diff --git a/components/salsa-macro-rules/src/setup_tracked_fn.rs b/components/salsa-macro-rules/src/setup_tracked_fn.rs
index 1a25b378..2c11d9ca 100644
--- a/components/salsa-macro-rules/src/setup_tracked_fn.rs
+++ b/components/salsa-macro-rules/src/setup_tracked_fn.rs
@@ -227,9 +227,8 @@ macro_rules! setup_tracked_fn {
                             $zalsa::AsId::as_id(&($($input_id),*))
                         }
                     };
-                    $Configuration::fn_ingredient($db).fetch($db, key);
-                    let database_key_index = $Configuration::fn_ingredient($db).database_key_index(key);
-                    $zalsa::accumulated_by($db.as_salsa_database(), database_key_index)
+
+                    $Configuration::fn_ingredient($db).accumulated_by::<A>($db, key)
                 }
 
                 $zalsa::macro_if! { $is_specifiable =>
diff --git a/src/accumulator.rs b/src/accumulator.rs
index cc96d29b..dad727ca 100644
--- a/src/accumulator.rs
+++ b/src/accumulator.rs
@@ -210,16 +210,3 @@ where
             .finish()
     }
 }
-
-pub fn accumulated_by<A>(db: &dyn Database, database_key_index: DatabaseKeyIndex) -> Vec<A>
-where
-    A: Accumulator,
-{
-    let Some(accumulator) = <IngredientImpl<A>>::from_db(db) else {
-        return vec![];
-    };
-    let runtime = db.runtime();
-    let mut output = vec![];
-    accumulator.produced_by(runtime, database_key_index, &mut output);
-    output
-}
diff --git a/src/function.rs b/src/function.rs
index 51c42587..7ee0cd04 100644
--- a/src/function.rs
+++ b/src/function.rs
@@ -16,6 +16,7 @@ use self::delete::DeletedEntries;
 
 use super::ingredient::Ingredient;
 
+mod accumulated;
 mod backdate;
 mod delete;
 mod diff_outputs;
diff --git a/src/function/accumulated.rs b/src/function/accumulated.rs
new file mode 100644
index 00000000..8bd86140
--- /dev/null
+++ b/src/function/accumulated.rs
@@ -0,0 +1,37 @@
+use crate::{accumulator, storage::DatabaseGen, Database, Id};
+
+use super::{Configuration, IngredientImpl};
+
+impl<C> IngredientImpl<C>
+where
+    C: Configuration,
+{
+    /// Helper used by `accumulate` functions. Computes the results accumulated by `database_key_index`
+    /// and its inputs.
+    pub fn accumulated_by<A>(&self, db: &C::DbView, key: Id) -> Vec<A>
+    where
+        A: accumulator::Accumulator,
+    {
+        let Some(accumulator) = <accumulator::IngredientImpl<A>>::from_db(db) else {
+            return vec![];
+        };
+        let runtime = db.runtime();
+        let mut output = vec![];
+
+        // First ensure the result is up to date
+        self.fetch(db, key);
+
+        let database_key_index = self.database_key_index(key);
+        accumulator.produced_by(runtime, database_key_index, &mut output);
+
+        if let Some(origin) = self.origin(key) {
+            for input in origin.inputs() {
+                if let Ok(input) = input.try_into() {
+                    accumulator.produced_by(runtime, input, &mut output);
+                }
+            }
+        }
+
+        output
+    }
+}
diff --git a/src/lib.rs b/src/lib.rs
index 299714e9..a68dd73c 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -73,7 +73,6 @@ pub mod prelude {
 ///
 /// The contents of this module are NOT subject to semver.
 pub mod plumbing {
-    pub use crate::accumulator::accumulated_by;
     pub use crate::accumulator::Accumulator;
     pub use crate::array::Array;
     pub use crate::cycle::Cycle;
diff --git a/src/runtime/local_state.rs b/src/runtime/local_state.rs
index 2fc21cb3..2213bf1f 100644
--- a/src/runtime/local_state.rs
+++ b/src/runtime/local_state.rs
@@ -76,7 +76,16 @@ pub enum QueryOrigin {
 }
 
 impl QueryOrigin {
-    /// Indices for queries *written* by this query (or `vec![]` if its value was assigned).
+    /// Indices for queries *read* by this query
+    pub(crate) fn inputs(&self) -> impl Iterator<Item = DependencyIndex> + '_ {
+        let opt_edges = match self {
+            QueryOrigin::Derived(edges) | QueryOrigin::DerivedUntracked(edges) => Some(edges),
+            QueryOrigin::Assigned(_) | QueryOrigin::BaseInput => None,
+        };
+        opt_edges.into_iter().flat_map(|edges| edges.inputs())
+    }
+
+    /// Indices for queries *written* by this query (if any)
     pub(crate) fn outputs(&self) -> impl Iterator<Item = DependencyIndex> + '_ {
         let opt_edges = match self {
             QueryOrigin::Derived(edges) | QueryOrigin::DerivedUntracked(edges) => Some(edges),
diff --git a/tests/accumulate-dag.rs b/tests/accumulate-dag.rs
new file mode 100644
index 00000000..5aa5b0df
--- /dev/null
+++ b/tests/accumulate-dag.rs
@@ -0,0 +1,68 @@
+mod common;
+use common::{HasLogger, Logger};
+
+use expect_test::expect;
+use salsa::{Accumulator, Database};
+use test_log::test;
+
+#[salsa::input]
+struct MyInput {
+    field_a: u32,
+    field_b: u32,
+}
+
+#[salsa::accumulator]
+#[derive(Clone, Debug)]
+struct Log(#[allow(dead_code)] String);
+
+#[salsa::tracked]
+fn push_logs(db: &dyn Database, input: MyInput) {
+    push_a_logs(db, input);
+    push_b_logs(db, input);
+}
+
+#[salsa::tracked]
+fn push_a_logs(db: &dyn Database, input: MyInput) {
+    let count = input.field_a(db);
+    for i in 0..count {
+        Log(format!("log_a({} of {})", i, count)).accumulate(db);
+    }
+}
+
+#[salsa::tracked]
+fn push_b_logs(db: &dyn Database, input: MyInput) {
+    // Note that b calls a
+    push_a_logs(db, input);
+    let count = input.field_b(db);
+    for i in 0..count {
+        Log(format!("log_b({} of {})", i, count)).accumulate(db);
+    }
+}
+
+#[test]
+fn accumulate_a_called_twice() {
+    salsa::default_database().attach(|db| {
+        let input = MyInput::new(db, 2, 3);
+        let logs = push_logs::accumulated::<Log>(db, input);
+        // Check that we don't see logs from `a` appearing twice in the input.
+        expect![[r#"
+            [
+                Log(
+                    "log_a(0 of 2)",
+                ),
+                Log(
+                    "log_a(1 of 2)",
+                ),
+                Log(
+                    "log_b(0 of 3)",
+                ),
+                Log(
+                    "log_b(1 of 3)",
+                ),
+                Log(
+                    "log_b(2 of 3)",
+                ),
+            ]"#]]
+        .assert_eq(&format!("{:#?}", logs));
+    })
+}
diff --git a/tests/accumulate.rs b/tests/accumulate.rs
index 2a5ddeb4..6fb4e05f 100644
--- a/tests/accumulate.rs
+++ b/tests/accumulate.rs
@@ -20,7 +20,7 @@ struct MyInput {
 
 #[salsa::accumulator]
 #[derive(Clone, Debug)]
-struct Logs(#[allow(dead_code)] String);
+struct Log(#[allow(dead_code)] String);
 
 #[salsa::tracked]
 fn push_logs(db: &dyn Db, input: MyInput) {
@@ -30,13 +30,13 @@ fn push_logs(db: &dyn Db, input: MyInput) {
         input.field_b(db)
     ));
 
-    // We don't invoke `push_a_logs` (or `push_b_logs`) with a value of 1 or less.
+    // We don't invoke `push_a_logs` (or `push_b_logs`) with a value of 0.
     // This allows us to test what happens a change in inputs causes a function not to be called at all.
-    if input.field_a(db) > 1 {
+    if input.field_a(db) > 0 {
         push_a_logs(db, input);
     }
 
-    if input.field_b(db) > 1 {
+    if input.field_b(db) > 0 {
         push_b_logs(db, input);
     }
 }
@@ -47,7 +47,7 @@ fn push_a_logs(db: &dyn Db, input: MyInput) {
     db.push_log(format!("push_a_logs({})", field_a));
 
     for i in 0..field_a {
-        Logs(format!("log_a({} of {})", i, field_a)).accumulate(db);
+        Log(format!("log_a({} of {})", i, field_a)).accumulate(db);
     }
 }
 
@@ -57,7 +57,7 @@ fn push_b_logs(db: &dyn Db, input: MyInput) {
     db.push_log(format!("push_b_logs({})", field_a));
 
     for i in 0..field_a {
-        Logs(format!("log_b({} of {})", i, field_a)).accumulate(db);
+        Log(format!("log_b({} of {})", i, field_a)).accumulate(db);
     }
 }
 
@@ -88,38 +88,115 @@ fn accumulate_once() {
 
     // Just call accumulate on a base input to see what happens.
     let input = MyInput::new(&db, 2, 3);
-    let logs = push_logs::accumulated::<Logs>(&db, input);
+    let logs = push_logs::accumulated::<Log>(&db, input);
     db.assert_logs(expect![[r#"
         [
             "push_logs(a = 2, b = 3)",
             "push_a_logs(2)",
             "push_b_logs(3)",
         ]"#]]);
+    // Check that we see logs from `a` first and then logs from `b`
+    // (execution order).
     expect![[r#"
         [
-            "log_b(0 of 3)",
-            "log_b(1 of 3)",
-            "log_b(2 of 3)",
-            "log_a(0 of 2)",
-            "log_a(1 of 2)",
+            Log(
+                "log_a(0 of 2)",
+            ),
+            Log(
+                "log_a(1 of 2)",
+            ),
+            Log(
+                "log_b(0 of 3)",
+            ),
+            Log(
+                "log_b(1 of 3)",
+            ),
+            Log(
+                "log_b(2 of 3)",
+            ),
         ]"#]]
     .assert_eq(&format!("{:#?}", logs));
 }
 
 #[test]
-fn change_a_and_reaccumulate() {
+fn change_a_from_2_to_0() {
     let mut db = Database::default();
 
     // Accumulate logs for `a = 2` and `b = 3`
     let input = MyInput::new(&db, 2, 3);
-    let logs = push_logs::accumulated::<Logs>(&db, input);
+    let logs = push_logs::accumulated::<Log>(&db, input);
     expect![[r#"
         [
-            "log_b(0 of 3)",
-            "log_b(1 of 3)",
-            "log_b(2 of 3)",
-            "log_a(0 of 2)",
-            "log_a(1 of 2)",
+            Log(
+                "log_a(0 of 2)",
+            ),
+            Log(
+                "log_a(1 of 2)",
+            ),
+            Log(
+                "log_b(0 of 3)",
+            ),
+            Log(
+                "log_b(1 of 3)",
+            ),
+            Log(
+                "log_b(2 of 3)",
+            ),
+        ]"#]]
+    .assert_eq(&format!("{:#?}", logs));
+    db.assert_logs(expect![[r#"
+        [
+            "push_logs(a = 2, b = 3)",
+            "push_a_logs(2)",
+            "push_b_logs(3)",
+        ]"#]]);
+
+    // Change to `a = 0`, which means `push_logs` does not call `push_a_logs` at all
+    input.set_field_a(&mut db).to(0);
+    let logs = push_logs::accumulated::<Log>(&db, input);
+    expect![[r#"
+        [
+            Log(
+                "log_b(0 of 3)",
+            ),
+            Log(
+                "log_b(1 of 3)",
+            ),
+            Log(
+                "log_b(2 of 3)",
+            ),
+        ]"#]]
+    .assert_eq(&format!("{:#?}", logs));
+    db.assert_logs(expect![[r#"
+        [
+            "push_logs(a = 1, b = 3)",
+        ]"#]]);
+}
+
+#[test]
+fn change_a_from_2_to_1() {
+    let mut db = Database::default();
+
+    // Accumulate logs for `a = 2` and `b = 3`
+    let input = MyInput::new(&db, 2, 3);
+    let logs = push_logs::accumulated::<Log>(&db, input);
+    expect![[r#"
+        [
+            Log(
+                "log_a(0 of 2)",
+            ),
+            Log(
+                "log_a(1 of 2)",
+            ),
+            Log(
+                "log_b(0 of 3)",
+            ),
+            Log(
+                "log_b(1 of 3)",
+            ),
+            Log(
+                "log_b(2 of 3)",
+            ),
         ]"#]]
     .assert_eq(&format!("{:#?}", logs));
     db.assert_logs(expect![[r#"
@@ -131,17 +208,27 @@ fn change_a_and_reaccumulate() {
 
     // Change to `a = 1`, which means `push_logs` does not call `push_a_logs` at all
     input.set_field_a(&mut db).to(1);
-    let logs = push_logs::accumulated::<Logs>(&db, input);
+    let logs = push_logs::accumulated::<Log>(&db, input);
     expect![[r#"
         [
-            "log_b(0 of 3)",
-            "log_b(1 of 3)",
-            "log_b(2 of 3)",
+            Log(
+                "log_a(0 of 1)",
+            ),
+            Log(
+                "log_b(0 of 3)",
+            ),
+            Log(
+                "log_b(1 of 3)",
+            ),
+            Log(
+                "log_b(2 of 3)",
+            ),
         ]"#]]
     .assert_eq(&format!("{:#?}", logs));
     db.assert_logs(expect![[r#"
         [
             "push_logs(a = 1, b = 3)",
+            "push_a_logs(1)",
         ]"#]]);
 }
 
@@ -151,11 +238,15 @@ fn get_a_logs_after_changing_b() {
 
     // Invoke `push_a_logs` with `a = 2` and `b = 3` (but `b` doesn't matter)
     let input = MyInput::new(&db, 2, 3);
-    let logs = push_a_logs::accumulated::<Logs>(&db, input);
+    let logs = push_a_logs::accumulated::<Log>(&db, input);
     expect![[r#"
         [
-            "log_a(0 of 2)",
-            "log_a(1 of 2)",
+            Log(
+                "log_a(0 of 2)",
+            ),
+            Log(
+                "log_a(1 of 2)",
+            ),
         ]"#]]
     .assert_eq(&format!("{:#?}", logs));
     db.assert_logs(expect![[r#"
@@ -166,11 +257,15 @@ fn get_a_logs_after_changing_b() {
     // Changing `b` does not cause `push_a_logs` to re-execute
     // and we still get the same result
     input.set_field_b(&mut db).to(5);
-    let logs = push_a_logs::accumulated::<Logs>(&db, input);
+    let logs = push_a_logs::accumulated::<Log>(&db, input);
     expect![[r#"
         [
-            "log_a(0 of 2)",
-            "log_a(1 of 2)",
+            Log(
+                "log_a(0 of 2)",
+            ),
+            Log(
+                "log_a(1 of 2)",
+            ),
         ]
     "#]]
     .assert_debug_eq(&logs);