diff --git a/src/nlp_expr.jl b/src/nlp_expr.jl
index 60763939f6a..b76cbcd706b 100644
--- a/src/nlp_expr.jl
+++ b/src/nlp_expr.jl
@@ -81,15 +81,11 @@ struct GenericNonlinearExpr{V<:AbstractVariableRef} <: AbstractJuMPScalar
     head::Symbol
     args::Vector{Any}
 
-    function GenericNonlinearExpr(head::Symbol, args::Vector{Any})
-        index = findfirst(Base.Fix2(isa, AbstractJuMPScalar), args)
-        if index === nothing
-            error(
-                "Unable to create a nonlinear expression because it did not " *
-                "contain any JuMP scalars. head = $head, args = $args.",
-            )
-        end
-        return new{variable_ref_type(args[index])}(head, args)
+    function GenericNonlinearExpr{V}(
+        head::Symbol,
+        args::Vararg{Any},
+    ) where {V<:AbstractVariableRef}
+        return new{V}(head, Any[a for a in args])
     end
 
     function GenericNonlinearExpr{V}(
@@ -100,6 +96,35 @@ struct GenericNonlinearExpr{V<:AbstractVariableRef} <: AbstractJuMPScalar
     end
 end
 
+variable_ref_type(::Type{GenericNonlinearExpr}, ::Any) = nothing
+
+function variable_ref_type(::Type{GenericNonlinearExpr}, x::AbstractJuMPScalar)
+    return variable_ref_type(x)
+end
+
+function _has_variable_ref_type(a)
+    return variable_ref_type(GenericNonlinearExpr, a) !== nothing
+end
+
+function _variable_ref_type(head, args)
+    if (i = findfirst(_has_variable_ref_type, args)) !== nothing
+        V = variable_ref_type(GenericNonlinearExpr, args[i])
+        return V::Type{<:AbstractVariableRef}
+    end
+    return error(
+        "Unable to create a nonlinear expression because it did not contain " *
+        "any JuMP scalars. head = `:$head`, args = `$args`.",
+    )
+end
+
+function GenericNonlinearExpr(head::Symbol, args::Vector{Any})
+    return GenericNonlinearExpr{_variable_ref_type(head, args)}(head, args)
+end
+
+function GenericNonlinearExpr(head::Symbol, args::Vararg{Any,N}) where {N}
+    return GenericNonlinearExpr{_variable_ref_type(head, args)}(head, args...)
+end
+
 """
     NonlinearExpr
 
@@ -110,15 +135,6 @@ const NonlinearExpr = GenericNonlinearExpr{VariableRef}
 
 variable_ref_type(::GenericNonlinearExpr{V}) where {V} = V
 
-# We include this method so that we can refactor the internal representation of
-# GenericNonlinearExpr without having to rewrite the method overloads.
-function GenericNonlinearExpr{V}(
-    head::Symbol,
-    args...,
-) where {V<:AbstractVariableRef}
-    return GenericNonlinearExpr{V}(head, Any[args...])
-end
-
 const _PREFIX_OPERATORS =
     (:+, :-, :*, :/, :^, :||, :&&, :>, :<, :(<=), :(>=), :(==))
 
@@ -527,6 +543,8 @@ function moi_function(f::GenericNonlinearExpr{V}) where {V}
     return ret
 end
 
+jump_function(::GenericModel{T}, x::Number) where {T} = convert(T, x)
+
 function jump_function(model::GenericModel, f::MOI.ScalarNonlinearFunction)
     V = variable_ref_type(typeof(model))
     ret = GenericNonlinearExpr{V}(f.head, Any[])
@@ -542,8 +560,6 @@ function jump_function(model::GenericModel, f::MOI.ScalarNonlinearFunction)
             for child in reverse(arg.args)
                 push!(stack, (new_ret, child))
             end
-        elseif arg isa Number
-            push!(parent.args, arg)
         else
             push!(parent.args, jump_function(model, arg))
         end
@@ -833,33 +849,10 @@ function Base.show(io::IO, f::NonlinearOperator)
     return print(io, "NonlinearOperator($(f.func), :$(f.head))")
 end
 
-# Fast overload for unary calls
-
-(f::NonlinearOperator)(x) = f.func(x)
-
-(f::NonlinearOperator)(x::AbstractJuMPScalar) = NonlinearExpr(f.head, Any[x])
-
-# Fast overload for binary calls
-
-(f::NonlinearOperator)(x, y) = f.func(x, y)
-
-function (f::NonlinearOperator)(x::AbstractJuMPScalar, y)
-    return GenericNonlinearExpr(f.head, Any[x, y])
-end
-
-function (f::NonlinearOperator)(x, y::AbstractJuMPScalar)
-    return GenericNonlinearExpr(f.head, Any[x, y])
-end
-
-function (f::NonlinearOperator)(x::AbstractJuMPScalar, y::AbstractJuMPScalar)
-    return GenericNonlinearExpr(f.head, Any[x, y])
-end
-
-# Fallback for more arguments
-function (f::NonlinearOperator)(x, y, z...)
-    args = (x, y, z...)
-    if any(Base.Fix2(isa, AbstractJuMPScalar), args)
-        return GenericNonlinearExpr(f.head, Any[a for a in args])
+function (f::NonlinearOperator)(args::Vararg{Any,N}) where {N}
+    types = variable_ref_type.(GenericNonlinearExpr, args)
+    if (i = findfirst(!isnothing, types)) !== nothing
+        return GenericNonlinearExpr{types[i]}(f.head, args...)
     end
     return f.func(args...)
 end
diff --git a/src/operators.jl b/src/operators.jl
index 7c0ec273ae4..5310234ddc0 100644
--- a/src/operators.jl
+++ b/src/operators.jl
@@ -195,20 +195,19 @@ function Base.:/(lhs::GenericAffExpr, rhs::_Constant)
     return map_coefficients(c -> c / rhs, lhs)
 end
 
-function Base.:^(lhs::AbstractVariableRef, rhs::Integer)
-    T = value_type(typeof(lhs))
+function Base.:^(lhs::V, rhs::Integer) where {V<:AbstractVariableRef}
     if rhs == 0
-        return one(T)
+        return one(value_type(V))
     elseif rhs == 1
         return lhs
     elseif rhs == 2
         return lhs * lhs
     else
-        return GenericNonlinearExpr(:^, Any[lhs, rhs])
+        return GenericNonlinearExpr{V}(:^, Any[lhs, rhs])
     end
 end
 
-function Base.:^(lhs::GenericAffExpr{T}, rhs::Integer) where {T}
+function Base.:^(lhs::GenericAffExpr{T,V}, rhs::Integer) where {T,V}
     if rhs == 0
         return one(T)
     elseif rhs == 1
@@ -216,7 +215,7 @@ function Base.:^(lhs::GenericAffExpr{T}, rhs::Integer) where {T}
     elseif rhs == 2
         return lhs * lhs
     else
-        return GenericNonlinearExpr(:^, Any[lhs, rhs])
+        return GenericNonlinearExpr{V}(:^, Any[lhs, rhs])
     end
 end
 
diff --git a/test/test_nlp.jl b/test/test_nlp.jl
index d4f34cfe56a..ff8be02a7bc 100644
--- a/test/test_nlp.jl
+++ b/test/test_nlp.jl
@@ -1605,7 +1605,7 @@ function test_parse_expression_nonlinearexpr_call()
     model = Model()
     @variable(model, x)
     @variable(model, y)
-    f = GenericNonlinearExpr(:ifelse, Any[x, 0, y])
+    f = NonlinearExpr(:ifelse, Any[x, 0, y])
     @NLexpression(model, ref, f)
     nlp = nonlinear_model(model)
     expr = :(ifelse($x, 0, $y))
@@ -1617,7 +1617,7 @@ function test_parse_expression_nonlinearexpr_or()
     model = Model()
     @variable(model, x)
     @variable(model, y)
-    f = GenericNonlinearExpr(:||, Any[x, y])
+    f = NonlinearExpr(:||, Any[x, y])
     @NLexpression(model, ref, f)
     nlp = nonlinear_model(model)
     expr = :($x || $y)
@@ -1629,7 +1629,7 @@ function test_parse_expression_nonlinearexpr_and()
     model = Model()
     @variable(model, x)
     @variable(model, y)
-    f = GenericNonlinearExpr(:&&, Any[x, y])
+    f = NonlinearExpr(:&&, Any[x, y])
     @NLexpression(model, ref, f)
     nlp = nonlinear_model(model)
     expr = :($x && $y)
@@ -1641,7 +1641,7 @@ function test_parse_expression_nonlinearexpr_unsupported()
     model = Model()
     @variable(model, x)
     @variable(model, y)
-    f = GenericNonlinearExpr(:foo, Any[x, y])
+    f = NonlinearExpr(:foo, Any[x, y])
     @test_throws(
         MOI.UnsupportedNonlinearOperator,
         @NLexpression(model, ref, f),
@@ -1653,8 +1653,8 @@ function test_parse_expression_nonlinearexpr_nested_comparison()
     model = Model()
     @variable(model, x)
     @variable(model, y)
-    f = GenericNonlinearExpr(:||, Any[x, y])
-    g = GenericNonlinearExpr(:&&, Any[f, x])
+    f = NonlinearExpr(:||, Any[x, y])
+    g = NonlinearExpr(:&&, Any[f, x])
     @NLexpression(model, ref, g)
     nlp = nonlinear_model(model)
     expr = :(($x || $y) && $x)
diff --git a/test/test_nlp_expr.jl b/test/test_nlp_expr.jl
index 092c2691b80..bd309f4c1d8 100644
--- a/test/test_nlp_expr.jl
+++ b/test/test_nlp_expr.jl
@@ -447,46 +447,46 @@ function test_extension_nl_macro(
     @variable(model, x)
     @test isequal_canonical(
         @expression(model, ifelse(x, 1, 2)),
-        GenericNonlinearExpr(:ifelse, Any[x, 1, 2]),
+        GenericNonlinearExpr{VariableRefType}(:ifelse, Any[x, 1, 2]),
     )
     @test isequal_canonical(
         @expression(model, x || 1),
-        GenericNonlinearExpr(:||, Any[x, 1]),
+        GenericNonlinearExpr{VariableRefType}(:||, Any[x, 1]),
     )
     @test isequal_canonical(
         @expression(model, x && 1),
-        GenericNonlinearExpr(:&&, Any[x, 1]),
+        GenericNonlinearExpr{VariableRefType}(:&&, Any[x, 1]),
     )
     @test isequal_canonical(
         @expression(model, x < 0),
-        GenericNonlinearExpr(:<, Any[x, 0]),
+        GenericNonlinearExpr{VariableRefType}(:<, Any[x, 0]),
     )
     @test isequal_canonical(
         @expression(model, x > 0),
-        GenericNonlinearExpr(:>, Any[x, 0]),
+        GenericNonlinearExpr{VariableRefType}(:>, Any[x, 0]),
     )
     @test isequal_canonical(
         @expression(model, x <= 0),
-        GenericNonlinearExpr(:<=, Any[x, 0]),
+        GenericNonlinearExpr{VariableRefType}(:<=, Any[x, 0]),
     )
     @test isequal_canonical(
         @expression(model, x >= 0),
-        GenericNonlinearExpr(:>=, Any[x, 0]),
+        GenericNonlinearExpr{VariableRefType}(:>=, Any[x, 0]),
     )
     @test isequal_canonical(
         @expression(model, x == 0),
-        GenericNonlinearExpr(:(==), Any[x, 0]),
+        GenericNonlinearExpr{VariableRefType}(:(==), Any[x, 0]),
     )
     @test isequal_canonical(
         @expression(model, 0 < x <= 1),
-        GenericNonlinearExpr(
+        GenericNonlinearExpr{VariableRefType}(
             :&&,
             Any[@expression(model, 0 < x), @expression(model, x <= 1)],
         ),
     )
     @test isequal_canonical(
         @expression(model, ifelse(x > 0, x^2, sin(x))),
-        GenericNonlinearExpr(
+        GenericNonlinearExpr{VariableRefType}(
             :ifelse,
             Any[@expression(model, x > 0), x^2, sin(x)],
         ),
@@ -501,7 +501,7 @@ function test_register_univariate()
     @test f isa NonlinearOperator
     @test sprint(show, f) == "NonlinearOperator($(f.func), :f)"
     @test isequal_canonical(@expression(model, f(x)), f(x))
-    @test isequal_canonical(f(x), GenericNonlinearExpr(:f, Any[x]))
+    @test isequal_canonical(f(x), NonlinearExpr(:f, Any[x]))
     attrs = MOI.get(model, MOI.ListOfModelAttributesSet())
     @test MOI.UserDefinedFunction(:f, 1) in attrs
     return
@@ -522,7 +522,7 @@ function test_register_univariate_gradient()
     @variable(model, x)
     @operator(model, f, 1, x -> x^2, x -> 2 * x)
     @test isequal_canonical(@expression(model, f(x)), f(x))
-    @test isequal_canonical(f(x), GenericNonlinearExpr(:f, Any[x]))
+    @test isequal_canonical(f(x), NonlinearExpr(:f, Any[x]))
     attrs = MOI.get(model, MOI.ListOfModelAttributesSet())
     @test MOI.UserDefinedFunction(:f, 1) in attrs
     return
@@ -533,7 +533,7 @@ function test_register_univariate_gradient_hessian()
     @variable(model, x)
     @operator(model, f, 1, x -> x^2, x -> 2 * x, x -> 2.0)
     @test isequal_canonical(@expression(model, f(x)), f(x))
-    @test isequal_canonical(f(x), GenericNonlinearExpr(:f, Any[x]))
+    @test isequal_canonical(f(x), NonlinearExpr(:f, Any[x]))
     attrs = MOI.get(model, MOI.ListOfModelAttributesSet())
     @test MOI.UserDefinedFunction(:f, 1) in attrs
     return
@@ -545,7 +545,7 @@ function test_register_multivariate()
     f = (x...) -> sum(x .^ 2)
     @operator(model, foo, 2, f)
     @test isequal_canonical(@expression(model, foo(x...)), foo(x...))
-    @test isequal_canonical(foo(x...), GenericNonlinearExpr(:foo, Any[x...]))
+    @test isequal_canonical(foo(x...), NonlinearExpr(:foo, Any[x...]))
     attrs = MOI.get(model, MOI.ListOfModelAttributesSet())
     @test MOI.UserDefinedFunction(:foo, 2) in attrs
     return
@@ -558,7 +558,7 @@ function test_register_multivariate_gradient()
     ∇f = (g, x...) -> (g .= 2 .* x)
     @operator(model, foo, 2, f, ∇f)
     @test isequal_canonical(@expression(model, foo(x...)), foo(x...))
-    @test isequal_canonical(foo(x...), GenericNonlinearExpr(:foo, Any[x...]))
+    @test isequal_canonical(foo(x...), NonlinearExpr(:foo, Any[x...]))
     attrs = MOI.get(model, MOI.ListOfModelAttributesSet())
     @test MOI.UserDefinedFunction(:foo, 2) in attrs
     return
@@ -576,7 +576,7 @@ function test_register_multivariate_gradient_hessian()
     end
     @operator(model, foo, 2, f, ∇f, ∇²f)
     @test isequal_canonical(@expression(model, foo(x...)), foo(x...))
-    @test isequal_canonical(foo(x...), GenericNonlinearExpr(:foo, Any[x...]))
+    @test isequal_canonical(foo(x...), NonlinearExpr(:foo, Any[x...]))
     attrs = MOI.get(model, MOI.ListOfModelAttributesSet())
     @test MOI.UserDefinedFunction(:foo, 2) in attrs
     return
@@ -587,7 +587,7 @@ function test_register_multivariate_many_args()
     @variable(model, x[1:10])
     f = (x...) -> sum(x .^ 2)
     @operator(model, foo, 10, f)
-    @test isequal_canonical(foo(x...), GenericNonlinearExpr(:foo, Any[x...]))
+    @test isequal_canonical(foo(x...), NonlinearExpr(:foo, Any[x...]))
     @test foo((1:10)...) == 385
     return
 end
@@ -607,18 +607,6 @@ function test_register_errors()
     return
 end
 
-function test_expression_no_variable()
-    head, args = :sin, Any[1]
-    @test_throws(
-        ErrorException(
-            "Unable to create a nonlinear expression because it did not " *
-            "contain any JuMP scalars. head = $head, args = $args.",
-        ),
-        GenericNonlinearExpr(head, args),
-    )
-    return
-end
-
 function test_value_expression()
     model = Model()
     @variable(model, x)
@@ -676,7 +664,7 @@ end
 function test_nonlinear_expr_owner_model()
     model = Model()
     @variable(model, x)
-    f = GenericNonlinearExpr(:sin, Any[x])
+    f = NonlinearExpr(:sin, Any[x])
     # This shouldn't happen in regular code, but let's test against it to check
     # we get something similar to AffExpr and QuadExpr.
     empty!(f.args)
@@ -900,4 +888,42 @@ function test_ma_zero_in_operate!!()
     return
 end
 
+function test_nonlinear_operator_inferred()
+    model = Model()
+    @variable(model, x)
+    @inferred op_less_than_or_equal_to(x, 1)
+    @test @inferred(op_less_than_or_equal_to(1, 2)) == true
+    return
+end
+
+function test_generic_nonlinear_expr_infer_variable_type()
+    model = Model()
+    @variable(model, x)
+    @inferred GenericNonlinearExpr(:sin, x)
+    @inferred GenericNonlinearExpr GenericNonlinearExpr(:sin, Any[x])
+    f = sin(x)
+    @test isequal_canonical(GenericNonlinearExpr(:sin, x), f)
+    @test isequal_canonical(GenericNonlinearExpr(:sin, Any[x]), f)
+    g = @expression(model, 1 <= x)
+    @inferred GenericNonlinearExpr(:<=, 1, x)
+    @inferred GenericNonlinearExpr GenericNonlinearExpr(:<=, Any[1, x])
+    @test isequal_canonical(GenericNonlinearExpr(:<=, 1, x), g)
+    @test isequal_canonical(GenericNonlinearExpr(:<=, Any[1, x]), g)
+    @test_throws(
+        ErrorException(
+            "Unable to create a nonlinear expression because it did not " *
+            "contain any JuMP scalars. head = `:sin`, args = `(1,)`.",
+        ),
+        GenericNonlinearExpr(:sin, 1),
+    )
+    @test_throws(
+        ErrorException(
+            "Unable to create a nonlinear expression because it did not " *
+            "contain any JuMP scalars. head = `:sin`, args = `Any[1]`.",
+        ),
+        GenericNonlinearExpr(:sin, Any[1]),
+    )
+    return
+end
+
 end  # module
diff --git a/test/test_operator.jl b/test/test_operator.jl
index ebda3be21b5..967fb8b666d 100644
--- a/test/test_operator.jl
+++ b/test/test_operator.jl
@@ -621,7 +621,7 @@ function test_complex_pow()
     @test y^0 == (1.0 + 0im)
     @test y^1 == y
     @test y^2 == y * y
-    @test isequal_canonical(y^3, GenericNonlinearExpr(:^, Any[y, 3]))
+    @test isequal_canonical(y^3, NonlinearExpr(:^, Any[y, 3]))
     return
 end