Incorrect spelling


Incorrect spelling, explanation: this spelling is incorrect because there is no reason to add the vowel i when adding the comparative suffix -r or -er. The core adjective is simple: simple + -r = simpler. When adding the suffix -er to the word ending with y we change this consonant to i and this may be the reason for this confusion.

Correct spelling


Correct spelling, explanation: simpler is a comparative form of the adjective simple. To create comparative from a short adjective (up to 2 syllables) -r or -er is added to the base form. The misspelling simplier may be a mistake based on adding the suffix to an adverb (simply), not an adjective. Simplier is therefore wrong.

Definition of simpler:
adjective, the comparative form of the adjective simple, something easier, more plain, and uncomplicated
I think it would be simpler to call him than write him an e-mail.
Don’t be angry at my uncle. He is very simple and doesn’t have proper manners.