diff --git a/src/libraries/adaptative-curve/ExpLib.sol b/src/libraries/adaptative-curve/ExpLib.sol
index 70381ed7..e8c6f8ff 100644
--- a/src/libraries/adaptative-curve/ExpLib.sol
+++ b/src/libraries/adaptative-curve/ExpLib.sol
@@ -19,7 +19,7 @@ library ExpLib {
     int256 internal constant WEXP_UPPER_BOUND = 93.859467695000404319 ether;
 
     /// @dev The value of wExp(`WEXP_UPPER_BOUND`).
-    int256 internal constant WEXP_UPPER_VALUE = 57716089161558943862588783571184261698504.523000224082296832 ether;
+    int256 internal constant WEXP_UPPER_VALUE = 57716089161558943949701069502944508345128.422502756744429568 ether;
 
     /// @dev Returns an approximation of exp.
     function wExp(int256 x) internal pure returns (int256) {
diff --git a/test/AdaptativeCurveIrmTest.sol b/test/AdaptativeCurveIrmTest.sol
index 808e8073..336ef784 100644
--- a/test/AdaptativeCurveIrmTest.sol
+++ b/test/AdaptativeCurveIrmTest.sol
@@ -215,10 +215,6 @@ contract AdaptativeCurveIrmTest is Test {
         assertApproxEqRel(irm.rateAtTarget(marketParams.id()), expectedRateAtTarget, 0.001 ether, "rateAtTarget");
     }
 
-    function testWExpWMulDownMaxRate() public pure {
-        ExpLib.wExp(ExpLib.WEXP_UPPER_BOUND).wMulDown(ConstantsLib.MAX_RATE_AT_TARGET);
-    }
-
     /* HANDLERS */
 
     function handleBorrowRate(uint256 totalSupplyAssets, uint256 totalBorrowAssets, uint256 elapsed) external {
diff --git a/test/ExpLibTest.sol b/test/ExpLibTest.sol
index 4497c409..77bc9e3b 100644
--- a/test/ExpLibTest.sol
+++ b/test/ExpLibTest.sol
@@ -1,12 +1,18 @@
 // SPDX-License-Identifier: UNLICENSED
 pragma solidity ^0.8.0;
 
+import {MathLib, WAD_INT} from "../src/libraries/MathLib.sol";
+import {ConstantsLib} from "../src/libraries/adaptative-curve/ConstantsLib.sol";
 import {ExpLib} from "../src/libraries/adaptative-curve/ExpLib.sol";
 import {wadExp} from "../lib/solmate/src/utils/SignedWadMath.sol";
+import {MathLib as MorphoMathLib} from "../lib/morpho-blue/src/libraries/MathLib.sol";
 
 import "../lib/forge-std/src/Test.sol";
 
 contract ExpLibTest is Test {
+    using MathLib for int256;
+    using MorphoMathLib for uint256;
+
     /// @dev ln(1e-9) truncated at 2 decimal places.
     int256 internal constant LN_GWEI_INT = -20.72 ether;
 
@@ -41,6 +47,7 @@ contract ExpLibTest is Test {
 
     function testWExpContinuousUpperBound() public {
         assertApproxEqRel(ExpLib.wExp(ExpLib.WEXP_UPPER_BOUND - 1), ExpLib.WEXP_UPPER_VALUE, 1e-10 ether);
+        assertEq(_wExpUnbounded(ExpLib.WEXP_UPPER_BOUND), ExpLib.WEXP_UPPER_VALUE);
     }
 
     function testWExpPositive(int256 x) public {
@@ -54,4 +61,28 @@ contract ExpLibTest is Test {
 
         assertLe(ExpLib.wExp(x), 1e18);
     }
+
+    function testWExpWMulDownMaxRate() public pure {
+        ExpLib.wExp(ExpLib.WEXP_UPPER_BOUND).wMulDown(ConstantsLib.MAX_RATE_AT_TARGET);
+    }
+
+    function _wExpUnbounded(int256 x) internal pure returns (int256) {
+        unchecked {
+            // Decompose x as x = q * ln(2) + r with q an integer and -ln(2)/2 <= r <= ln(2)/2.
+            // q = x / ln(2) rounded half toward zero.
+            int256 roundingAdjustment = (x < 0) ? -(ExpLib.LN_2_INT / 2) : (ExpLib.LN_2_INT / 2);
+            // Safe unchecked because x is bounded.
+            int256 q = (x + roundingAdjustment) / ExpLib.LN_2_INT;
+            // Safe unchecked because |q * ln(2) - x| <= ln(2)/2.
+            int256 r = x - q * ExpLib.LN_2_INT;
+
+            // Compute e^r with a 2nd-order Taylor polynomial.
+            // Safe unchecked because |r| < 1e18.
+            int256 expR = WAD_INT + r + (r * r) / WAD_INT / 2;
+
+            // Return e^x = 2^q * e^r.
+            if (q >= 0) return expR << uint256(q);
+            else return expR >> uint256(-q);
+        }
+    }
 }