diff --git a/src/transaction-allocator/modules/transaction-allocation/interfaces/ITATransactionAllocation.sol b/src/transaction-allocator/modules/transaction-allocation/interfaces/ITATransactionAllocation.sol
index f56a956..7b75728 100644
--- a/src/transaction-allocator/modules/transaction-allocation/interfaces/ITATransactionAllocation.sol
+++ b/src/transaction-allocator/modules/transaction-allocation/interfaces/ITATransactionAllocation.sol
@@ -50,5 +50,5 @@ interface ITATransactionAllocation is ITATransactionAllocationEventsErrors, ITAT
         uint256 _totalStake,
         uint256 _totalTransactions,
         FixedPointType _zScore
-    ) external view returns (FixedPointType);
+    ) external pure returns (FixedPointType);
 }
diff --git a/test/core/RelayerLivenessAndJailing.t.sol b/test/core/RelayerLivenessAndJailing.t.sol
index 0aa2ee2..f3ac42b 100644
--- a/test/core/RelayerLivenessAndJailing.t.sol
+++ b/test/core/RelayerLivenessAndJailing.t.sol
@@ -21,6 +21,7 @@ contract RelayerLivenessAndJailingTest is
     uint256 constant initialApplicationFunds = 10 ether;
 
     mapping(RelayerAddress => uint256) penalty;
+    VerifyRelayerLivenessDifferentialHelper v = new VerifyRelayerLivenessDifferentialHelper();
 
     function setUp() public override {
         if (tx.gasprice == 0) {
@@ -535,4 +536,63 @@ contract RelayerLivenessAndJailingTest is
         ta.unjailAndReenter(latestRelayerState, initialRelayerStake[inactiveRelayer]);
         vm.stopPrank();
     }
+
+    /// forge-config: test.fuzz.runs = 2048
+    function testDifferentialOptimisedVerifyRelayerLivenessAgainstReferenceImplementation(
+        uint256 _relayerStake,
+        uint256 _totalStake,
+        uint256 _transactionsDoneByRelayer,
+        uint256 _totalTransactions
+    ) external {
+        vm.assume(_relayerStake > 0);
+        vm.assume(_totalStake > 0);
+        vm.assume(_transactionsDoneByRelayer > 0);
+        vm.assume(_totalTransactions > 0);
+        vm.assume(_relayerStake <= _totalStake);
+        vm.assume(_transactionsDoneByRelayer <= _totalTransactions);
+        vm.assume(_totalStake <= 1_000_000_000 ether);
+        vm.assume(_totalTransactions <= 1_000_000_000);
+
+        assertEq(
+            v.verifyRelayerLivenessReferenceImplementation(
+                _relayerStake, _totalStake, _transactionsDoneByRelayer, _totalTransactions, ta.livenessZParameter()
+            ),
+            v.verifyRelayerLivenessOptimisedImplementation(
+                _relayerStake, _totalStake, _transactionsDoneByRelayer, _totalTransactions, ta.livenessZParameter()
+            )
+        );
+    }
+}
+
+contract VerifyRelayerLivenessDifferentialHelper is TATransactionAllocation {
+    TATransactionAllocation t;
+
+    using Uint256WrapperHelper for uint256;
+
+    constructor() {
+        t = new TATransactionAllocation();
+    }
+
+    function verifyRelayerLivenessReferenceImplementation(
+        uint256 _relayerStake,
+        uint256 _totalStake,
+        uint256 _transactionsDoneByRelayer,
+        uint256 _totalTransactions,
+        FixedPointType _zScore
+    ) external view returns (bool) {
+        return _transactionsDoneByRelayer.fp()
+            >= t.calculateMinimumTranasctionsForLiveness(_relayerStake, _totalStake, _totalTransactions, _zScore);
+    }
+
+    function verifyRelayerLivenessOptimisedImplementation(
+        uint256 _relayerStake,
+        uint256 _totalStake,
+        uint256 _transactionsDoneByRelayer,
+        uint256 _totalTransactions,
+        FixedPointType _zScore
+    ) external pure returns (bool) {
+        return _checkRelayerLiveness(
+            _relayerStake, _totalStake, _transactionsDoneByRelayer, _totalTransactions, _zScore * _zScore
+        );
+    }
 }