diff --git a/src/eval.rs b/src/eval.rs
index db97273..f61f2c5 100644
--- a/src/eval.rs
+++ b/src/eval.rs
@@ -2,6 +2,7 @@ pub mod normalise;
 pub mod const_fold;
 pub mod compose;
 pub mod differentiate;
+pub mod simplify;
 
 #[derive(Debug, PartialEq)]
 pub enum Error {
diff --git a/src/eval/simplify.rs b/src/eval/simplify.rs
new file mode 100644
index 0000000..ac1cb14
--- /dev/null
+++ b/src/eval/simplify.rs
@@ -0,0 +1,279 @@
+use crate::expression::Expression;
+use crate::eval::{Error, Evaluator};
+
+pub struct Simplifier;
+
+impl Simplifier {
+	pub fn new() -> Self {
+		Self {}
+	}
+}
+
+impl Evaluator for Simplifier {
+	type Expr = Expression;
+	type Error = Error;
+
+	fn eval(&mut self, input: Expression) -> Result<Expression, Error> {
+		Ok(simplify(input))
+	}
+}
+
+fn simplify(expr: Expression) -> Expression {
+	match expr {
+		Expression::Sum(x, y) => recurse(sum, x, y),
+		Expression::Product(x, y) => recurse(product, x, y),
+		Expression::Exponent(x, y) => recurse(exponent, x, y),
+		_ => expr
+	}
+}
+
+fn sum(
+	x: std::boxed::Box<Expression>,
+	y: std::boxed::Box<Expression>)
+	-> Expression
+{
+	if y.integer() == Some(0) {
+		*x
+	} else if x.integer() == Some(0) {
+		*y
+	} else {
+		Expression::Sum(x, y)
+	}
+}
+
+fn product(
+	x: std::boxed::Box<Expression>,
+	y: std::boxed::Box<Expression>)
+	-> Expression
+{
+	if y.integer() == Some(0) || x.integer() == Some(0) {
+		Expression::Integer(0)
+	} else if y.integer() == Some(1) {
+		*x
+	} else if x.integer() == Some(1) {
+		*y
+	} else {
+		Expression::Product(x, y)
+	}
+}
+
+fn exponent(
+	base: std::boxed::Box<Expression>,
+	power: std::boxed::Box<Expression>)
+	-> Expression
+{
+	if power.integer() == Some(0) {
+		Expression::Integer(1)
+	} else if base.integer() == Some(0) {
+		Expression::Integer(0)
+	} else if power.integer() == Some(1) || base.integer() == Some(1) {
+		*base
+	} else {
+		Expression::Exponent(base, power)
+	}
+}
+
+fn recurse(
+	f: impl Fn(
+		std::boxed::Box<Expression>, 
+		std::boxed::Box<Expression>) -> Expression,
+	x: std::boxed::Box<Expression>,
+	y: std::boxed::Box<Expression>)
+	-> Expression
+{
+	f(boxed(x), boxed(y))
+}
+
+fn boxed(
+	mut expr: std::boxed::Box<Expression>) -> std::boxed::Box<Expression>
+{
+	*expr = simplify(*expr);
+	expr
+}
+
+#[cfg(test)]
+mod tests {
+	use super::*;
+
+	#[test]
+	fn integer_is_unchanged() {
+		let input = Expression::Integer(1);
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Integer(1));
+	}
+
+	#[test]
+	fn symbol_is_unchanged() {
+		let input = Expression::Symbol('x');
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Symbol('x'));
+	}
+
+	#[test]
+	fn sum_of_symbol_with_zero_reduces() {
+		let input = Expression::sum(
+			Expression::Symbol('x'),
+			Expression::Integer(0));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Symbol('x'));
+	}
+
+	#[test]
+	fn sum_of_zero_with_symbol_reduces() {
+		let input = Expression::sum(
+			Expression::Integer(0),
+			Expression::Symbol('x'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Symbol('x'));
+	}
+
+	#[test]
+	fn sum_of_non_zero_integer_with_symbol_is_unchanged() {
+		let input = Expression::sum(
+			Expression::Integer(1),
+			Expression::Symbol('x'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::sum(
+			Expression::Integer(1),
+			Expression::Symbol('x')));
+	}
+
+	#[test]
+	fn nested_sum_with_zero_is_reduced() {
+		let input = Expression::sum(
+			Expression::sum(
+				Expression::Symbol('x'),
+				Expression::Integer(0)),
+			Expression::Symbol('y'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(
+			result,
+			Expression::sum(
+				Expression::Symbol('x'),
+				Expression::Symbol('y')));
+	}
+
+	#[test]
+	fn product_of_symbol_with_zero_becomes_zero() {
+		let input = Expression::product(
+			Expression::Symbol('x'),
+			Expression::Integer(0));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Integer(0));
+	}
+
+	#[test]
+	fn product_of_zero_with_symbol_becomes_zero() {
+		let input = Expression::product(
+			Expression::Integer(0),
+			Expression::Symbol('x'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Integer(0));
+	}
+
+	#[test]
+	fn product_of_symbol_with_one_reduces() {
+		let input = Expression::product(
+			Expression::Symbol('x'),
+			Expression::Integer(1));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Symbol('x'));
+	}
+
+	#[test]
+	fn product_of_one_with_symbol_reduces() {
+		let input = Expression::product(
+			Expression::Integer(1),
+			Expression::Symbol('x'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Symbol('x'));
+	}
+
+	#[test]
+	fn product_of_two_with_symbol_is_unchanged() {
+		let input = Expression::product(
+			Expression::Integer(2),
+			Expression::Symbol('x'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::product(
+			Expression::Integer(2),
+			Expression::Symbol('x')));
+	}
+
+	#[test]
+	fn nested_product_with_one_is_reduced() {
+		let input = Expression::product(
+			Expression::product(
+				Expression::Symbol('x'),
+				Expression::Integer(1)),
+			Expression::Symbol('y'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(
+			result,
+			Expression::product(
+				Expression::Symbol('x'),
+				Expression::Symbol('y')));
+	}
+
+	#[test]
+	fn exponent_of_symbol_with_zero_becomes_one() {
+		let input = Expression::exponent(
+			Expression::Symbol('x'),
+			Expression::Integer(0));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Integer(1));
+	}
+
+	#[test]
+	fn exponent_of_zero_with_symbol_becomes_zero() {
+		let input = Expression::exponent(
+			Expression::Integer(0),
+			Expression::Symbol('x'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Integer(0));
+	}
+
+	#[test]
+	fn exponent_of_symbol_with_one_reduces() {
+		let input = Expression::exponent(
+			Expression::Symbol('x'),
+			Expression::Integer(1));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Symbol('x'));
+	}
+
+	#[test]
+	fn exponent_of_one_with_symbol_becomes_one() {
+		let input = Expression::exponent(
+			Expression::Integer(1),
+			Expression::Symbol('x'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::Integer(1));
+	}
+
+	#[test]
+	fn exponent_of_symbol_with_two_is_unchanged() {
+		let input = Expression::exponent(
+			Expression::Symbol('x'),
+			Expression::Integer(2));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(result, Expression::exponent(
+			Expression::Symbol('x'),
+			Expression::Integer(2)));
+	}
+
+	#[test]
+	fn nested_exponent_with_one_is_reduced() {
+		let input = Expression::exponent(
+			Expression::exponent(
+				Expression::Symbol('x'),
+				Expression::Integer(1)),
+			Expression::Symbol('y'));
+		let result = Simplifier::new().eval(input).unwrap();
+		assert_eq!(
+			result,
+			Expression::exponent(
+				Expression::Symbol('x'),
+				Expression::Symbol('y')));
+	}
+}