diff --git a/.DS_Store b/.DS_Store
new file mode 100644
index 0000000..ea3fae1
Binary files /dev/null and b/.DS_Store differ
diff --git a/.gitignore b/.gitignore
index 71c04ed..8e859cd 100644
--- a/.gitignore
+++ b/.gitignore
@@ -26,3 +26,5 @@ go.work.sum
 .env
 
 *.log
+
+profile/
\ No newline at end of file
diff --git a/Makefile b/Makefile
index 8e821b5..d7db258 100644
--- a/Makefile
+++ b/Makefile
@@ -13,5 +13,13 @@ thunk: it
 saccharine: it
 	@ ./lambda.exe - < ./samples/saccharine.txt
 
+prof:
+	@ go tool pprof -top profile/cpu.prof
+
+graph:
+	@ go tool pprof -raw -output=profile/cpu.raw profile/cpu.prof
+	@ go tool pprof -svg profile/cpu.prof > profile/cpu.svg
+	@ open profile/cpu.svg
+
 saccharineX: it
-	@ ./lambda.exe -x - < ./samples/saccharine.txt > saccharine.out
\ No newline at end of file
+	@ ./lambda.exe -x - < ./samples/saccharine.txt > saccharine.out
diff --git a/cmd/.DS_Store b/cmd/.DS_Store
new file mode 100644
index 0000000..85ac39e
Binary files /dev/null and b/cmd/.DS_Store differ
diff --git a/cmd/lambda/lambda.go b/cmd/lambda/lambda.go
index bbc9242..b593434 100644
--- a/cmd/lambda/lambda.go
+++ b/cmd/lambda/lambda.go
@@ -3,6 +3,7 @@ package main
 import (
 	"fmt"
 	"os"
+	"runtime/pprof"
 	"time"
 
 	"git.maximhutz.com/max/lambda/internal/cli"
@@ -14,6 +15,14 @@ import (
 
 // Run main application.
 func main() {
+	f, err := os.Create("profile/cpu.prof")
+	cli.HandleError(err)
+	defer f.Close()
+
+	err = pprof.StartCPUProfile(f)
+	cli.HandleError(err)
+	defer pprof.StopCPUProfile()
+
 	options, err := config.FromArgs()
 	cli.HandleError(err)
 
diff --git a/internal/.DS_Store b/internal/.DS_Store
new file mode 100644
index 0000000..40a0c4e
Binary files /dev/null and b/internal/.DS_Store differ
diff --git a/pkg/.DS_Store b/pkg/.DS_Store
new file mode 100644
index 0000000..65e24b3
Binary files /dev/null and b/pkg/.DS_Store differ
diff --git a/pkg/lambda/is_free_variable.go b/pkg/lambda/is_free_variable.go
new file mode 100644
index 0000000..deb3492
--- /dev/null
+++ b/pkg/lambda/is_free_variable.go
@@ -0,0 +1,14 @@
+package lambda
+
+func IsFreeVariable(n string, e Expression) bool {
+	switch e := e.(type) {
+	case *Variable:
+		return e.Value == n
+	case *Abstraction:
+		return e.Parameter != n && IsFreeVariable(n, e.Body)
+	case *Application:
+		return IsFreeVariable(n, e.Abstraction) || IsFreeVariable(n, e.Argument)
+	default:
+		return false
+	}
+}
diff --git a/pkg/lambda/substitute.go b/pkg/lambda/substitute.go
index ebc83c5..96d4ec2 100644
--- a/pkg/lambda/substitute.go
+++ b/pkg/lambda/substitute.go
@@ -11,12 +11,12 @@ func Substitute(e *Expression, target string, replacement Expression) {
 			return
 		}
 
-		replacementFreeVars := GetFreeVariables(replacement)
-		if !replacementFreeVars.Has(typed.Parameter) {
+		if !IsFreeVariable(typed.Parameter, replacement) {
 			Substitute(&typed.Body, target, replacement)
 			return
 		}
 
+		replacementFreeVars := GetFreeVariables(replacement)
 		used := GetFreeVariables(typed.Body)
 		used.Merge(replacementFreeVars)
 		freshVar := GenerateFreshName(used)
diff --git a/pkg/saccharine/.DS_Store b/pkg/saccharine/.DS_Store
new file mode 100644
index 0000000..6342c25
Binary files /dev/null and b/pkg/saccharine/.DS_Store differ