diff --git a/src/dilax/util.py b/src/dilax/util.py
index 7622565..6ac9bbb 100644
--- a/src/dilax/util.py
+++ b/src/dilax/util.py
@@ -244,13 +244,75 @@ class HistDB(FrozenDB):
 
 
 def as1darray(x: float | jax.Array) -> jax.Array:
+    """
+    Converts `x` to a 1d array.
+
+    Example:
+
+    .. code-block:: python
+
+        import jax.numpy as jnp
+
+
+        as1darray(1.0)
+        # -> Array([1.], dtype=float32, weak_type=True)
+
+        as1darray(jnp.array(1.0))
+        # -> Array([1.], dtype=float32, weak_type=True)
+    """
+
     return jnp.atleast_1d(jnp.asarray(x))
 
 
 def dump_jaxpr(fun: Callable, *args: Any, **kwargs: Any) -> str:
+    """Helper function to dump the Jaxpr of a function.
+
+    Example:
+
+    .. code-block:: python
+
+        import jax
+        import jax.numpy as jnp
+
+        def f(x: jax.Array) -> jax.Array:
+            return jnp.sin(x) ** 2 + jnp.cos(x) ** 2
+
+        x = jnp.array([1.0, 2.0, 3.0])
+
+        print(dump_jaxpr(f, x))
+        # -> { lambda ; a:f32[3]. let
+        #        b:f32[3] = sin a              # []
+        #        c:f32[3] = integer_pow[y=2] b # []
+        #        d:f32[3] = cos a              # []
+        #        e:f32[3] = integer_pow[y=2] d # []
+        #        f:f32[3] = add c e            # []
+        #      in (f,) }
+    """
     jaxpr = jax.make_jaxpr(fun)(*args, **kwargs)
     return jaxpr.pretty_print(name_stack=True)
 
 
 def dump_hlo_graph(fun: Callable, *args: Any, **kwargs: Any) -> str:
+    """
+    Helper to dump the HLO graph of a function as a `dot` graph.
+
+    Example:
+
+    .. code-block:: python
+
+        import jax
+        import jax.numpy as jnp
+
+        import path
+
+
+        def f(x: jax.Array) -> jax.Array:
+            return x + 1.0
+
+        x = jnp.array([1.0, 2.0, 3.0])
+
+        # dump dot graph to file
+        filepath = pathlib.Path('graph.gv')
+        filepath.write_text(dump_hlo_graph(f, x), encoding='ascii')
+    """
     return jax.xla_computation(fun)(*args, **kwargs).as_hlo_dot_graph()