Extremely slow in autocompletion & code analysis for Kotlin projects in Intellij IDEA

The problem visible in your snapshot is resolved in Kotlin 1.1.4. As of this writing, it's available as an EAP (Early Access Preview) release; the final version will be released soon (and bundled with IntelliJ IDEA 2017.2.2).

Still happens in Kotlin 1.3.50. Got resolved by disabling Add unambiguous imports on the fly in Settings > Editor > General > Auto Import

I recently ran into this with a Kotlin gradle multi module project. I managed to get back to a good code analysis and completion speed by massively increasing my memory settings in the vmoptions, this is what they look like now

-Xms512m
-Xmx16384m
-XX:ReservedCodeCacheSize=960m
-XX:+UseConcMarkSweepGC
-XX:SoftRefLRUPolicyMSPerMB=100
-ea
-XX:CICompilerCount=2
-Dsun.io.useCanonPrefixCache=false
-Djava.net.preferIPv4Stack=true
-Djdk.http.auth.tunneling.disabledSchemes=""
-XX:+HeapDumpOnOutOfMemoryError
-XX:-OmitStackTraceInFastThrow
-Djdk.attach.allowAttachSelf=true
-Dkotlinx.coroutines.debug=off
-Djdk.module.illegalAccess.silent=true
-Dawt.useSystemAAFontSettings=lcd
-Dsun.java2d.renderer=sun.java2d.marlin.MarlinRenderingEngine
-Dsun.tools.attach.tmp.only=true