and well-documented techniques available, and the subjective nature of assessing "quality" with respect to how an image "looks", I doubt there is anything original there. You've enhanced the workflow for casual users, the uninformed, and those who prefer to spend their time on something else. That arguably has value. While it seems a bit of a stretch to call it "technology" to this audience but, that is what the word means.
IMO, you'd receive a "warmer" welcome from the more technically-minded folks here if you'd dispense with the marketing hype (definitely stop making impossible claims), and show some real evidence of just how much "better" your output is over some reasonable defaults, including cases where your system fails to meet your stated goals (even a random quality assessment will get it right sometimes). Nobody is ever going to believe that any system as you've described works for every case, every time (simply impossible). In other words, you aren't going to sell any ice to these Eskimos.
edit: accidentally posted comment before I was finished blathering.