diff --git a/frontend/cs/r1cs/api_assertions.go b/frontend/cs/r1cs/api_assertions.go
index 60d66e9a75..acbb602c24 100644
--- a/frontend/cs/r1cs/api_assertions.go
+++ b/frontend/cs/r1cs/api_assertions.go
@@ -78,9 +78,18 @@ func (builder *builder[E]) AssertIsBoolean(i1 frontend.Variable) {
 }
 
 func (builder *builder[E]) AssertIsCrumb(i1 frontend.Variable) {
-	i1 = builder.MulAcc(builder.Mul(-3, i1), i1, i1)
-	i1 = builder.MulAcc(builder.Mul(2, i1), i1, i1)
-	builder.AssertIsEqual(i1, 0)
+	if c, ok := builder.constantValue(i1); ok {
+		if i, ok := builder.cs.Uint64(c); ok && i < 4 {
+			return
+		}
+		panic(fmt.Sprintf("AssertIsCrumb constant input %s is not a crumb", builder.cs.String(c)))
+	}
+
+	// i1 (i1-1) (i1-2) (i1-3) = (i1² - 3i1) (i1² - 3i1 + 2)
+	// take X := i1² - 3i1 and we get X (X+2) = 0
+	x := builder.MulAcc(builder.Mul(-3, i1), i1, i1)
+	x = builder.MulAcc(builder.Mul(2, x), x, x)
+	builder.AssertIsEqual(x, 0)
 }
 
 // AssertIsLessOrEqual adds assertion in constraint builder  (v ⩽ bound)
diff --git a/frontend/cs/scs/api_assertions.go b/frontend/cs/scs/api_assertions.go
index e96554bdf5..a7253e3aaf 100644
--- a/frontend/cs/scs/api_assertions.go
+++ b/frontend/cs/scs/api_assertions.go
@@ -119,21 +119,24 @@ func (builder *builder[E]) AssertIsBoolean(i1 frontend.Variable) {
 }
 
 func (builder *builder[E]) AssertIsCrumb(i1 frontend.Variable) {
-	const errorMsg = "AssertIsCrumb: input is not a crumb"
 	if c, ok := builder.constantValue(i1); ok {
 		if i, ok := builder.cs.Uint64(c); ok && i < 4 {
 			return
 		}
-		panic(errorMsg)
+		panic(fmt.Sprintf("AssertIsCrumb constant input %s is not a crumb", builder.cs.String(c)))
 	}
 
 	// i1 (i1-1) (i1-2) (i1-3) = (i1² - 3i1) (i1² - 3i1 + 2)
 	// take X := i1² - 3i1 and we get X (X+2) = 0
 
+	// usually MulAcc is a composition in PLONK, unless we have the condition
+	// a/c == const. This holds here so this is only a single constraint.
 	x := builder.MulAcc(builder.Mul(-3, i1), i1, i1).(expr.Term[E])
 
-	// TODO @Tabaie Ideally this entire function would live in std/math/bits as it is quite specialized;
-	// however using two generic MulAccs and an AssertIsEqual results in three constraints rather than two.
+	// usually bit assertions are defined in [std/math/bits] package, but we
+	// already have it and want to keep it backwards compatible. By doing it
+	// directly we can avoid a constraint as we do 2X + X^2 == 0 in a single
+	// constraint.
 	builder.addPlonkConstraint(sparseR1C[E]{
 		xa: x.VID,
 		xb: x.VID,
diff --git a/internal/stats/latest_stats.csv b/internal/stats/latest_stats.csv
index 962a452fe1..9bfb2e9a09 100644
--- a/internal/stats/latest_stats.csv
+++ b/internal/stats/latest_stats.csv
@@ -1,4 +1,18 @@
 circuit,curve,backend,nbConstraints,nbWires
+api/AssertIsCrumb,bn254,groth16,3,2
+api/AssertIsCrumb,bls12_377,groth16,3,2
+api/AssertIsCrumb,bls12_381,groth16,3,2
+api/AssertIsCrumb,bls24_315,groth16,3,2
+api/AssertIsCrumb,bls24_317,groth16,3,2
+api/AssertIsCrumb,bw6_761,groth16,3,2
+api/AssertIsCrumb,bw6_633,groth16,3,2
+api/AssertIsCrumb,bn254,plonk,2,1
+api/AssertIsCrumb,bls12_377,plonk,2,1
+api/AssertIsCrumb,bls12_381,plonk,2,1
+api/AssertIsCrumb,bls24_315,plonk,2,1
+api/AssertIsCrumb,bls24_317,plonk,2,1
+api/AssertIsCrumb,bw6_761,plonk,2,1
+api/AssertIsCrumb,bw6_633,plonk,2,1
 api/AssertIsLessOrEqual,bn254,groth16,1523,1367
 api/AssertIsLessOrEqual,bls12_377,groth16,1517,1349
 api/AssertIsLessOrEqual,bls12_381,groth16,1529,1405
diff --git a/internal/stats/snippet.go b/internal/stats/snippet.go
index b63e1eb527..c5d1d253b1 100644
--- a/internal/stats/snippet.go
+++ b/internal/stats/snippet.go
@@ -59,6 +59,10 @@ func initSnippets() {
 		api.AssertIsLessOrEqual(newVariable(), bound)
 	})
 
+	registerSnippet("api/AssertIsCrumb", func(api frontend.API, newVariable func() frontend.Variable) {
+		api.AssertIsCrumb(newVariable())
+	})
+
 	// add std snippets
 	registerSnippet("math/bits.ToBinary", func(api frontend.API, newVariable func() frontend.Variable) {
 		_ = bits.ToBinary(api, newVariable())