diff --git a/include/ceres/rotation.h b/include/ceres/rotation.h
index 1220173dd..ab1e69e6a 100644
--- a/include/ceres/rotation.h
+++ b/include/ceres/rotation.h
@@ -743,10 +743,10 @@ inline void UnitQuaternionRotatePoint(const T q[4],
 template <typename T>
 inline void QuaternionRotatePoint(const T q[4], const T pt[3], T result[3]) {
   DCHECK_NE(pt, result) << "Inplace rotation is not supported.";
-  using std::hypot;
 
   // 'scale' is 1 / norm(q).
-  const T scale = T(1) / hypot(q[0], q[1], hypot(q[2], q[3]));
+  const T scale =
+      T(1) / sqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
 
   // Make unit-norm version of q.
   const T unit[4] = {
diff --git a/internal/ceres/rotation_test.cc b/internal/ceres/rotation_test.cc
index b59c48737..28a4271c4 100644
--- a/internal/ceres/rotation_test.cc
+++ b/internal/ceres/rotation_test.cc
@@ -30,6 +30,7 @@
 
 #include "ceres/rotation.h"
 
+#include <array>
 #include <cmath>
 #include <limits>
 #include <random>
@@ -969,8 +970,8 @@ void ExpectJetArraysClose(const Jet<double, N>* x, const Jet<double, N>* y) {
 }
 
 // Log-10 of a value well below machine precision.
-static const int kSmallTinyCutoff =
-    static_cast<int>(2 * log(std::numeric_limits<double>::epsilon()) / log(10.0));
+static const int kSmallTinyCutoff = static_cast<int>(
+    2 * log(std::numeric_limits<double>::epsilon()) / log(10.0));
 
 // Log-10 of a value just below values representable by double.
 static const int kTinyZeroLimit =
@@ -1221,6 +1222,23 @@ TEST(AngleAxis, RotatePointGivesSameAnswerAsRotationMatrix) {
   }
 }
 
+TEST(Quaternion, UnitQuaternion) {
+  using Jet = ceres::Jet<double, 4>;
+  std::array<Jet, 4> quaternion = {
+      Jet(1.0, 0), Jet(0.0, 1), Jet(0.0, 2), Jet(0.0, 3)};
+  std::array<Jet, 3> point = {Jet(0.0), Jet(0.0), Jet(0.0)};
+  Eigen::Vector3<Jet> rotated_point;
+  QuaternionRotatePoint(quaternion.data(), point.data(), rotated_point.data());
+  LOG(INFO) << rotated_point[0];
+  LOG(INFO) << rotated_point[1];
+  LOG(INFO) << rotated_point[2];
+
+  for (int i = 0; i < 3; ++i) {
+    EXPECT_EQ(rotated_point[i], point[i]);
+    EXPECT_FALSE(rotated_point[i].v.array().isNaN().any());
+  }
+}
+
 TEST(AngleAxis, NearZeroRotatePointGivesSameAnswerAsRotationMatrix) {
   std::mt19937 prng;
   std::uniform_real_distribution<double> uniform_distribution{-1.0, 1.0};