Use same PrecompileTools.jl approach as REPL to precompile (#4024)

src/precompile.jl

@@ -165,7 +165,31 @@ let
         return nothing
     end
 
-    if Base.generating_output()
-        pkg_precompile()
+    # Copied from REPL (originally PrecompileTools.jl)
+    function check_edges(node)
+        parentmi = node.mi_info.mi
+        for child in node.children
+            childmi = child.mi_info.mi
+            if !(isdefined(childmi, :backedges) && parentmi ∈ childmi.backedges)
+                Base.precompile(childmi.specTypes)
+            end
+            check_edges(child)
+        end
+    end
+
+    if Base.generating_output() && Base.JLOptions().use_pkgimages != 0
+        Core.Compiler.Timings.reset_timings()
+        Core.Compiler.__set_measure_typeinf(true)
+        try
+            pkg_precompile()
+        finally
+            Core.Compiler.__set_measure_typeinf(false)
+            Core.Compiler.Timings.close_current_timer()
+        end
+        roots = Core.Compiler.Timings._timings[1].children
+        for child in roots
+            Base.precompile(child.mi_info.mi.specTypes)
+            check_edges(child)
+        end
     end
 end