diff --git a/src/Algebra/Expr.hs b/src/Algebra/Expr.hs
index cc4acb0..82f89dc 100644
--- a/src/Algebra/Expr.hs
+++ b/src/Algebra/Expr.hs
@@ -11,6 +11,8 @@ import Prelude hiding ( (^) )
 
 import Data.Array
 import Data.Char
+import Data.Monoid
+import Data.Semigroup
 
 import Text.Show
 
@@ -35,10 +37,10 @@ data Expr v
 -- instance Pretty var => Show (Expr var) where show = pretty
 
 -- | Degree of the expression
-exprDegree :: Expr var -> Int
-exprDegree = go where
+exprDegree :: (var -> Int) -> Expr var -> Int
+exprDegree varDeg = go where
   go expr = case expr of
-    VarE  _    -> 1
+    VarE  v    -> varDeg v
     LitE  _    -> 0
     AddE e1 e2 -> max (go e1) (go e2)
     SubE e1 e2 -> max (go e1) (go e2)
@@ -68,6 +70,31 @@ mulE :: Expr var -> Expr var -> Expr var
 mulE = MulE 
 -}
 
+--------------------------------------------------------------------------------
+-- * Operation counting
+
+data OperCount = MkOperCount 
+  { numberOfAdds :: Int
+  , numberOfMuls :: Int
+  }
+  deriving (Eq,Show)
+
+instance Semigroup OperCount where
+  (<>) (MkOperCount a1 m1) (MkOperCount a2 m2) = MkOperCount (a1+a2) (m1+m2)
+
+instance Monoid OperCount where
+  mempty = MkOperCount 0 0
+
+exprOperCount :: Expr var -> OperCount
+exprOperCount = go where
+  go expr = case expr of
+    VarE _     -> mempty
+    LitE e     -> mempty
+    AddE e1 e2 -> go e1 <> go e2 <> MkOperCount 1 0
+    SubE e1 e2 -> go e1 <> go e2 <> MkOperCount 1 0
+    MulE e1 e2 -> go e1 <> go e2 <> MkOperCount 0 1
+    ImgE e     -> go e           <> MkOperCount 0 1
+
 --------------------------------------------------------------------------------
 -- * pretty printing
 
diff --git a/src/Gate/Computation.hs b/src/Gate/Computation.hs
index c275bb5..a5cd381 100644
--- a/src/Gate/Computation.hs
+++ b/src/Gate/Computation.hs
@@ -61,7 +61,13 @@ type Def_     = LocalDef Var_
 type Compute a = Program (Instr Var_) a
 
 let_ :: String -> Expr Var_ -> Compute (Expr Var_)
-let_ name rhs = VarE <$> Instr (Let name rhs)
+let_ name rhs = case rhs of
+  VarE _  -> return rhs
+  LitE _  -> return rhs
+  _       -> VarE <$> Instr (Let name rhs)
+
+lets_ :: [Expr Var_] -> Compute [Expr Var_]
+lets_ = mapM (let_ "") 
 
 commit :: Expr Var_ -> Compute ()
 commit what = Instr (Commit what)
@@ -72,8 +78,11 @@ commitList = mapM_ commit
 --------------------------------------------------------------------------------
 -- | Straightline programs
 
-data LocalDef v 
-  = MkLocalDef Int String (Expr v)
+data LocalDef v = MkLocalDef 
+  { localDefVarIdx  :: Int
+  , localDefVarName :: String 
+  , localDefRHS     :: Expr v
+  }
   deriving (Eq,Show)
 
 instance Pretty v => Pretty (LocalDef v) where
@@ -109,6 +118,12 @@ compileToStraightLine = fst . go emptyStraightLine where
                              state' = MkStraightLine (def:localdefs) commits (counter+1)
                          in  (state', LocalVar counter name)
 
+straightLineOperCount :: StraightLine -> OperCount
+straightLineOperCount (MkStraightLine{..}) = final where
+  defs  = map exprOperCount $ map localDefRHS localdefs
+  coms  = map exprOperCount $ commits
+  final = mconcat defs <> mconcat coms  
+
 --------------------------------------------------------------------------------
 
 type Scope a = IntMap a
diff --git a/src/Gate/Poseidon.hs b/src/Gate/Poseidon.hs
index 20c9fd4..9bb60c4 100644
--- a/src/Gate/Poseidon.hs
+++ b/src/Gate/Poseidon.hs
@@ -24,11 +24,13 @@ import Hash.Constants
 --------------------------------------------------------------------------------
 
 sbox :: Expr Var_ -> Compute (Expr Var_)
-sbox x = do
+sbox x0 = do
+  x  <- let_ "x1_" x0
   x2 <- let_ "x2_" (x *x )
   x3 <- let_ "x3_" (x *x2)
   x4 <- let_ "x4_" (x2*x2)
-  return (x3*x4)
+  x7 <- let_ "x7_" (x3*x4)
+  return x7
 
 flipFoldM :: (Foldable t, Monad m) => b -> t a -> (b -> a -> m b) -> m b
 flipFoldM s0 list action = foldM action s0 list
@@ -70,15 +72,15 @@ poseidonGateConstraints = do
     return $ mds state4
 
   -- partial rounds
-  let state'  = zipWith (+) phase1 (map LitE $ elems fast_PARTIAL_FIRST_ROUND_CONSTANT)
-  let state'' = mdsInitPartial state'
+  state'  <- lets_ $ zipWith (+) phase1 (map LitE $ elems fast_PARTIAL_FIRST_ROUND_CONSTANT)
+  state'' <- lets_ $ mdsInitPartial state'
   phase2 <- flipFoldM state'' [0..21] $ \state1 r -> do
     let sbox_in = partial_sbox_in r 
     commit $ (state1!!0) - sbox_in 
     y <- sbox sbox_in
     let z = if r < 21 then y + LitE (fast_PARTIAL_ROUND_CONSTANTS!r) else y
-    let state2 = z : tail state1
-    return $ mdsFastPartial r state2
+    state2 <- lets_ (z : tail state1)
+    lets_ (mdsFastPartial r state2)
   
   -- final full rounds
   phase3 <- flipFoldM phase2 [0..3] $ \state1 r -> do
diff --git a/src/Test/Witness.hs b/src/Test/Witness.hs
index 86e4ab0..19d806f 100644
--- a/src/Test/Witness.hs
+++ b/src/Test/Witness.hs
@@ -16,9 +16,12 @@ import Algebra.Goldilocks
 import Algebra.GoldilocksExt
 
 import Gate.Base
+import Gate.Vars
 import Gate.Computation
 import Gate.Constraints
 
+import Misc.Pretty
+
 --------------------------------------------------------------------------------
 
 -- | As exported into JSON by our Plonky2 fork
@@ -68,15 +71,26 @@ test_fibonacci = do
   let const_prg = gateProgram (ConstantGate    2)
 
   let arith_evals = runStraightLine (fmap fromBase arith_row) arith_prg  
-  let const_evals = runStraightLine (fmap fromBase const_row) const_prg
   let posei_evals = runStraightLine (fmap fromBase posei_row) posei_prg
+  let const_evals = runStraightLine (fmap fromBase const_row) const_prg
 
-  putStrLn $ "number of constants in ArithmeticGate = " ++ show (length arith_evals)
-  putStrLn $ "number of constants in ConstantGate   = " ++ show (length const_evals)
-  putStrLn $ "number of constants in PosiedoGate    = " ++ show (length posei_evals)
+  putStrLn $ "number of constraints in ArithmeticGate  = " ++ show (length arith_evals)
+  putStrLn $ "number of constraints in PosiedonGate    = " ++ show (length posei_evals)
+  -- putStrLn $ "number of constraints in PublicInputGate = " ++ show (length pubio_evals)
+  putStrLn $ "number of constraints in ConstGate       = " ++ show (length const_evals)
+
+  putStrLn $ "number of operations in ArithmeticGate  = " ++ show (straightLineOperCount arith_prg)
+  putStrLn $ "number of operations in PosiedonGate    = " ++ show (straightLineOperCount posei_prg)
+  putStrLn $ "number of operations in PublicInputGate = " ++ show (straightLineOperCount pubio_prg)
+  putStrLn $ "number of operations in ConstGate       = " ++ show (straightLineOperCount const_prg)
 
   print arith_evals
-  print const_evals
   print posei_evals
+  print const_evals
+
+  -- printStraightLine posei_prg
   
 --------------------------------------------------------------------------------
+
+main :: IO
+main = test_fibonacci