diff --git a/tests/base/test_float.py b/tests/base/test_float.py
index 97f98aff..0b9318cd 100644
--- a/tests/base/test_float.py
+++ b/tests/base/test_float.py
@@ -104,10 +104,16 @@ def forward(y):
                                 np.arccosh,
                                 np.arctanh,
                                 np.exp,
+                                np.exp2,
                                 np.expm1,
                                 np.log,
+                                np.log2,
                                 np.log10,
-                                np.sqrt])
+                                np.log1p,
+                                np.sqrt,
+                                np.square,
+                                np.cbrt,
+                                np.reciprocal])
 @seed_test
 def test_float_unary_overloading(setup_test,  # noqa: F811
                                  op):
@@ -123,7 +129,7 @@ def forward(y):
 
         return (c - 1.0) ** 4
 
-    if op is np.arccosh:
+    if op in {np.arccosh, np.reciprocal}:
         y = Float(1.1)
     else:
         y = Float(0.1)
@@ -165,11 +171,13 @@ def forward(y):
                                 operator.mul,
                                 operator.truediv,
                                 operator.pow,
-                                np.arctan2])
+                                np.arctan2,
+                                np.hypot])
 @seed_test
 def test_float_binary_overloading(setup_test,  # noqa: F811
                                   dtype, op):
-    if op is np.arctan2 and issubclass(dtype, (complex, np.complexfloating)):
+    if op in {np.arctan2, np.hypot} \
+            and issubclass(dtype, (complex, np.complexfloating)):
         pytest.skip()
     set_default_float_dtype(dtype)
 
diff --git a/tests/base/test_jax.py b/tests/base/test_jax.py
index d3d771a7..ead987a1 100644
--- a/tests/base/test_jax.py
+++ b/tests/base/test_jax.py
@@ -98,10 +98,16 @@ def forward(y):
                                 np.arccosh,
                                 np.arctanh,
                                 np.exp,
+                                np.exp2,
                                 np.expm1,
                                 np.log,
+                                np.log2,
                                 np.log10,
-                                np.sqrt])
+                                np.log1p,
+                                np.sqrt,
+                                np.square,
+                                np.cbrt,
+                                np.reciprocal])
 @seed_test
 def test_jax_unary_overloading(setup_test, jax_tlm_config,  # noqa: F811
                                op):
@@ -119,7 +125,7 @@ def forward(y):
 
         return (c - 1.0) ** 4
 
-    if op is np.arccosh:
+    if op in {np.arccosh, np.reciprocal}:
         y = np.array([1.1, 1.2], dtype=np.double)
     else:
         y = np.array([0.1, 0.2], dtype=np.double)
@@ -160,16 +166,17 @@ def forward(y):
                                 operator.mul,
                                 operator.truediv,
                                 operator.pow,
-                                np.arctan2])
+                                np.arctan2,
+                                np.hypot])
 @seed_test
 def test_jax_binary_overloading(setup_test, jax_tlm_config,  # noqa: F811
                                 dtype, op):
+    if op in {np.arctan2, np.hypot} \
+            and issubclass(dtype, (complex, np.complexfloating)):
+        pytest.skip()
     set_default_float_dtype(dtype)
     set_default_jax_dtype(dtype)
 
-    if op is np.arctan2 and issubclass(dtype, (complex, np.complexfloating)):
-        pytest.skip()
-
     def forward(y):
         x = y * y
         x = op(x, y)
diff --git a/tlm_adjoint/overloaded_float.py b/tlm_adjoint/overloaded_float.py
index f81427b2..abb1d158 100644
--- a/tlm_adjoint/overloaded_float.py
+++ b/tlm_adjoint/overloaded_float.py
@@ -580,6 +580,24 @@ def fdiff(self, argindex=1):
             return sp.exp(self.args[0])
 
 
+@register_function(np.log1p, "numpy.log1p")
+class _tlm_adjoint__log1p(sp.Function):  # noqa: N801
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return sp.Integer(1) / (sp.Integer(1) + self.args[0])
+
+
+@register_function(np.hypot, "numpy.hypot")
+class _tlm_adjoint__hypot(sp.Function):  # noqa: N801
+    def fdiff(self, argindex=1):
+        if argindex == 1:
+            return self.args[0] / _tlm_adjoint__hypot(self.args[0],
+                                                      self.args[1])
+        elif argindex == 2:
+            return self.args[1] / _tlm_adjoint__hypot(self.args[0],
+                                                      self.args[1])
+
+
 class _tlm_adjoint__OverloadedFloat(np.lib.mixins.NDArrayOperatorsMixin,  # noqa: E501,N801
                                     SymbolicFloat):
     """A subclass of :class:`.SymbolicFloat` with operator overloading.
@@ -702,6 +720,11 @@ def arctan(x):
     def arctan2(x1, x2):
         return sp.atan2(x1, x2)
 
+    @staticmethod
+    @register_operation(np.hypot)
+    def hypot(x1, x2):
+        return _tlm_adjoint__hypot(x1, x2)
+
     @staticmethod
     @register_operation(np.sinh)
     def sinh(x):
@@ -737,6 +760,11 @@ def arctanh(x):
     def exp(x):
         return sp.exp(x)
 
+    @staticmethod
+    @register_operation(np.exp2)
+    def exp2(x):
+        return 2 ** x
+
     @staticmethod
     @register_operation(np.expm1)
     def expm1(x):
@@ -747,16 +775,41 @@ def expm1(x):
     def log(x):
         return sp.log(x)
 
+    @staticmethod
+    @register_operation(np.log2)
+    def log2(x):
+        return sp.log(x, 2)
+
     @staticmethod
     @register_operation(np.log10)
     def log10(x):
         return sp.log(x, 10)
 
+    @staticmethod
+    @register_operation(np.log1p)
+    def log1p(x):
+        return _tlm_adjoint__log1p(x)
+
     @staticmethod
     @register_operation(np.sqrt)
     def sqrt(x):
         return sp.sqrt(x)
 
+    @staticmethod
+    @register_operation(np.square)
+    def square(x):
+        return x ** 2
+
+    @staticmethod
+    @register_operation(np.cbrt)
+    def cbrt(x):
+        return x ** sp.Rational(1, 3)
+
+    @staticmethod
+    @register_operation(np.reciprocal)
+    def reciprocal(x):
+        return sp.Integer(1) / x
+
 
 # Required by Sphinx
 class OverloadedFloat(_tlm_adjoint__OverloadedFloat):