diff --git a/Cargo.lock b/Cargo.lock
index bcfa1b29..4029cdde 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -449,6 +449,7 @@ dependencies = [
  "codspeed-criterion-compat",
  "egraph-serialize",
  "env_logger",
+ "foldhash",
  "generic_symbolic_expressions",
  "getrandom",
  "glob",
@@ -543,6 +544,12 @@ version = "0.4.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "0ce7134b9999ecaf8bcd65542e436736ef32ddca1b3e06094cb6ec5755203b80"
 
+[[package]]
+name = "foldhash"
+version = "0.1.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f81ec6369c545a7d40e4589b5597581fa1c441fe1cce96dd1de43159910a36a2"
+
 [[package]]
 name = "generic-array"
 version = "0.14.7"
diff --git a/Cargo.toml b/Cargo.toml
index c1664496..4ed63d39 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -38,6 +38,7 @@ num-integer = "0.1.45"
 num-rational = "0.4.1"
 num-traits = "0.2.15"
 smallvec = "1.11"
+foldhash = "0.1.3"
 
 generic_symbolic_expressions = "5.0.4"
 
diff --git a/src/function/table.rs b/src/function/table.rs
index 300cd851..178f03a5 100644
--- a/src/function/table.rs
+++ b/src/function/table.rs
@@ -35,7 +35,7 @@ use std::{
 use hashbrown::raw::RawTable;
 
 use super::binary_search::binary_search_table_by_key;
-use crate::{util::BuildHasher as BH, TupleOutput, Value, ValueVec};
+use crate::{util::BuildFxHasher as BH, TupleOutput, Value, ValueVec};
 
 type Offset = usize;
 
diff --git a/src/util.rs b/src/util.rs
index 47191c23..db74b186 100644
--- a/src/util.rs
+++ b/src/util.rs
@@ -1,18 +1,32 @@
 #![allow(unused)]
 
-use std::fmt::Display;
+use std::{fmt::Display, hash::BuildHasher};
 
 use crate::core::SpecializedPrimitive;
 #[allow(unused_imports)]
 use crate::*;
 
-pub(crate) type BuildHasher = std::hash::BuildHasherDefault<rustc_hash::FxHasher>;
+pub(crate) type BuildFxHasher = std::hash::BuildHasherDefault<rustc_hash::FxHasher>;
 
-pub(crate) type HashMap<K, V> = hashbrown::HashMap<K, V, BuildHasher>;
-pub(crate) type HashSet<K> = hashbrown::HashSet<K, BuildHasher>;
+#[derive(Debug, Clone, Default)]
+pub struct DeterministicHashBuilder;
 
-pub type IndexMap<K, V> = indexmap::IndexMap<K, V, BuildHasher>;
-pub type IndexSet<K> = indexmap::IndexSet<K, BuildHasher>;
+impl BuildHasher for DeterministicHashBuilder {
+    type Hasher = foldhash::fast::FoldHasher;
+    fn build_hasher(&self) -> Self::Hasher {
+        foldhash::fast::FixedState::with_seed(0).build_hasher()
+    }
+}
+
+/// Use deterministic hasher to make egglog deterministic
+/// when rule application order matters.
+pub(crate) type HashMap<K, V> = hashbrown::HashMap<K, V, DeterministicHashBuilder>;
+pub(crate) type HashSet<K> = hashbrown::HashSet<K, DeterministicHashBuilder>;
+
+/// Index maps don't need deterministic hashing,
+/// since iteration order is guaranteed to be insertion order.
+pub type IndexMap<K, V> = indexmap::IndexMap<K, V, BuildFxHasher>;
+pub type IndexSet<K> = indexmap::IndexSet<K, BuildFxHasher>;
 
 pub(crate) fn concat_vecs<T>(to: &mut Vec<T>, mut from: Vec<T>) {
     if to.len() < from.len() {