diff --git a/src/ADNLPProblems/bard.jl b/src/ADNLPProblems/bard.jl
index 3fa0ee76..cf4d8d30 100644
--- a/src/ADNLPProblems/bard.jl
+++ b/src/ADNLPProblems/bard.jl
@@ -8,7 +8,8 @@ end
 function bard(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   y = Rational{Int}[0.14 0.18 0.22 0.25 0.29 0.32 0.35 0.39 0.37 0.58 0.73 0.16 1.34 2.10 4.39]
   function f(x)
-    return 1 // 2 * sum(y[i] - (x[1] + i / ((16 - i) * x[2] + min(i, 16 - i) * x[3])) for i = 1:15)
+    return 1 // 2 *
+           sum((y[i] - (x[1] + i / ((16 - i) * x[2] + min(i, 16 - i) * x[3])))^2 for i = 1:15)
   end
   x0 = ones(T, 3)
   return ADNLPModels.ADNLPModel(f, x0, name = "bard"; kwargs...)
diff --git a/src/ADNLPProblems/hs6.jl b/src/ADNLPProblems/hs6.jl
index 96b9e95c..0625fae2 100644
--- a/src/ADNLPProblems/hs6.jl
+++ b/src/ADNLPProblems/hs6.jl
@@ -23,7 +23,7 @@ end
 
 function hs6(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, kwargs...) where {T}
   function F!(r, x)
-    r[1] = 1 // 2 * (x[1] - 1)^2
+    r[1] = (x[1] - 1)
     return r
   end
   function c!(cx, x)
diff --git a/src/ADNLPProblems/penalty1.jl b/src/ADNLPProblems/penalty1.jl
index 207880b3..1b47fe0c 100644
--- a/src/ADNLPProblems/penalty1.jl
+++ b/src/ADNLPProblems/penalty1.jl
@@ -22,6 +22,6 @@ function penalty1(::Val{:nls}; n::Int = default_nvar, type::Type{T} = Float64, k
     r[n + 1] = sum(x[j]^2 for j = 1:n) - 1 // 4
     return r
   end
-  x0 = ones(T, n)
+  x0 = T[j for j = 1:n]
   return ADNLPModels.ADNLSModel!(F!, x0, n + 1, name = "penalty1-nls"; kwargs...)
 end
diff --git a/src/ADNLPProblems/watson.jl b/src/ADNLPProblems/watson.jl
index 57b4a485..56e1f275 100644
--- a/src/ADNLPProblems/watson.jl
+++ b/src/ADNLPProblems/watson.jl
@@ -20,10 +20,11 @@ function watson(::Val{:nlp}; n::Int = default_nvar, type::Type{T} = Float64, kwa
              sum((j - 1) * x[j] * x[1]^(j - 2) for j = 2:n) -
              sum(x[j] * x[1]^(j - 1) for j = 1:n)^2 - 1
            )^2 +
-           1 // 2 * (
+           1 // 2 *
+           (
              sum((j - 1) * x[j] * (x[2] - x[1]^2 - 1)^(j - 2) for j = 2:n) -
              sum(x[j] * (x[2] - x[1]^2 - 1)^(j - 1) for j = 1:n)^2 - 1
-           )
+           )^2
   end
   x0 = zeros(T, n)
   return ADNLPModels.ADNLPModel(f, x0, name = "watson"; kwargs...)
diff --git a/src/PureJuMP/bard.jl b/src/PureJuMP/bard.jl
index dd54e0cf..cfe0e4ec 100644
--- a/src/PureJuMP/bard.jl
+++ b/src/PureJuMP/bard.jl
@@ -23,7 +23,7 @@ function bard(args...; n::Int = default_nvar, m::Int = 2n, kwargs...)
   @objective(
     nlp,
     Min,
-    0.5 * sum(y[i] - (x[1] + i / ((16 - i) * x[2] + min(i, 16 - i) * x[3])) for i = 1:15)
+    0.5 * sum((y[i] - (x[1] + i / ((16 - i) * x[2] + min(i, 16 - i) * x[3])))^2 for i = 1:15)
   )
 
   return nlp
diff --git a/src/PureJuMP/hs6.jl b/src/PureJuMP/hs6.jl
index 23014e4c..c9b18111 100644
--- a/src/PureJuMP/hs6.jl
+++ b/src/PureJuMP/hs6.jl
@@ -19,7 +19,7 @@ function hs6(args...; kwargs...)
   x0 = [-1.2, 1]
   @variable(nlp, x[i = 1:2], start = x0[i])
 
-  @objective(nlp, Min, 0.5 * (1 - x[1])^2)
+  @objective(nlp, Min, 0.5 * (x[1] - 1)^2)
 
   @constraint(nlp, 10 * (x[2] - x[1]^2) == 0)
 
diff --git a/src/PureJuMP/watson.jl b/src/PureJuMP/watson.jl
index f1f6028c..6dc9def6 100644
--- a/src/PureJuMP/watson.jl
+++ b/src/PureJuMP/watson.jl
@@ -37,10 +37,11 @@ function watson(args...; n::Int = default_nvar, kwargs...)
     (
       sum((j - 1) * x[j] * x[1]^(j - 2) for j = 2:n) - sum(x[j] * x[1]^(j - 1) for j = 1:n)^2 - 1
     )^2 +
-    0.5 * (
+    0.5 *
+    (
       sum((j - 1) * x[j] * (x[2] - x[1]^2 - 1)^(j - 2) for j = 2:n) -
       sum(x[j] * (x[2] - x[1]^2 - 1)^(j - 1) for j = 1:n)^2 - 1
-    )
+    )^2
   )
 
   return nlp
diff --git a/test/runtests.jl b/test/runtests.jl
index 74538ca5..22ce11bf 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -14,17 +14,22 @@ addprocs(np - 1)
   [n for n in names(mod) if isdefined(mod, n)]
 end
 
-const list_problems =
+@everywhere const list_problems =
   setdiff(union(defined_names(ADNLPProblems), defined_names(PureJuMP)), [:PureJuMP, :ADNLPProblems])
 
+@testset "Test that all problems have a meta" begin
+  @test sort(list_problems) == sort(Symbol.(OptimizationProblems.meta[!, :name]))
+end
+
 # The problems included should be carefully argumented and issues
 # to create them added.
 # TODO: tests are limited for JuMP-only problems
-const list_problems_not_ADNLPProblems =
+@everywhere const list_problems_not_ADNLPProblems =
   Symbol[:catmix, :gasoil, :glider, :methanol, :minsurf, :pinene, :rocket, :steering, :torsion]
-const list_problems_ADNLPProblems = setdiff(list_problems, list_problems_not_ADNLPProblems)
-const list_problems_not_PureJuMP = Symbol[]
-const list_problems_PureJuMP = setdiff(list_problems, list_problems_not_PureJuMP)
+@everywhere const list_problems_ADNLPProblems =
+  setdiff(list_problems, list_problems_not_ADNLPProblems)
+@everywhere const list_problems_not_PureJuMP = Symbol[]
+@everywhere const list_problems_PureJuMP = setdiff(list_problems, list_problems_not_PureJuMP)
 
 include("test-defined-problems.jl")
 include("test-utils.jl")
@@ -45,7 +50,7 @@ end
     error("Problem $(prob) is not defined in $mod on pid $(myid()).")
   end
   ctor = getfield(mod, prob)
-  return MathOptNLPModel(ctor(; kwargs...))
+  return MathOptNLPModel(ctor(; kwargs...); name = "$prob")
 end
 
 @everywhere function make_ad_nlp(prob::Symbol; kwargs...)
@@ -57,6 +62,8 @@ end
   return ctor(matrix_free = true; kwargs...)
 end
 
+include("test-in-place-residual.jl")
+
 @everywhere function test_one_problem(prob::Symbol)
   pb = string(prob)
 
@@ -75,41 +82,33 @@ end
 
   nlp_ad = timed_info("Instantiating $(pb)", make_nlp, prob)
 
-  @test nlp_ad.meta.name == pb
+  @testset "Sanity check (name, obj)" begin
+    @test nlp_ad.meta.name == pb
+    @test !isnothing(obj(nlp_ad, nlp_ad.meta.x0))
+  end
 
-  if pb in meta[(meta.contype .== :quadratic) .| (meta.contype .== :general), :name]
+  if (typeof(nlp_ad) <: ADNLPModels.AbstractADNLPModel) &&
+     (pb in meta[(meta.contype .== :quadratic) .| (meta.contype .== :general), :name])
     @testset "Test In-place Nonlinear Constraints for AD-$prob" begin
       test_in_place_constraints(prob, nlp_ad)
     end
   end
 
-  @testset "Test multi-precision ADNLPProblems for $prob" begin
-    test_multi_precision(prob, nlp_ad)
-  end
-
-  if pb in meta[meta.objtype .== :least_squares, :name]
-    @testset "Test Nonlinear Least Squares for $prob" begin
-      test_in_place_residual(prob)
+  if typeof(nlp_ad) <: ADNLPModels.AbstractADNLPModel
+    @testset "Test multi-precision ADNLPProblems for $prob" begin
+      test_multi_precision(prob, nlp_ad)
     end
   end
 
-  model = begin
-    mod = PureJuMP
-    if isdefined(mod, prob)
-      getfield(mod, prob)(n = ndef)
-    else
-      nothing
-    end
-  end
-  if !isnothing(model)
+  if mod in intersect(list_problems_PureJuMP, list_problems_ADNLPProblems)
     @testset "Test problems compatibility for $prob" begin
-      nlp_jump = MathOptNLPModel(model)
+      nlp_jump = make_jump_nlp(prob; n = ndef)
       test_compatibility(prob, nlp_jump, nlp_ad, ndef)
     end
   end
 end
 
-pmap(test_one_problem, list_problems_ADNLPProblems)
+pmap(test_one_problem, list_problems)
 
 include("test-scalable.jl")
 
diff --git a/test/test-in-place-residual.jl b/test/test-in-place-residual.jl
new file mode 100644
index 00000000..7e32e7c2
--- /dev/null
+++ b/test/test-in-place-residual.jl
@@ -0,0 +1,41 @@
+@everywhere function test_in_place_residual(prob::Symbol)
+  nlp = make_ad_nlp(prob; use_nls = false)
+  @test typeof(nlp) <: ADNLPModels.ADNLPModel
+  nls = make_ad_nlp(prob; use_nls = true)
+  @test typeof(nls) <: ADNLPModels.ADNLSModel
+  return test_in_place_residual(prob, nlp, nls)
+end
+
+@everywhere function test_in_place_residual(
+  prob::Symbol,
+  nlp::AbstractNLPModel,
+  nls::AbstractNLSModel,
+)
+  @testset "Test in-place residual $prob" begin
+    x = nls.meta.x0
+    Fx = similar(x, nls.nls_meta.nequ)
+    pb = String(prob)
+    if VERSION ≥ v"1.7" && !occursin("palmer", pb) && (pb != "watson") # palmer residual allocate
+      @allocated residual!(nls, x, Fx)
+      @test (@allocated residual!(nls, x, Fx)) == 0
+    end
+    m = OptimizationProblems.eval(Meta.parse("get_$(prob)_nls_nequ"))()
+    @test nls.nls_meta.nequ == m
+  end
+
+  @testset "Compare NLS with NLP $prob: x0 and obj are the same." begin
+    x0 = nlp.meta.x0
+    @test x0 == nls.meta.x0
+    nlp_fx = obj(nlp, x0)
+    nls_fx = obj(nls, x0)
+    are_almost_same = (nlp_fx ≈ nls_fx) | (nlp_fx ≈ 2 * nls_fx)
+    if !(are_almost_same)
+      @info "$prob : NLS $(nls_fx) ≈ NLP $(nlp_fx)"
+    end
+    @test are_almost_same
+  end
+end
+
+nls_name_list =
+  intersect(Symbol.(meta[meta.objtype .== :least_squares, :name]), list_problems_ADNLPProblems)
+pmap(test_in_place_residual, nls_name_list)
diff --git a/test/test-utils.jl b/test/test-utils.jl
index 5ae09609..b5ff1829 100644
--- a/test/test-utils.jl
+++ b/test/test-utils.jl
@@ -46,24 +46,6 @@ end
   @test ncon == m
 end
 
-@everywhere function test_in_place_residual(prob::Symbol)
-  nls = OptimizationProblems.ADNLPProblems.eval(prob)(use_nls = true)
-  @test typeof(nls) <: ADNLPModels.ADNLSModel
-  return test_in_place_residual(prob, nls)
-end
-
-@everywhere function test_in_place_residual(prob::Symbol, nls::AbstractNLSModel)
-  x = nls.meta.x0
-  Fx = similar(x, nls.nls_meta.nequ)
-  pb = String(prob)
-  if VERSION ≥ v"1.7" && !occursin("palmer", pb) && (pb != "watson") # palmer residual allocate
-    @allocated residual!(nls, x, Fx)
-    @test (@allocated residual!(nls, x, Fx)) == 0
-  end
-  m = OptimizationProblems.eval(Meta.parse("get_$(prob)_nls_nequ"))()
-  @test nls.nls_meta.nequ == m
-end
-
 @everywhere function test_compatibility(prob::Symbol, ndef::Integer = ndef)
   prob_fn = eval(Meta.parse("PureJuMP.$(prob)"))
   model = prob_fn(n = ndef)