diff --git a/src/sage/matrix/matrix2.pyx b/src/sage/matrix/matrix2.pyx
index f5f0eac7ea8..d0c1550aa1f 100644
--- a/src/sage/matrix/matrix2.pyx
+++ b/src/sage/matrix/matrix2.pyx
@@ -15900,7 +15900,7 @@ cdef class Matrix(Matrix1):
             sage: a.exp()                                                               # needs sage.symbolic
             [ 1/11882424341266*((11*sqrt(227345670387496707609) + 5941212170633)*e^(3/1275529100*sqrt(227345670387496707609)) - 11*sqrt(227345670387496707609) + 5941212170633)*e^(-3/2551058200*sqrt(227345670387496707609) + 101/200)                            445243650/75781890129165569203*(sqrt(227345670387496707609)*e^(3/1275529100*sqrt(227345670387496707609)) - sqrt(227345670387496707609))*e^(-3/2551058200*sqrt(227345670387496707609) + 101/200)]
             [                                     10000/53470909535697*(sqrt(227345670387496707609)*e^(3/1275529100*sqrt(227345670387496707609)) - sqrt(227345670387496707609))*e^(-3/2551058200*sqrt(227345670387496707609) + 101/200) -1/11882424341266*((11*sqrt(227345670387496707609) - 5941212170633)*e^(3/1275529100*sqrt(227345670387496707609)) - 11*sqrt(227345670387496707609) - 5941212170633)*e^(-3/2551058200*sqrt(227345670387496707609) + 101/200)]
-            sage: a.change_ring(RDF).exp()  # rel tol 1e-14                             # needs sage.symbolic
+            sage: a.change_ring(RDF).exp()  # rel tol 6e-14                             # needs sage.symbolic
             [42748127.31532951 7368259.244159399]
             [234538976.1381042 40426191.45156228]
 
diff --git a/src/sage/matrix/matrix_double_dense.pyx b/src/sage/matrix/matrix_double_dense.pyx
index e7ca7b00d3a..d3fcde93fec 100644
--- a/src/sage/matrix/matrix_double_dense.pyx
+++ b/src/sage/matrix/matrix_double_dense.pyx
@@ -3663,7 +3663,7 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
             sage: A = matrix(RDF, 2, [1,2,3,4]); A
             [1.0 2.0]
             [3.0 4.0]
-            sage: A.exp()  # tol 1e-14
+            sage: A.exp()  # tol 5e-14
             [51.968956198705044  74.73656456700327]
             [112.10484685050491 164.07380304920997]
             sage: A = matrix(CDF, 2, [1,2+I,3*I,4]); A                                  # needs sage.symbolic
@@ -3676,7 +3676,7 @@ cdef class Matrix_double_dense(Matrix_numpy_dense):
         TESTS::
 
             sage: A = matrix(RDF, 2, [1,2,3,4])
-            sage: A.exp()   # tol 1e-14
+            sage: A.exp()   # tol 5e-14
             [51.968956198705044  74.73656456700327]
             [112.10484685050491 164.07380304920997]
 
diff --git a/src/sage/symbolic/constants_c_impl.pxi b/src/sage/symbolic/constants_c_impl.pxi
index 63a90c71fd9..0ebd28e8aa3 100644
--- a/src/sage/symbolic/constants_c_impl.pxi
+++ b/src/sage/symbolic/constants_c_impl.pxi
@@ -159,7 +159,7 @@ cdef class E(Expression):
             [e 0]
             [0 e]
             sage: A = matrix(RDF, [[1,2],[3,4]])
-            sage: e^A  # rel tol 1e-14
+            sage: e^A  # rel tol 5e-14
             [51.968956198705044  74.73656456700327]
             [112.10484685050491 164.07380304920997]
         """