diff --git a/include/mlir-hlo/Dialect/mhlo/IR/chlo_ops.td b/include/mlir-hlo/Dialect/mhlo/IR/chlo_ops.td
index 9e43188..37e6727 100644
--- a/include/mlir-hlo/Dialect/mhlo/IR/chlo_ops.td
+++ b/include/mlir-hlo/Dialect/mhlo/IR/chlo_ops.td
@@ -398,6 +398,19 @@ def HLOClient_ConjOp : HLOClient_UnaryElementwiseOp<"conj", [],
   }];
 }
 
+def HLOClient_CoshOp : HLOClient_UnaryElementwiseOp<"cosh", [],
+    HLO_FpOrComplexTensor> {
+  let summary = "Cosh operator";
+
+  let description = [{
+    Returns `Cosh(operand)` element-wise.
+
+    $$
+    \cosh(x) = (e^x + e^-x) / 2
+    $$
+  }];
+}
+
 def HLOClient_SinhOp : HLOClient_UnaryElementwiseOp<"sinh", [],
     HLO_FpOrComplexTensor> {
   let summary = "Sinh operation";
diff --git a/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td b/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td
index 26a1da2..3d89f92 100644
--- a/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td
+++ b/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td
@@ -62,7 +62,7 @@ def : Pat<(HLOClient_AcosOp NonComplexElementType:$input),
 
 // Expand asin to MHLO dialect as follows:
 //   asin(x) = 2 * atan(x / (1 + sqrt(1 - x^2)))
-def : Pat<(HLOClient_AsinOp $input),
+def : Pat<(HLOClient_AsinOp NonComplexElementType:$input),
   (HLO_MulOp
     (HLO_ConstantLike<"2"> $input),
     (HLO_Atan2Op
@@ -92,6 +92,36 @@ def : Pat<(HLOClient_AtanOp $input),
 def : Pat<(HLOClient_ConjOp $v),
           (HLO_ComplexOp (HLO_RealOp $v), (HLO_NegOp (HLO_ImagOp $v)))>;
 
+// Express `cosh` as
+//   cosh(x) = (e^x + e^-x) / 2
+//           = e^(x + log(1/2)) + e^(-x + log(1/2))
+//
+// The second formulation avoids overflowing when e^x = inf but (e^x)/2 is not.
+//
+// This incorrectly overflows to inf for two f32 input values, namely
+// +/-89.4159851, due to rounding error when computing x +/- log(1/2).  The
+// correct answer of 3.40281961e+38 (0x7f7fffec) is very close to max-float, so
+// we deem this acceptable.
+def : Pat<(HLOClient_CoshOp NonComplexElementType:$input),
+  (HLO_AddOp
+    (HLO_ExpOp
+      (HLO_AddOp
+        $input,
+        (HLO_LogOp
+          (HLO_ConstantLike<"0.5"> $input)
+        )
+      )
+    ),
+    (HLO_ExpOp
+      (HLO_AddOp
+        (HLO_NegOp $input),
+        (HLO_LogOp
+          (HLO_ConstantLike<"0.5"> $input)
+        )
+      )
+    )
+  )>;
+
 // Express `sinh` as
 //   sinh(x) = (e^x - e^-x) / 2                     if |x| < 1
 //           = e^(x + log(1/2)) - e^(-x + log(1/2)) otherwise.
@@ -136,7 +166,7 @@ def : Pat<(HLOClient_SinhOp NonComplexElementType:$input),
 
 // Express tan in MHLO dialect as
 //   tan(x) = sin(x) / cos(x).
-def : Pat<(HLOClient_TanOp $input),
+def : Pat<(HLOClient_TanOp NonComplexElementType:$input),
   (HLO_DivOp
     (HLO_SinOp $input),
     (HLO_CosOp $input)
diff --git a/lib/Dialect/mhlo/transforms/transform_unranked_hlo.cc b/lib/Dialect/mhlo/transforms/transform_unranked_hlo.cc
index eb78100..152be21 100644
--- a/lib/Dialect/mhlo/transforms/transform_unranked_hlo.cc
+++ b/lib/Dialect/mhlo/transforms/transform_unranked_hlo.cc
@@ -50,9 +50,9 @@ namespace {
               sep fn(ShiftRightLogicalOp) sep fn(SubOp) sep fn(XorOp)
 
 // TODO(herhut): Generate these out of op definitions.
-#define MAP_CHLO_OPERATION_CWISE_UNARY(fn, sep)                         \
-  fn(AcosOp) sep fn(AsinOp) sep fn(AtanOp) sep fn(ConjOp) sep fn(ErfOp) \
-      sep fn(ErfcOp) sep fn(SinhOp) sep fn(TanOp)
+#define MAP_CHLO_OPERATION_CWISE_UNARY(fn, sep)                          \
+  fn(AcosOp) sep fn(AsinOp) sep fn(AtanOp) sep fn(ConjOp) sep fn(CoshOp) \
+      sep fn(ErfOp) sep fn(ErfcOp) sep fn(SinhOp) sep fn(TanOp)
 
 template <typename OpTy>
 inline void AddLegalOpOnRankedTensor(ConversionTarget *target) {