diff --git a/src/overloads.jl b/src/overloads.jl
index 5d85c638e..69eaef3cb 100644
--- a/src/overloads.jl
+++ b/src/overloads.jl
@@ -59,24 +59,43 @@ for (jlop, hloop, RT) in (
             )
         end
 
-        function $jlop(lhs::TracedRArray{ElType,Shape,N}, rhs) where {ElType,Shape,N}
-            rhs = promote_to(lhs, rhs)
-            return TracedRArray{$RT,Shape,N}(
+        function $jlop(
+            lhs::TracedRArray{ElType,(),0}, rhs::TracedRArray{ElType,(),0}
+        ) where {ElType}
+            return TracedRArray{$RT,(),0}(
                 (),
                 MLIR.IR.result(
                     MLIR.Dialects.stablehlo.$hloop(lhs.mlir_data, rhs.mlir_data), 1
                 ),
             )
         end
+    end
 
-        function $jlop(lhs, rhs::TracedRArray{ElType,Shape,N}) where {ElType,Shape,N}
-            lhs = promote_to(rhs, lhs)
-            return TracedRArray{$RT,Shape,N}(
-                (),
-                MLIR.IR.result(
-                    MLIR.Dialects.stablehlo.$hloop(lhs.mlir_data, rhs.mlir_data), 1
-                ),
-            )
+    for otherType in (Number, Any, TracedRArray{S,(),0} where {S})
+        @eval begin
+            function $jlop(
+                lhs::TracedRArray{ElType,Shape,N}, rhs::$otherType
+            ) where {ElType,Shape,N}
+                rhs = promote_to(lhs, rhs)
+                return TracedRArray{$RT,Shape,N}(
+                    (),
+                    MLIR.IR.result(
+                        MLIR.Dialects.stablehlo.$hloop(lhs.mlir_data, rhs.mlir_data), 1
+                    ),
+                )
+            end
+
+            function $jlop(
+                lhs::$otherType, rhs::TracedRArray{ElType,Shape,N}
+            ) where {ElType,Shape,N}
+                lhs = promote_to(rhs, lhs)
+                return TracedRArray{$RT,Shape,N}(
+                    (),
+                    MLIR.IR.result(
+                        MLIR.Dialects.stablehlo.$hloop(lhs.mlir_data, rhs.mlir_data), 1
+                    ),
+                )
+            end
         end
     end
 end
@@ -203,6 +222,13 @@ function Statistics.mean(A::TracedRArray{T,Shape,N}; dims=:) where {T,Shape,N}
     denom = dims isa Colon ? length(A) : prod(Base.Fix1(size, A), dims)
     return mapreduce(identity, +, A; dims) / denom
 end
+function Statistics.var(
+    A::TracedRArray{T,Shape,N}; dims=:, mean=nothing, corrected=true
+) where {T,Shape,N}
+    mean === nothing && (mean = Statistics.mean(A; dims))
+    denom = (dims isa Colon ? length(A) : prod(Base.Fix1(size, A), dims)) - corrected
+    return mapreduce(abs2, +, A .- mean; dims) / denom
+end
 
 function elem_apply(f, args::Vararg{Any,Nargs}) where {Nargs}
     fnwrap, func2, traced_result, result, seen_args, ret, linear_args, in_tys, linear_results = make_mlir_fn(