diff --git a/crates/prover/src/constraint_framework/expr.rs b/crates/prover/src/constraint_framework/expr.rs
index 5d8013402..30d6f04d4 100644
--- a/crates/prover/src/constraint_framework/expr.rs
+++ b/crates/prover/src/constraint_framework/expr.rs
@@ -36,7 +36,6 @@ pub enum Expr {
 }
 
 impl Expr {
-    #[allow(dead_code)]
     pub fn format_expr(&self) -> String {
         match self {
             Expr::Col(ColumnExpr {
@@ -67,6 +66,10 @@ impl Expr {
             Expr::Inv(a) => format!("1 / ({})", a.format_expr()),
         }
     }
+
+    pub fn simplify_and_format(&self) -> String {
+        simplify(self.clone()).format_expr()
+    }
 }
 
 impl From<BaseField> for Expr {
@@ -190,6 +193,91 @@ impl AddAssign<BaseField> for Expr {
     }
 }
 
+pub fn simplify(expr: Expr) -> Expr {
+    match expr {
+        Expr::Add(a, b) => {
+            let a = simplify(*a);
+            let b = simplify(*b);
+            if let (Expr::Const(a), Expr::Const(b)) = (a.clone(), b.clone()) {
+                Expr::Const(a + b)
+            } else if a == Expr::zero() {
+                b
+            } else if b == Expr::zero() {
+                a
+            } else if let Expr::Neg(a) = a {
+                if let Expr::Neg(b) = b {
+                    -(*a + *b)
+                } else {
+                    b - *a
+                }
+            } else if let Expr::Neg(b) = b {
+                a - *b
+            } else {
+                a + b
+            }
+        }
+        Expr::Sub(a, b) => {
+            let a = simplify(*a);
+            let b = simplify(*b);
+            if a == Expr::zero() {
+                -b
+            } else if b == Expr::zero() {
+                a
+            } else if a == b {
+                Expr::zero()
+            } else {
+                a - b
+            }
+        }
+        Expr::Mul(a, b) => {
+            let a = simplify(*a);
+            let b = simplify(*b);
+            let minus_one = Expr::Const(-BaseField::one());
+            if let (Expr::Const(a), Expr::Const(b)) = (a.clone(), b.clone()) {
+                Expr::Const(a * b)
+            } else if a == Expr::zero() || b == Expr::zero() {
+                Expr::zero()
+            } else if a == Expr::one() {
+                b
+            } else if b == Expr::one() {
+                a
+            } else if a == minus_one {
+                -b
+            } else if b == minus_one {
+                -a
+            } else {
+                a * b
+            }
+        }
+        Expr::Col(colexpr) => Expr::Col(colexpr),
+        Expr::SecureCol([a, b, c, d]) => Expr::SecureCol([
+            Box::new(simplify(*a)),
+            Box::new(simplify(*b)),
+            Box::new(simplify(*c)),
+            Box::new(simplify(*d)),
+        ]),
+        Expr::Const(c) => Expr::Const(c),
+        Expr::Param(x) => Expr::Param(x),
+        Expr::Neg(a) => {
+            let a = simplify(*a);
+            match a {
+                Expr::Neg(b) => *b,
+                Expr::Const(c) => Expr::Const(-c),
+                Expr::Sub(a, b) => Expr::Sub(b, a),
+                _ => -a,
+            }
+        }
+        Expr::Inv(a) => {
+            let a = simplify(*a);
+            match a {
+                Expr::Inv(b) => *b,
+                Expr::Const(c) => Expr::Const(c.inverse()),
+                _ => Expr::Inv(Box::new(a)),
+            }
+        }
+    }
+}
+
 /// Returns the expression
 /// `value[0] * <relation>_alpha0 + value[1] * <relation>_alpha1 + ... - <relation>_z.`
 fn combine_formal<R: Relation<Expr, Expr>>(relation: &R, values: &[Expr]) -> Expr {
@@ -273,7 +361,7 @@ impl ExprEvaluator {
         let lets_string = self
             .intermediates
             .iter()
-            .map(|(name, expr)| format!("let {} = {};", name, expr.format_expr()))
+            .map(|(name, expr)| format!("let {} = {};", name, expr.simplify_and_format()))
             .collect::<Vec<String>>()
             .join("\n");
 
@@ -281,7 +369,7 @@ impl ExprEvaluator {
             .constraints
             .iter()
             .enumerate()
-            .map(|(i, c)| format!("let constraint_{i} = ") + &c.format_expr() + ";")
+            .map(|(i, c)| format!("let constraint_{i} = ") + &c.simplify_and_format() + ";")
             .collect::<Vec<String>>()
             .join("\n\n");
 
@@ -369,8 +457,7 @@ mod tests {
     fn test_format_expr() {
         let test_struct = TestStruct {};
         let eval = test_struct.evaluate(ExprEvaluator::new(16, false));
-        let expected = "let intermediate0 = 0 \
-            + (TestRelation_alpha0) * (col_1_0[0]) \
+        let expected = "let intermediate0 = (TestRelation_alpha0) * (col_1_0[0]) \
             + (TestRelation_alpha1) * (col_1_1[0]) \
             + (TestRelation_alpha2) * (col_1_2[0]) \
             - (TestRelation_z);
@@ -382,8 +469,8 @@ mod tests {
 \
         let constraint_1 = (SecureCol(col_2_4[0], col_2_6[0], col_2_8[0], col_2_10[0]) \
             - (SecureCol(col_2_5[-1], col_2_7[-1], col_2_9[-1], col_2_11[-1]) \
-                - ((col_0_3[0]) * (total_sum))) \
-            - (0)) \
+                - ((col_0_3[0]) * (total_sum)))\
+            ) \
             * (intermediate0) \
             - (1);"
             .to_string();
diff --git a/crates/prover/src/examples/state_machine/mod.rs b/crates/prover/src/examples/state_machine/mod.rs
index 787394dd3..2cf8bc2f2 100644
--- a/crates/prover/src/examples/state_machine/mod.rs
+++ b/crates/prover/src/examples/state_machine/mod.rs
@@ -300,13 +300,11 @@ mod tests {
         );
 
         let eval = component.evaluate(ExprEvaluator::new(log_n_rows, true));
-        let expected = "let intermediate0 = 0 \
-            + (StateMachineElements_alpha0) * (col_1_0[0]) \
+        let expected = "let intermediate0 = (StateMachineElements_alpha0) * (col_1_0[0]) \
             + (StateMachineElements_alpha1) * (col_1_1[0]) \
             - (StateMachineElements_z);
 \
-        let intermediate1 = 0 \
-            + (StateMachineElements_alpha0) * (col_1_0[0] + 1) \
+        let intermediate1 = (StateMachineElements_alpha0) * (col_1_0[0] + 1) \
             + (StateMachineElements_alpha1) * (col_1_1[0]) \
             - (StateMachineElements_z);
 
@@ -322,10 +320,10 @@ mod tests {
 \
         let constraint_1 = (SecureCol(col_2_3[0], col_2_6[0], col_2_9[0], col_2_12[0]) \
             - (SecureCol(col_2_4[-1], col_2_7[-1], col_2_10[-1], col_2_13[-1]) \
-                - ((col_0_2[0]) * (total_sum))) \
-            - (0)) \
+                - ((col_0_2[0]) * (total_sum)))\
+            ) \
             * ((intermediate0) * (intermediate1)) \
-            - ((intermediate1) * (1) + (intermediate0) * (-(1)));"
+            - (intermediate1 - (intermediate0));"
             .to_string();
 
         assert_eq!(eval.format_constraints(), expected);