diff --git a/test/mooncake.jl b/test/mooncake.jl
index 7aed68cf..3e19e44d 100644
--- a/test/mooncake.jl
+++ b/test/mooncake.jl
@@ -22,7 +22,7 @@ make_mooncake_tangent(T::Tuple) = Mooncake.build_tangent(typeof(T), T...)
 make_mooncake_fdata(x) = make_mooncake_tangent(x)
 make_mooncake_fdata(x::Diagonal) = Mooncake.FData((diag = make_mooncake_tangent(x.diag),))
 
-ETs = (Float64, Float32, ComplexF64, ComplexF32)
+ETs = (Float32, ComplexF64)
 
 # no `alg` argument
 function _get_copying_derivative(f_c, rrule, A, ΔA, args, Δargs, ::Nothing, rdata)
@@ -251,7 +251,10 @@ end
     dV = make_mooncake_tangent(ΔV)
     dDV = Mooncake.build_tangent(typeof((ΔD2, ΔV)), dD, dV)
     # compute the dA corresponding to the above dD, dV
-    @testset for alg in (LAPACK_Simple(), LAPACK_Expert())
+    @testset for alg in (
+            LAPACK_Simple(),
+            #LAPACK_Expert(), # expensive on CI
+        )
         @testset "eig_full" begin
             Mooncake.TestUtils.test_rule(rng, eig_full, A, alg; mode = Mooncake.ReverseMode, output_tangent = dDV, is_primitive = false, atol = atol, rtol = rtol)
             test_pullbacks_match(rng, eig_full!, eig_full, A, (D, V), (ΔD2, ΔV), alg)
@@ -340,9 +343,9 @@ MatrixAlgebraKit.copy_input(::typeof(copy_eigh_trunc), A) = MatrixAlgebraKit.cop
     Ddiag = diagview(D)
     @testset for alg in (
             LAPACK_QRIteration(),
-            LAPACK_DivideAndConquer(),
-            LAPACK_Bisection(),
-            LAPACK_MultipleRelativelyRobustRepresentations(),
+            #LAPACK_DivideAndConquer(),
+            #LAPACK_Bisection(),
+            #LAPACK_MultipleRelativelyRobustRepresentations(), # expensive on CI
         )
         @testset "eigh_full" begin
             Mooncake.TestUtils.test_rule(rng, copy_eigh_full, A, alg; mode = Mooncake.ReverseMode, output_tangent = dDV, is_primitive = false, atol = atol, rtol = rtol)
@@ -390,7 +393,7 @@ end
         minmn = min(m, n)
         @testset for alg in (
                 LAPACK_QRIteration(),
-                LAPACK_DivideAndConquer(),
+                #LAPACK_DivideAndConquer(), # expensive on CI
             )
             @testset "svd_compact" begin
                 ΔU = randn(rng, T, m, minmn)
@@ -490,7 +493,12 @@ end
     @testset "size ($m, $n)" for n in (17, m, 23)
         atol = rtol = m * n * precision(T)
         A = randn(rng, T, m, n)
-        @testset for alg in PolarViaSVD.((LAPACK_QRIteration(), LAPACK_DivideAndConquer()))
+        @testset for alg in PolarViaSVD.(
+                (
+                    LAPACK_QRIteration(),
+                    #LAPACK_DivideAndConquer(), # expensive on CI
+                )
+            )
             if m >= n
                 WP = left_polar(A, alg)
                 Mooncake.TestUtils.test_rule(rng, left_polar, A, alg; mode = Mooncake.ReverseMode, is_primitive = false, atol = atol, rtol = rtol)