A complete search of the internet has found these results:
simpler is the most popular phrase on the web.
"simpler" is a comparative adjective, while "more simply" is a comparative adverb.
23,033,399 results on the web
It was a **simpler **time back then.
Did you know that there is a simpler way to make cheese?
I need a simpler method for this task.
Simpler doesn't always mean less sophisticated.
Simpler times call for simpler men.
There must be a simpler way to clean the house than this.
I am hoping to create a simpler method of online shopping.
Simpler does not always mean less complicated.
Is this process simpler than the one we used last time?
3,022,486 results on the web
More simply put, I don't like this job.
Could you figure out a way to do this more simply?
More simply speaking, tell him he's not invited.
The 21st century has seen ways to communicate more simply.
The sun's gravitational force holds the Earth in orbit--or, more simply put, the Earth rotates around the sun.
It couldn't be put more simply than this: there is no reason to continue with this policy.