diff --git a/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo.cc b/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo.cc
index bd0ec23..9d36a0f 100644
--- a/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo.cc
+++ b/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo.cc
@@ -648,6 +648,51 @@ Value MaterializeLgamma(ConversionPatternRewriter &rewriter, Location loc,
       lgamma);
 }
 
+// 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.
+Value MaterializeCoshApproximation(ConversionPatternRewriter &rewriter,
+                                   Location loc, ValueRange operands) {
+  CoshOp::Adaptor transformed(operands);
+  Value x = transformed.operand();
+
+  Value log_one_half =
+      rewriter.create<mhlo::LogOp>(loc, getConstantLike(rewriter, loc, 0.5, x));
+  Value exp_add = rewriter.create<mhlo::ExpOp>(
+      loc, rewriter.create<mhlo::AddOp>(loc, x, log_one_half));
+  Value exp_sub = rewriter.create<mhlo::ExpOp>(
+      loc, rewriter.create<mhlo::SubOp>(loc, log_one_half, x));
+  return rewriter.create<mhlo::AddOp>(loc, exp_add, exp_sub);
+}
+
+struct ConvertCoshOp : public OpConversionPattern<CoshOp> {
+  using OpConversionPattern<CoshOp>::OpConversionPattern;
+  LogicalResult matchAndRewrite(
+      CoshOp op, ArrayRef<Value> operands,
+      ConversionPatternRewriter &rewriter) const override {
+    CoshOp::Adaptor transformed(operands);
+    Value x = transformed.operand();
+    if (x.getType().cast<ShapedType>().getElementType().isa<ComplexType>()) {
+      // TODO(hinsu): Support operands with complex element types by always
+      // using the formula for large x. The compare op is not legal for complex
+      // numbers.
+      return failure();
+    }
+    rewriter.replaceOp(op,
+                       MaterializeWithUpcast(rewriter, op.getLoc(), operands,
+                                             rewriter.getF32Type(),
+                                             &MaterializeCoshApproximation));
+    return success();
+  }
+};
+
 // Compute the Digamma function using Lanczos' approximation from "A Precision
 // Approximation of the Gamma Function". SIAM Journal on Numerical Analysis
 // series B. Vol. 1:
@@ -1318,7 +1363,8 @@ void PopulateDecomposeChloPatterns(MLIRContext *context,
 
   // Other patterns.
   // clang-format off
-  patterns->insert<ConvertDigammaOp,
+  patterns->insert<ConvertCoshOp,
+                   ConvertDigammaOp,
                    ConvertErfOp,
                    ConvertErfcOp,
                    ConvertLgammaOp,
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 559abad..f1692ed 100644
--- a/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td
+++ b/lib/Dialect/mhlo/transforms/chlo_legalize_to_hlo_patterns.td
@@ -255,36 +255,6 @@ def : Pat<(HLOClient_AtanhOp NonComplexElementType:$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"> $input)
-        )
-      )
-    )
-  )>;
-
 // Express `is_inf` as
 //   is_inf(x) = is_pos_inf(|x|)
 def : Pat<(HLOClient_IsInfOp NonComplexElementType:$input),
diff --git a/tests/chlo_legalize_to_mhlo.mlir b/tests/chlo_legalize_to_mhlo.mlir
index f94bb8d..81e18f1 100644
--- a/tests/chlo_legalize_to_mhlo.mlir
+++ b/tests/chlo_legalize_to_mhlo.mlir
@@ -2187,3 +2187,32 @@ func @sinh_complex(%x : tensor<2xcomplex<f32>>) -> tensor<2xcomplex<f32>> {
   %1 = chlo.sinh %x : tensor<2xcomplex<f32>> -> tensor<2xcomplex<f32>>
   return %1 : tensor<2xcomplex<f32>>
 }
+
+// ----
+
+// CHECK-LABEL: @cosh_f32
+// CHECK-SAME: (%[[X:.*]]: tensor<f32>)
+func @cosh_f32(%x : tensor<f32>) -> tensor<f32> {
+  // CHECK: %[[HALF:.*]] = mhlo.constant dense<5.000000e-01> : tensor<f32>
+  // CHECK: %[[LOG_HALF:.*]] = "mhlo.log"(%[[HALF]]) : (tensor<f32>) -> tensor<f32>
+  // CHECK: %[[X_PLUS_LOG_HALF:.*]] = mhlo.add %[[X]], %[[LOG_HALF]] : tensor<f32>
+  // CHECK: %[[EXP_1:.*]] = "mhlo.exponential"(%[[X_PLUS_LOG_HALF]]) : (tensor<f32>) -> tensor<f32>
+  // CHECK: %[[LOG_HALF_MINUS_X:.*]] = mhlo.subtract %[[LOG_HALF]], %[[X]] : tensor<f32>
+  // CHECK: %[[EXP_2:.*]] = "mhlo.exponential"(%[[LOG_HALF_MINUS_X]]) : (tensor<f32>) -> tensor<f32>
+  // CHECK: %[[RESULT:.*]] = mhlo.add %[[EXP_1]], %[[EXP_2]] : tensor<f32>
+  // CHECK: return %[[RESULT]] : tensor<f32>
+  %1 = chlo.cosh %x : tensor<f32> -> tensor<f32>
+  return %1 : tensor<f32>
+}
+
+// ----
+
+// CHECK-LABEL: @cosh_f16
+// CHECK-SAME: (%[[ARG0:.*]]: tensor<f16>)
+func @cosh_f16(%x : tensor<f16>) -> tensor<f16> {
+  // CHECK: "mhlo.convert"(%[[ARG0]]) : (tensor<f16>) -> tensor<f32>
+  // CHECK: %[[RES:.*]] = "mhlo.convert"(%{{.*}}) : (tensor<f32>) -> tensor<f16>
+  // CHECK: return %[[RES]]
+  %1 = chlo.cosh %x : tensor<f16> -> tensor<f16>
+  return %1 : tensor<f16>
+}