diff --git a/gtsam/geometry/Rot3M.cpp b/gtsam/geometry/Rot3M.cpp
index eb1bd6461..02e5b771f 100644
--- a/gtsam/geometry/Rot3M.cpp
+++ b/gtsam/geometry/Rot3M.cpp
@@ -176,13 +176,17 @@ Vector3 Rot3::CayleyChart::Local(const Rot3& R, OptionalJacobian<3,3> H) {
   if (H) throw std::runtime_error("Rot3::CayleyChart::Local Derivative");
   // Create a fixed-size matrix
   Matrix3 A = R.matrix();
-  const Matrix3 P = A + I_3x3;
-  // Check if (A+I) is invertible. Same as checking for -1 eigenvalue.
-  if (P.determinant() == 0.0) {
-    throw std::runtime_error("Rot3::CayleyChart::Local Invalid Rotation");
-  }
-  Matrix3 Pinv = (A + I_3x3).inverse();
-  return SO3::Vee(Pinv * (A - I_3x3)) * 2;
+  // Mathematica closed form optimization (procrastination?) gone wild:
+  const double a = A(0, 0), b = A(0, 1), c = A(0, 2);
+  const double d = A(1, 0), e = A(1, 1), f = A(1, 2);
+  const double g = A(2, 0), h = A(2, 1), i = A(2, 2);
+  const double di = d * i, ce = c * e, cd = c * d, fg = f * g;
+  const double M = 1 + e - f * h + i + e * i;
+  const double K = -4.0 / (cd * h + M + a * M - g * (c + ce) - b * (d + di - fg));
+  const double x = a * f - cd + f;
+  const double y = b * f - ce - c;
+  const double z = fg - di - d;
+  return K * Vector3(x, y, z);
 }
 
 /* ************************************************************************* */