diff --git a/datafusion/core/src/physical_optimizer/projection_pushdown.rs b/datafusion/core/src/physical_optimizer/projection_pushdown.rs
index 77135d73373f6..2c2ff6d48aecc 100644
--- a/datafusion/core/src/physical_optimizer/projection_pushdown.rs
+++ b/datafusion/core/src/physical_optimizer/projection_pushdown.rs
@@ -1389,7 +1389,6 @@ mod tests {
 
     #[test]
     fn test_update_matching_exprs() -> Result<()> {
-        let udf = Arc::new(ScalarUDF::new_from_impl(DummyUDF::new()));
         let exprs: Vec<Arc<dyn PhysicalExpr>> = vec![
             Arc::new(BinaryExpr::new(
                 Arc::new(Column::new("a", 3)),
@@ -1404,7 +1403,7 @@ mod tests {
             Arc::new(NegativeExpr::new(Arc::new(Column::new("f", 4)))),
             Arc::new(ScalarFunctionExpr::new(
                 "scalar_expr",
-                Arc::clone(&udf),
+                Arc::new(ScalarUDF::new_from_impl(DummyUDF::new())),
                 vec![
                     Arc::new(BinaryExpr::new(
                         Arc::new(Column::new("b", 1)),
@@ -1469,7 +1468,7 @@ mod tests {
             Arc::new(NegativeExpr::new(Arc::new(Column::new("f", 5)))),
             Arc::new(ScalarFunctionExpr::new(
                 "scalar_expr",
-                Arc::clone(&udf),
+                Arc::new(ScalarUDF::new_from_impl(DummyUDF::new())),
                 vec![
                     Arc::new(BinaryExpr::new(
                         Arc::new(Column::new("b", 1)),
@@ -1523,7 +1522,6 @@ mod tests {
 
     #[test]
     fn test_update_projected_exprs() -> Result<()> {
-        let udf = Arc::new(ScalarUDF::new_from_impl(DummyUDF::new()));
         let exprs: Vec<Arc<dyn PhysicalExpr>> = vec![
             Arc::new(BinaryExpr::new(
                 Arc::new(Column::new("a", 3)),
@@ -1538,7 +1536,7 @@ mod tests {
             Arc::new(NegativeExpr::new(Arc::new(Column::new("f", 4)))),
             Arc::new(ScalarFunctionExpr::new(
                 "scalar_expr",
-                Arc::clone(&udf),
+                Arc::new(ScalarUDF::new_from_impl(DummyUDF::new())),
                 vec![
                     Arc::new(BinaryExpr::new(
                         Arc::new(Column::new("b", 1)),
@@ -1603,7 +1601,7 @@ mod tests {
             Arc::new(NegativeExpr::new(Arc::new(Column::new("f_new", 5)))),
             Arc::new(ScalarFunctionExpr::new(
                 "scalar_expr",
-                Arc::clone(&udf),
+                Arc::new(ScalarUDF::new_from_impl(DummyUDF::new())),
                 vec![
                     Arc::new(BinaryExpr::new(
                         Arc::new(Column::new("b_new", 1)),
diff --git a/datafusion/expr/src/expr.rs b/datafusion/expr/src/expr.rs
index 9f4c58a7fa31f..83d35c3d25b16 100644
--- a/datafusion/expr/src/expr.rs
+++ b/datafusion/expr/src/expr.rs
@@ -2503,51 +2503,6 @@ mod test {
         assert_eq!(udf.signature().volatility, Volatility::Volatile);
     }
 
-    #[test]
-    fn test_scalar_udf_eq_pointer() {
-        #[derive(Debug)]
-        struct DummyUDF {
-            signature: Signature,
-        }
-
-        impl DummyUDF {
-            fn new() -> Self {
-                Self {
-                    signature: Signature::variadic_any(Volatility::Immutable),
-                }
-            }
-        }
-
-        impl ScalarUDFImpl for DummyUDF {
-            fn as_any(&self) -> &dyn Any {
-                self
-            }
-
-            fn name(&self) -> &str {
-                "dummy_udf"
-            }
-
-            fn signature(&self) -> &Signature {
-                &self.signature
-            }
-
-            fn return_type(&self, _arg_types: &[DataType]) -> Result<DataType> {
-                Ok(DataType::Int32)
-            }
-
-            fn invoke(&self, _args: &[ColumnarValue]) -> Result<ColumnarValue> {
-                unimplemented!("DummyUDF::invoke")
-            }
-        }
-
-        let udf1 = ScalarUDF::new_from_impl(DummyUDF::new());
-        let udf1_clone = udf1.clone();
-        let udf2 = ScalarUDF::new_from_impl(DummyUDF::new());
-
-        assert!(udf1.eq(&udf1_clone));
-        assert!(!udf1.eq(&udf2));
-    }
-
     use super::*;
 
     #[test]
diff --git a/datafusion/expr/src/udf.rs b/datafusion/expr/src/udf.rs
index d1ca4d601cd05..1a5d50477b1c8 100644
--- a/datafusion/expr/src/udf.rs
+++ b/datafusion/expr/src/udf.rs
@@ -61,7 +61,7 @@ pub struct ScalarUDF {
 
 impl PartialEq for ScalarUDF {
     fn eq(&self, other: &Self) -> bool {
-        Arc::ptr_eq(&self.inner, &other.inner)
+        self.inner.equals(other.inner.as_ref())
     }
 }
 
@@ -678,11 +678,9 @@ pub trait ScalarUDFImpl: Debug + Send + Sync {
     /// - symmetric: `a.equals(b)` implies `b.equals(a)`;
     /// - transitive: `a.equals(b)` and `b.equals(c)` implies `a.equals(c)`.
     ///
-    /// By default, checks for pointer equality.
+    /// By default, compares [`Self::name`] and [`Self::signature`].
     fn equals(&self, other: &dyn ScalarUDFImpl) -> bool {
-        let self_ptr = self as *const _ as *const ();
-        let other_ptr = other as *const _ as *const ();
-        std::ptr::eq(self_ptr, other_ptr)
+        self.name() == other.name() && self.signature() == other.signature()
     }
 
     /// Returns a hash value for this scalar UDF.