diff --git a/src/broyden.jl b/src/broyden.jl
index a6981a668..6be29a77b 100644
--- a/src/broyden.jl
+++ b/src/broyden.jl
@@ -101,7 +101,8 @@ function perform_step!(cache::GeneralBroydenCache{true})
     else
         mul!(_vec(J⁻¹df), J⁻¹, _vec(dfu))
         mul!(J⁻¹₂, _vec(du)', J⁻¹)
-        du .= (du .- J⁻¹df) ./ (dot(du, J⁻¹df) .+ T(1e-5))
+        denom = dot(du, J⁻¹df)
+        du .= (du .- J⁻¹df) ./ ifelse(iszero(denom), T(1e-5), denom)
         mul!(J⁻¹, _vec(du), J⁻¹₂, 1, 1)
     end
     fu .= fu2
@@ -136,7 +137,8 @@ function perform_step!(cache::GeneralBroydenCache{false})
     else
         cache.J⁻¹df = _restructure(cache.J⁻¹df, cache.J⁻¹ * _vec(cache.dfu))
         cache.J⁻¹₂ = _vec(cache.du)' * cache.J⁻¹
-        cache.du = (cache.du .- cache.J⁻¹df) ./ (dot(cache.du, cache.J⁻¹df) .+ T(1e-5))
+        denom = dot(cache.du, cache.J⁻¹df)
+        cache.du = (cache.du .- cache.J⁻¹df) ./ ifelse(iszero(denom), T(1e-5), denom)
         cache.J⁻¹ = cache.J⁻¹ .+ _vec(cache.du) * cache.J⁻¹₂
     end
     cache.fu = cache.fu2
diff --git a/src/lbroyden.jl b/src/lbroyden.jl
index efaa1bb04..d045d0b20 100644
--- a/src/lbroyden.jl
+++ b/src/lbroyden.jl
@@ -123,8 +123,8 @@ function perform_step!(cache::LimitedMemoryBroydenCache{true})
         __lbroyden_matvec!(_vec(cache.vᵀ_cache), cache.Ux, U_part, Vᵀ_part, _vec(cache.du))
         __lbroyden_rmatvec!(_vec(cache.u_cache), cache.xᵀVᵀ, U_part, Vᵀ_part,
             _vec(cache.dfu))
-        cache.u_cache .= (du .- cache.u_cache) ./
-                         (dot(cache.vᵀ_cache, cache.dfu) .+ T(1e-5))
+        denom = dot(cache.vᵀ_cache, cache.dfu)
+        cache.u_cache .= (du .- cache.u_cache) ./ ifelse(iszero(denom), T(1e-5), denom)
 
         idx = mod1(cache.iterations_since_reset + 1, size(cache.U, 1))
         selectdim(cache.U, 1, idx) .= _vec(cache.u_cache)
@@ -179,8 +179,8 @@ function perform_step!(cache::LimitedMemoryBroydenCache{false})
             __lbroyden_matvec(U_part, Vᵀ_part, _vec(cache.du)))
         cache.u_cache = _restructure(cache.u_cache,
             __lbroyden_rmatvec(U_part, Vᵀ_part, _vec(cache.dfu)))
-        cache.u_cache = (cache.du .- cache.u_cache) ./
-                        (dot(cache.vᵀ_cache, cache.dfu) .+ T(1e-5))
+        denom = dot(cache.vᵀ_cache, cache.dfu)
+        cache.u_cache = (cache.du .- cache.u_cache) ./ ifelse(iszero(denom), T(1e-5), denom)
 
         idx = mod1(cache.iterations_since_reset + 1, size(cache.U, 1))
         selectdim(cache.U, 1, idx) .= _vec(cache.u_cache)
diff --git a/test/23_test_problems.jl b/test/23_test_problems.jl
index 57f9de68c..a35476dc3 100644
--- a/test/23_test_problems.jl
+++ b/test/23_test_problems.jl
@@ -7,7 +7,7 @@ function test_on_library(problems, dicts, alg_ops, broken_tests, ϵ = 1e-4)
     for (idx, (problem, dict)) in enumerate(zip(problems, dicts))
         x = dict["start"]
         res = similar(x)
-        nlprob = NonlinearProblem(problem, x)
+        nlprob = NonlinearProblem(problem, copy(x))
         @testset "$idx: $(dict["title"])" begin
             for alg in alg_ops
                 try
@@ -86,9 +86,9 @@ end
         GeneralBroyden(; linesearch = BackTracking()))
 
     broken_tests = Dict(alg => Int[] for alg in alg_ops)
-    broken_tests[alg_ops[1]] = [1, 3, 4, 5, 6, 11, 12, 13, 14]
-    broken_tests[alg_ops[2]] = [1, 2, 3, 4, 5, 6, 9, 11, 13, 15, 16, 21, 22]
-    broken_tests[alg_ops[3]] = [1, 2, 4, 5, 6, 11, 12, 13, 14, 21]
+    broken_tests[alg_ops[1]] = [1, 2, 4, 5, 6, 11, 12, 13, 14]
+    broken_tests[alg_ops[2]] = [1, 2, 3, 4, 5, 6, 9, 11, 13, 22]
+    broken_tests[alg_ops[3]] = [1, 4, 5, 6, 11, 12, 13, 14, 21]
 
     test_on_library(problems, dicts, alg_ops, broken_tests)
 end