diff --git a/hal_test.go b/hal_test.go
index f80dd99..edcf6f5 100644
--- a/hal_test.go
+++ b/hal_test.go
@@ -120,26 +120,107 @@ func TestNewton1(t *testing.T) {
 	err = module.Run()
 	assert.NoError(t, err)
 
-	assert.Len(t, outputMock.Outputs, 1)
-	assert.Equal(t, float64(15), outputMock.Outputs[0])
+	calculateNewton := func(start float64) float64 {
+		f1 := func(x float64) float64 {
+			return math.Pow(x, 5) + 5*math.Pow(x, 3) - 5
+		}
+
+		f1derived := func(x float64) float64 {
+			return 5*math.Pow(x, 4) + 15*math.Pow(x, 2)
+		}
+
+		var last float64
+		x := start
+		for x != last {
+			last = x
+			x = x - f1(x)/f1derived(x)
+		}
+		return x
+	}
 
 	assert.Equal(t, calculateNewton(1), module.IO[1])
 }
 
-func f1(x float64) float64 {
-	return math.Pow(x, 5) + 5*math.Pow(x, 3) - 5
-}
+func TestNewton2(t *testing.T) {
+	input := []string{
+		"01 START",
+		"02 LOADNUM 1",
+		"03 STORE 10", // Every x is saved to reg 10
+
+		// f(x)
+		"10 MUL 10",   // x²
+		"11 STORE 11", // Save x² to reg 11 for later use since we need that in the second part of the function
+		"12 MUL 10",   // x³
+		"13 MUL 10",   // x⁴
+		"14 MUL 10",   // x⁵
+		"15 STORE 20", // This is x⁵ which we save here to save a few instructions
+		"16 MUL 10",   // x⁶
+		"17 MULNUM 8", // x⁶ * 8
+		"18 STORE 12", // Reg 12 now contains the result of the first part of f(x)
+		"19 LOAD 11",  // Put x² from earlier back in the accumulator
+		"20 MULNUM 3", // x² * 3
+		"21 ADD 12",   // Add the first and second part of the function together, basically 8x⁶ + 3x²
+		"22 SUBNUM 3", // (8x⁶ + 3x²) - 3
+		"23 STORE 15", // Result in reg 15
+
+		// f'(x)
+		"30 LOAD 20",   // x⁵ which we saved earlier while calculating x⁶
+		"31 MULNUM 48", // x⁵ * 48
+		"32 STORE 21",  // Store the result in 21
+		"33 LOAD 10",   // Load our x
+		"34 MULNUM 6",  // x * 6
+		"35 ADD 21",    // (x * 6) + 48x⁵
+		"36 STORE 25",  // Store the result, which is the total result of f'(x) in reg 25
+
+		// x - f(x) / f'(x)
+		"40 LOAD 15",   // load f(x)
+		"41 DIV 25",    // f(x) / f'(x)
+		"42 MULNUM -1", // Invert the result
+		"43 ADD 10",    // Add x: Because we inverted the result before, we can do this instead of SUB - lets us reuse the content of the accumulator
+
+		"44 STORE 35", // Reg 35 now contains the end result of x - f(x) / f'(x)
+
+		// This is our exit condition:
+		// We compare the current result with the last calculated result, if both are equal, we exit
+		"50 SUB 50",      // Reg 50 contains the last result
+		"51 JUMPNULL 60", // If both are equal, we exit
+		"52 LOAD 35",     // Otherwise load reg 15 again, store it as the current last result and continue
+		"53 STORE 50",
+
+		// Go to the beginning
+		"54 JUMP 03",
+
+		"60 LOAD 10", // Load the result
+		"61 OUT 1",   // Print it
+		"62 STOP",
+	}
 
-func f1derived(x float64) float64 {
-	return 5*math.Pow(x, 4) + 15*math.Pow(x, 2)
-}
+	program, err := parser.ParseProgram(input)
+	assert.NoError(t, err)
 
-func calculateNewton(start float64) float64 {
-	var last float64
-	x := start
-	for x != last {
-		last = x
-		x = x - f1(x)/f1derived(x)
+	module, err := hal.NewHALModule(program, 256, 2, false)
+	assert.NoError(t, err)
+
+	err = module.Run()
+	assert.NoError(t, err)
+
+	calculateNewton := func(start float64) float64 {
+		f1 := func(x float64) float64 {
+			return 8*math.Pow(x, 6) + 3*math.Pow(x, 2) - 3
+		}
+
+		f1derived := func(x float64) float64 {
+			return 48*math.Pow(x, 5) + 6*x
+		}
+
+		var last float64
+		x := start
+		for x != last {
+			last = x
+			x = x - f1(x)/f1derived(x)
+		}
+		return x
 	}
-	return x
+
+	assert.Equal(t, calculateNewton(1), module.IO[1])
 }
diff --git a/newton2.hal b/newton2.hal
index 72cf628..3e51a0b 100644
--- a/newton2.hal
+++ b/newton2.hal
@@ -17,11 +17,6 @@
 22 SUBNUM 3
 23 STORE 15
 
-24 SUB 50
-25 JUMPNULL 45
-26 LOAD 15
-27 STORE 50
-
 30 LOAD 20
 31 MULNUM 48
 32 STORE 21
@@ -34,6 +29,16 @@
 41 DIV 25
 42 MULNUM -1
 43 ADD 10
-44 JUMP 03
-45 OUT 10
-46 STOP
\ No newline at end of file
+
+44 STORE 35
+
+50 SUB 50
+51 JUMPNULL 60
+52 LOAD 35
+53 STORE 50
+
+54 JUMP 03
+
+60 LOAD 10
+61 OUT 1
+62 STOP