--optimize-relinearization fails for multiple return values

[AlexanderViand-Intel]

// heir-opt --mlir-to-bgv
func.func @foo(%x: i16 {secret.secret}, %y: i16 {secret.secret}) -> (i16, i16) {
  %0 = arith.addi %x, %y : i16
  return %0, %0: i16, i16
}

fails with

Error solving the problem: INVALID_ARGUMENT: duplicate name inserted: RequireLinearized_secret.yield_1; ModelProto.linear_constraints are invalid
/home/aviand/code/heir/tests/Emitter/heracles/emit_heracles_bgv.mlir:11:1: error: Failed to solve the optimization problem
func.func @foo(%x: i16 {secret.secret}, %y: i16 {secret.secret}) -> (i16, i16) {
^
/home/aviand/code/heir/tests/Emitter/heracles/emit_heracles_bgv.mlir:11:1: note: see current operation: 
%0:2 = "secret.generic"(%arg0, %arg1) ({
^bb0(%arg2: i16, %arg3: i16):
  %1 = "arith.addi"(%arg2, %arg3) <{overflowFlags = #arith.overflow<none>}> {mgmt.mgmt = #mgmt.mgmt<level = 0>} : (i16, i16) -> i16
  "secret.yield"(%1, %1) : (i16, i16) -> ()
}) {arg0 = {mgmt.mgmt = #mgmt.mgmt<level = 0>}, arg1 = {mgmt.mgmt = #mgmt.mgmt<level = 0>}} : (!secret.secret<i16>, !secret.secret<i16>) -> (!secret.secret<i16>, !secret.secret<i16>)

This also occurs when the return values aren't duplicates:

// heir-opt --mlir-to-bgv
func.func @foo(%x: i16 {secret.secret}, %y: i16 {secret.secret}) -> (i16, i16) {
  %0 = arith.addi %x, %y : i16
  %1 = arith.addi %x, %x : i16
  return %0, %1: i16, i16
}

fails with

Error solving the problem: INVALID_ARGUMENT: duplicate name inserted: RequireLinearized_secret.yield_2; ModelProto.linear_constraints are invalid
/home/aviand/code/heir/tests/Emitter/heracles/emit_heracles_bgv.mlir:11:1: error: Failed to solve the optimization problem
func.func @foo(%x: i16 {secret.secret}, %y: i16 {secret.secret}) -> (i16, i16) {
^
/home/aviand/code/heir/tests/Emitter/heracles/emit_heracles_bgv.mlir:11:1: note: see current operation: 
%0:2 = "secret.generic"(%arg0, %arg1) ({
^bb0(%arg2: i16, %arg3: i16):
  %1 = "arith.addi"(%arg2, %arg3) <{overflowFlags = #arith.overflow<none>}> {mgmt.mgmt = #mgmt.mgmt<level = 0>} : (i16, i16) -> i16
  %2 = "arith.addi"(%arg2, %arg2) <{overflowFlags = #arith.overflow<none>}> {mgmt.mgmt = #mgmt.mgmt<level = 0>} : (i16, i16) -> i16
  "secret.yield"(%1, %2) : (i16, i16) -> ()
}) {arg0 = {mgmt.mgmt = #mgmt.mgmt<level = 0>}, arg1 = {mgmt.mgmt = #mgmt.mgmt<level = 0>}} : (!secret.secret<i16>, !secret.secret<i16>) -> (!secret.secret<i16>, !secret.secret<i16>)

Unlike the previous issue, this seems like it's actually be a bug/ intended limitation of the relin solver 😉