diff --git a/src/function/accumulated.rs b/src/function/accumulated.rs
index 7d54a9f..f0f0450 100644
--- a/src/function/accumulated.rs
+++ b/src/function/accumulated.rs
@@ -26,18 +26,16 @@ where
         let mut stack: Vec<DatabaseKeyIndex> = vec![db_key];
 
         while let Some(k) = stack.pop() {
-            visited.insert(k);
-            accumulator.produced_by(runtime, k, &mut output);
+            if visited.insert(k) {
+                accumulator.produced_by(runtime, k, &mut output);
 
-            let origin = db.lookup_ingredient(k.ingredient_index).origin(k.key_index);
-            let inputs = origin.iter().flat_map(|origin| origin.inputs());
-
-            for input in inputs.rev() {
-                if let Ok(input) = input.try_into() {
-                    if !visited.contains(&input) {
-                        stack.push(input);
-                    }
-                }
+                let origin = db.lookup_ingredient(k.ingredient_index).origin(k.key_index);
+                let inputs = origin.iter().flat_map(|origin| origin.inputs());
+                stack.extend(
+                    inputs
+                        .flat_map(|input| TryInto::<DatabaseKeyIndex>::try_into(input).into_iter())
+                        .rev(),
+                );
             }
         }
 
diff --git a/tests/accumulate-chain.rs b/tests/accumulate-chain.rs
index aa3a8ea..7cf3d3b 100644
--- a/tests/accumulate-chain.rs
+++ b/tests/accumulate-chain.rs
@@ -39,7 +39,7 @@ fn push_d_logs(db: &dyn Database) {
 fn accumulate_chain() {
     salsa::default_database().attach(|db| {
         let logs = push_logs::accumulated::<Log>(db);
-        // Check that we don't see logs from `a` appearing twice in the input.
+        // Check that we get all the logs.
         expect![[r#"
             [
                 Log(
diff --git a/tests/accumulate-execution-order.rs b/tests/accumulate-execution-order.rs
new file mode 100644
index 0000000..ddc2e02
--- /dev/null
+++ b/tests/accumulate-execution-order.rs
@@ -0,0 +1,61 @@
+mod common;
+
+use expect_test::expect;
+use salsa::{Accumulator, Database};
+use test_log::test;
+
+#[salsa::accumulator]
+struct Log(#[allow(dead_code)] String);
+
+#[salsa::tracked]
+fn push_logs(db: &dyn Database) {
+    push_a_logs(db);
+}
+
+#[salsa::tracked]
+fn push_a_logs(db: &dyn Database) {
+    Log("log a".to_string()).accumulate(db);
+    push_b_logs(db);
+    push_c_logs(db);
+    push_d_logs(db);
+}
+
+#[salsa::tracked]
+fn push_b_logs(db: &dyn Database) {
+    Log("log b".to_string()).accumulate(db);
+    push_d_logs(db);
+}
+
+#[salsa::tracked]
+fn push_c_logs(db: &dyn Database) {
+    Log("log c".to_string()).accumulate(db);
+}
+
+#[salsa::tracked]
+fn push_d_logs(db: &dyn Database) {
+    Log("log d".to_string()).accumulate(db);
+}
+
+#[test]
+fn accumulate_chain() {
+    salsa::default_database().attach(|db| {
+        let logs = push_logs::accumulated::<Log>(db);
+        // Check that we get logs in execution order
+        expect![[r#"
+            [
+                Log(
+                    "log a",
+                ),
+                Log(
+                    "log b",
+                ),
+                Log(
+                    "log d",
+                ),
+                Log(
+                    "log c",
+                ),
+            ]"#]]
+        .assert_eq(&format!("{:#?}", logs));
+    })
+}