diff --git a/symbolic-base/src/ZkFold/Symbolic/Compiler.hs b/symbolic-base/src/ZkFold/Symbolic/Compiler.hs
index 316356b32..609093cba 100644
--- a/symbolic-base/src/ZkFold/Symbolic/Compiler.hs
+++ b/symbolic-base/src/ZkFold/Symbolic/Compiler.hs
@@ -19,8 +19,8 @@ import           Data.Ord                                   (Ord)
 import           Data.Proxy                                 (Proxy (..))
 import           Data.Traversable                           (for)
 import           GHC.Generics                               (Par1 (Par1))
-import           Prelude                                    (FilePath, IO, Monoid (mempty), Show (..), Traversable,
-                                                             putStrLn, return, type (~), ($), (++))
+import           Prelude                                    (FilePath, IO, Show (..), Traversable, putStrLn, return,
+                                                             type (~), ($), (++))
 
 import           ZkFold.Base.Algebra.Basic.Class
 import           ZkFold.Prelude                             (writeFileJSON)
@@ -60,7 +60,7 @@ solder f = fromCircuit2F (pieces f input) b $ \r (Par1 i) -> do
     return r
   where
     Bool b = isValid input
-    input = restore @(Support f) $ const mempty { acOutput = acInput }
+    input = restore @(Support f) $ const idCircuit
 
 -- | Compiles function `f` into an arithmetic circuit with all outputs equal to 1.
 compileForceOne ::
diff --git a/symbolic-base/src/ZkFold/Symbolic/Compiler/ArithmeticCircuit.hs b/symbolic-base/src/ZkFold/Symbolic/Compiler/ArithmeticCircuit.hs
index 7c9f2964b..5d2b41896 100644
--- a/symbolic-base/src/ZkFold/Symbolic/Compiler/ArithmeticCircuit.hs
+++ b/symbolic-base/src/ZkFold/Symbolic/Compiler/ArithmeticCircuit.hs
@@ -1,3 +1,4 @@
+{-# LANGUAGE TypeOperators #-}
 module ZkFold.Symbolic.Compiler.ArithmeticCircuit (
         ArithmeticCircuit,
         Constraint,
@@ -6,6 +7,8 @@ module ZkFold.Symbolic.Compiler.ArithmeticCircuit (
         -- high-level functions
         optimize,
         desugarRanges,
+        idCircuit,
+        guessOutput,
         -- low-level functions
         eval,
         eval1,
@@ -30,16 +33,18 @@ module ZkFold.Symbolic.Compiler.ArithmeticCircuit (
         checkClosedCircuit
     ) where
 
+import           Control.DeepSeq                                     (NFData)
 import           Control.Monad                                       (foldM)
 import           Control.Monad.State                                 (execState)
 import           Data.Binary                                         (Binary)
-import           Data.Functor.Rep                                    (Representable (..))
+import           Data.Foldable                                       (for_)
+import           Data.Functor.Rep                                    (Representable (..), mzipRep)
 import           Data.Map                                            hiding (drop, foldl, foldr, map, null, splitAt,
                                                                       take)
 import qualified Data.Map.Monoidal                                   as M
 import qualified Data.Set                                            as S
 import           Data.Void                                           (absurd)
-import           GHC.Generics                                        (U1 (..))
+import           GHC.Generics                                        (U1 (..), (:*:))
 import           Numeric.Natural                                     (Natural)
 import           Prelude                                             hiding (Num (..), drop, length, product, splitAt,
                                                                       sum, take, (!!), (^))
@@ -49,7 +54,10 @@ import           Text.Pretty.Simple                                  (pPrint)
 
 import           ZkFold.Base.Algebra.Basic.Class
 import           ZkFold.Base.Algebra.Polynomials.Multivariate        (evalMonomial, evalPolynomial)
+import           ZkFold.Base.Data.HFunctor                           (hmap)
+import           ZkFold.Base.Data.Product                            (fstP, sndP)
 import           ZkFold.Prelude                                      (length)
+import           ZkFold.Symbolic.Class                               (fromCircuit2F)
 import           ZkFold.Symbolic.Compiler.ArithmeticCircuit.Instance ()
 import           ZkFold.Symbolic.Compiler.ArithmeticCircuit.Internal (Arithmetic, ArithmeticCircuit (..), Constraint,
                                                                       SysVar (..), Var (..), acInput, eval, eval1, exec,
@@ -90,6 +98,23 @@ desugarRanges c =
   let r' = flip execState c {acOutput = U1} . traverse (uncurry desugarRange) $ [(SysVar v, k) | (k, s) <- M.toList (acRange c), v <- S.toList s]
    in r' { acRange = mempty, acOutput = acOutput c }
 
+idCircuit :: Representable i => ArithmeticCircuit a p i i
+idCircuit = ArithmeticCircuit
+  { acSystem = empty
+  , acRange = M.empty
+  , acWitness = empty
+  , acOutput = acInput
+  }
+
+guessOutput ::
+  (Arithmetic a, Binary a, Binary (Rep p), Binary (Rep i), Binary (Rep o)) =>
+  (Ord (Rep i), Ord (Rep o), NFData (Rep i), NFData (Rep o)) =>
+  (Representable i, Representable o, Foldable o) =>
+  ArithmeticCircuit a p i o -> ArithmeticCircuit a p (i :*: o) U1
+guessOutput c = fromCircuit2F (hlmap fstP c) (hmap sndP idCircuit) $ \o o' -> do
+  for_ (mzipRep o o') $ \(i, j) -> constraint (\x -> x i - x j)
+  return U1
+
 ----------------------------------- Information -----------------------------------
 
 -- | Calculates the number of constraints in the system.