diff --git a/src/stim/dem/detector_error_model.cc b/src/stim/dem/detector_error_model.cc
index 6f663dbf..2e3167c7 100644
--- a/src/stim/dem/detector_error_model.cc
+++ b/src/stim/dem/detector_error_model.cc
@@ -16,9 +16,11 @@
 
 #include "stim/dem/detector_error_model.h"
 
+#include <algorithm> 
 #include <cmath>
 #include <iomanip>
 #include <limits>
+#include <numeric>
 
 #include "stim/util_bot/str_util.h"
 
@@ -793,3 +795,30 @@ DetectorErrorModel DetectorErrorModel::without_tags() const {
     }
     return result;
 }
+
+bool DetectorErrorModel::equal_up_to_instruction_ordering(const DetectorErrorModel &other) const {
+    if (instructions.size() != other.instructions.size()) {
+        return false;
+    }
+
+    auto get_sorted_indices = [](const std::vector<DemInstruction> &ins) {
+        std::vector<size_t> indices(ins.size());
+        std::iota(indices.begin(), indices.end(), 0);
+        std::sort(indices.begin(), indices.end(), [&ins](size_t i, size_t j) {
+            return ins[i] < ins[j];
+        });
+        return indices;
+    };
+
+    // sort the indices to avoid copying instructions
+    auto sorted_lhs_indices = get_sorted_indices(instructions);
+    auto sorted_rhs_indices = get_sorted_indices(other.instructions);
+
+    for (size_t i = 0; i < sorted_lhs_indices.size(); i++) {
+        if (!(instructions[sorted_lhs_indices[i]] == other.instructions[sorted_rhs_indices[i]])) {
+            return false;
+        }
+    }
+
+    return true;
+}
diff --git a/src/stim/dem/detector_error_model.h b/src/stim/dem/detector_error_model.h
index 0f5d53d5..2f4edc80 100644
--- a/src/stim/dem/detector_error_model.h
+++ b/src/stim/dem/detector_error_model.h
@@ -135,6 +135,13 @@ struct DetectorErrorModel {
 
     /// Returns an equivalent detector error model with no repeat blocks or detector_shift instructions.
     DetectorErrorModel flattened() const;
+
+    /// Returns true if the detector error model is equal to the other detector error model up to instruction ordering.
+    ///
+    /// For example, error(0.01) D0 error(0.002) D1 L0 is considered the same as error(0.002) D1 L0 error(0.01) D0.
+    ///
+    /// Note: requires O(n log n) time due to sorting. Prefer `==` when you know the instructions are in the same order.
+    bool equal_up_to_instruction_ordering(const DetectorErrorModel &other) const;
 };
 
 void print_detector_error_model(std::ostream &out, const DetectorErrorModel &v, size_t indent);
diff --git a/src/stim/dem/detector_error_model.test.cc b/src/stim/dem/detector_error_model.test.cc
index 429642c9..484ad1e9 100644
--- a/src/stim/dem/detector_error_model.test.cc
+++ b/src/stim/dem/detector_error_model.test.cc
@@ -894,3 +894,21 @@ TEST(detector_error_model, parse_windows_newlines) {
         DetectorErrorModel("error(0.125) D0\r\ndetector(5) D10\r\n"),
         DetectorErrorModel("error(0.125) D0\r\ndetector(5) D10\r\n"));
 }
+
+TEST(detector_error_model, equal_up_to_instruction_ordering) {
+    DetectorErrorModel lhs(R"MODEL(
+        error(0.01) D0
+        error(0.002) D1 L0
+        detector(5, 10) D0
+        detector(5, 15) D1
+        logical_observable L0
+    )MODEL");
+    DetectorErrorModel rhs(R"MODEL(
+        error(0.002) D1 L0
+        error(0.01) D0
+        detector(5, 15) D1
+        detector(5, 10) D0
+        logical_observable L0
+    )MODEL");
+    EXPECT_TRUE(lhs.equal_up_to_instruction_ordering(rhs));
+}