fixed it!

src/factorization.rs

@@ -0,0 +1,256 @@
+use core::fmt;
+use std::{cmp::Ordering, fmt::Display};
+use crate::language::{EquationLanguage, Rational, RATIONAL_ONE, RATIONAL_ZERO};
+use egg::{Id, RecExpr};
+
+
+#[derive(Debug,Clone,Copy)]
+pub struct PolyStat {
+	degree: usize,
+	factors: usize, // non-constant factors
+	ops: usize,
+	monomial: bool,
+	sum_of_monomials: bool,
+	monic: bool,
+	factorized: bool, // a product of monic polynomials and at least one constant
+}
+
+#[derive(Debug,Clone,Copy)]
+pub enum FactorizationCost {
+	UnwantedOps,
+	Polynomial(PolyStat)
+}
+
+fn score(cost: FactorizationCost) -> usize {
+	match cost {
+		FactorizationCost::UnwantedOps => 10000,
+		FactorizationCost::Polynomial(p) =>
+			if !p.factorized {
+				1000 + p.ops
+			} else {
+				100 * (9 - p.factors) + p.ops
+			},
+	}
+}
+
+impl PartialEq for FactorizationCost {
+	fn eq(&self, other: &Self) -> bool {
+		score(*self) == score(*other)
+	}
+}
+
+impl PartialOrd for FactorizationCost {
+	fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+		usize::partial_cmp(&score(*self), &score(*other))
+	}
+}
+
+pub struct FactorizationCostFn;
+impl egg::CostFunction<EquationLanguage> for FactorizationCostFn {
+	type Cost = FactorizationCost;
+
+	fn cost<C>(&mut self, enode: &EquationLanguage, mut costs: C) -> Self::Cost
+	where
+		C: FnMut(Id) -> Self::Cost,
+	{
+		match enode {
+			EquationLanguage::Add([a,b]) => {
+				match (costs(*a), costs(*b)) {
+					(FactorizationCost::Polynomial(p1),FactorizationCost::Polynomial(p2)) => {
+						// we only ever want to add monomials
+						let result_monic = if p1.degree > p2.degree {
+							p1.monic
+						} else if p2.degree > p1.degree {
+							p2.monic
+						} else {
+							false
+						};
+
+						/*
+						if *a == Id::from(4) && *b == Id::from(19) {
+							println!("HERE {:?} {:?}", p1, p2);
+					}
+						*/
+
+
+						if !p1.sum_of_monomials || !p2.sum_of_monomials {
+							FactorizationCost::UnwantedOps
+						} else {
+							FactorizationCost::Polynomial(PolyStat {
+								degree: usize::max(p1.degree, p2.degree),
+								factors: 1,
+								ops: p1.ops + p2.ops + 1,
+								monomial: false,
+								sum_of_monomials: p1.sum_of_monomials && p2.sum_of_monomials,
+								monic: result_monic,
+								factorized: result_monic,
+							})
+						}
+					},
+					_ => FactorizationCost::UnwantedOps
+				}
+			},
+			EquationLanguage::Mul([a,b]) => {
+				match (costs(*a), costs(*b)) {
+					(FactorizationCost::Polynomial(p1), FactorizationCost::Polynomial(p2)) => {
+						FactorizationCost::Polynomial(PolyStat {
+							degree: p1.degree + p2.degree,
+							factors: p1.factors + p2.factors,
+							ops: p1.ops + p2.ops + 1,
+							monomial: p1.monomial && p2.monomial,
+							sum_of_monomials: p1.monomial && p2.monomial,
+							monic: p1.monic && p2.monic,
+							factorized: (p1.monic && p2.factorized) || (p2.monic && p1.factorized)
+						})
+					},
+					_ => FactorizationCost::UnwantedOps
+				}
+			},
+			EquationLanguage::Num(c) => {
+				FactorizationCost::Polynomial(PolyStat {
+					degree: 0,
+					factors: 0,
+					ops: 0,
+					monomial: true,
+					sum_of_monomials: true,
+					monic: false,
+					factorized: true
+				})
+			},
+			EquationLanguage::Unknown => {
+				FactorizationCost::Polynomial(PolyStat {
+					degree: 1,
+					factors: 1,
+					ops: 0,
+					monomial: true,
+					sum_of_monomials: true,
+					monic: true,
+					factorized: true
+				})
+			},
+			_ => FactorizationCost::UnwantedOps,
+		}
+	}
+}
+
+#[derive(Debug,Clone)]
+pub struct Factorization {
+	pub constant_factor: Rational,
+	pub polynomials: Vec<Vec<Rational>>,
+}
+
+impl Display for Factorization {
+	fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+		if self.constant_factor != RATIONAL_ONE {
+			write!(f, "{}", self.constant_factor)?;
+		}
+
+		for poly in &self.polynomials {
+			write!(f, "(")?;
+			for (deg, coeff) in poly.iter().enumerate() {
+				if deg == 0 {
+					write!(f, "{}", coeff)?;
+				} else if deg == 1 {
+					write!(f, " + {}x", coeff)?;
+				} else {
+					write!(f, " + {}x^{}", coeff, deg)?;
+				}
+			}
+			write!(f, ")")?;
+		}
+
+		Ok(())
+	}
+}
+
+pub fn extract_factorization(expr: &RecExpr<EquationLanguage>) -> Factorization {
+	let root_id: Id = Id::from(expr.as_ref().len()-1);
+
+	let mut constant_factor: Option<Rational> = None;
+	let mut factors: Vec<Vec<Rational>> = Vec::new();
+	let mut todo: Vec<Id> = Vec::new();
+	todo.push(root_id);
+
+	while todo.len() > 0 {
+		let id = todo.pop().unwrap();
+
+		match &expr[id] {
+			EquationLanguage::Mul([a,b]) => {
+				todo.push(*a);
+				todo.push(*b);
+			},
+			EquationLanguage::Num(x) => {
+				assert!(constant_factor.is_none());
+				constant_factor = Some(x.clone());
+			},
+			_ => {
+				factors.push(extract_polynomial(expr, id));
+			}
+		}
+	}
+
+	Factorization {
+		constant_factor: constant_factor.unwrap_or_else(||RATIONAL_ONE.clone()),
+		polynomials: factors
+	}
+}
+
+fn extract_polynomial(expr: &RecExpr<EquationLanguage>, id: Id) -> Vec<Rational> {
+	let mut result: Vec<Rational> = Vec::new();
+	let mut todo: Vec<Id> = Vec::new();
+	todo.push(id);
+
+	while todo.len() > 0 {
+		let id = todo.pop().unwrap();
+
+		match &expr[id] {
+			EquationLanguage::Add([a,b]) => {
+				todo.push(*a);
+				todo.push(*b);
+			},
+			_ => {
+				let (deg, coeff) = extract_monomial(expr, id);
+				result.resize(result.len().max(deg), RATIONAL_ZERO.clone());
+
+				if result.len() <= deg {
+					result.push(coeff);
+				} else {
+					assert!(result[deg] == RATIONAL_ZERO);
+					result[deg] = coeff;
+				}
+			}
+		}
+	}
+
+	result
+}
+
+fn extract_monomial(expr: &RecExpr<EquationLanguage>, id: Id) -> (usize, Rational) {
+	let mut coeff: Option<Rational> = None;
+	let mut deg: usize = 0;
+	let mut todo: Vec<Id> = Vec::new();
+	todo.push(id);
+
+	while todo.len() > 0 {
+		let id = todo.pop().unwrap();
+
+		match &expr[id] {
+			EquationLanguage::Unknown => {
+				deg += 1;
+			},
+			EquationLanguage::Mul([a,b]) => {
+				todo.push(*a);
+				todo.push(*b);
+			},
+			EquationLanguage::Num(x) => {
+				assert!(coeff.is_none());
+				coeff = Some(x.clone());
+			},
+			_ => {
+				panic!("Not a rational polynomial in normal form!");
+			}
+		}
+	}
+
+	(deg, coeff.unwrap_or_else(||RATIONAL_ONE.clone()))
+}

src/language.rs

@@ -167,6 +167,13 @@ fn is_nonzero_const(var: &str) -> impl Fn(&mut EGraph, Id, &Subst) -> bool {
 	}
 }
 
+fn is_const(var: &str) -> impl Fn(&mut EGraph, Id, &Subst) -> bool {
+	let var: Var = var.parse().unwrap();
+	move |egraph, _, subst| {
+		egraph[subst[var]].data.is_some()
+	}
+}
+
 pub static RULES: LazyLock<Vec<Rewrite>> = LazyLock::new(||vec![
 	rw!("commute-add"; "(+ ?x ?y)" => "(+ ?y ?x)"),
 	rw!("commute-mul"; "(* ?x ?y)" => "(* ?y ?x)"),
@@ -187,10 +194,6 @@ pub static RULES: LazyLock<Vec<Rewrite>> = LazyLock::new(||vec![
 
 	rw!("square"; "(^ ?x 2)" => "(* ?x ?x)"),
 	rw!("cube"; "(^ ?x 3)" => "(* ?x (* ?x ?x))"),
-	/*
-	rw!("inv-square"; "(* ?x ?x)" => "(^ ?x 2)"),
-	rw!("inv-cube"; "(* ?x (* ?x ?x))" => "(^ ?x 3)"),
-	 */
 
 	rw!("sub"; "(- ?x ?y)" => "(+ ?x (* -1 ?y))"),
 	rw!("neg"; "(- ?x)" => "(* -1 ?x)"),
@@ -198,6 +201,8 @@ pub static RULES: LazyLock<Vec<Rewrite>> = LazyLock::new(||vec![
 	rw!("div"; "(/ ?x ?y)" => "(* ?x (rec ?y))" if is_nonzero_const("?y")),
 
 	rw!("factor_poly"; "(+ (* x ?x) ?y)" => "(* ?x (+ x (* ?y (rec ?x))))" if is_nonzero_const("?x")),
+
+//	rw!("integer_sqrt"; "(^ ?x (1/2))" => {} if is_const("?x")),
 ]);
 
 pub struct PlusTimesCostFn;
@@ -218,125 +223,3 @@ impl egg::CostFunction<EquationLanguage> for PlusTimesCostFn {
         enode.fold(op_cost, |sum, i| sum + costs(i))
     }
 }
-
-#[derive(Debug,Clone,Copy)]
-pub struct PolyStat {
-	degree: usize,
-	factors: usize, // non-constant factors
-	ops: usize,
-	monomial: bool,
-	sum_of_monomials: bool,
-	monic: bool,
-	factorized: bool, // a product of monic polynomials and at least one constant
-}
-
-#[derive(Debug,Clone,Copy)]
-pub enum FactorizationCost {
-	UnwantedOps,
-	Polynomial(PolyStat)
-}
-
-fn score(cost: FactorizationCost) -> usize {
-	match cost {
-		FactorizationCost::UnwantedOps => 10000,
-		FactorizationCost::Polynomial(p) =>
-			if !p.factorized {
-				1000
-			} else {
-				100 * (9 - p.factors) + p.ops
-			},
-	}
-}
-
-impl PartialEq for FactorizationCost {
-	fn eq(&self, other: &Self) -> bool {
-		score(*self) == score(*other)
-	}
-}
-
-impl PartialOrd for FactorizationCost {
-	fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-		usize::partial_cmp(&score(*self), &score(*other))
-	}
-}
-
-pub struct FactorizationCostFn;
-impl egg::CostFunction<EquationLanguage> for FactorizationCostFn {
-	type Cost = FactorizationCost;
-
-	fn cost<C>(&mut self, enode: &EquationLanguage, mut costs: C) -> Self::Cost
-	where
-		C: FnMut(Id) -> Self::Cost,
-	{
-		match enode {
-			EquationLanguage::Add([a,b]) => {
-				match (costs(*a), costs(*b)) {
-					(FactorizationCost::Polynomial(p1),FactorizationCost::Polynomial(p2)) => {
-						// we only ever want to add monomials
-						let result_monic = if p1.degree > p2.degree {
-							p1.monic
-						} else if p2.degree > p1.degree {
-							p2.monic
-						} else {
-							false
-						};
-
-						if !p1.sum_of_monomials || !p2.sum_of_monomials {
-							FactorizationCost::UnwantedOps
-						} else {
-							FactorizationCost::Polynomial(PolyStat {
-								degree: usize::max(p1.degree, p2.degree),
-								factors: 1,
-								ops: p1.ops + p2.ops,
-								monomial: false,
-								sum_of_monomials: p1.sum_of_monomials && p2.sum_of_monomials,
-								monic: result_monic,
-								factorized: result_monic,
-							})
-						}
-					},
-					_ => FactorizationCost::UnwantedOps
-				}
-			},
-			EquationLanguage::Mul([a,b]) => {
-				match (costs(*a), costs(*b)) {
-					(FactorizationCost::Polynomial(p1), FactorizationCost::Polynomial(p2)) => {
-						FactorizationCost::Polynomial(PolyStat {
-							degree: p1.degree + p2.degree,
-							factors: p1.factors + p2.factors,
-							ops: p1.ops + p2.ops,
-							monomial: p1.monomial && p2.monomial,
-							sum_of_monomials: p1.monomial && p2.monomial,
-							monic: p1.monic && p2.monic,
-							factorized: (p1.monic && p2.factorized) || (p2.monic && p1.factorized)
-						})
-					},
-					_ => FactorizationCost::UnwantedOps
-				}
-			},
-			EquationLanguage::Num(c) => {
-				FactorizationCost::Polynomial(PolyStat {
-					degree: 0,
-					factors: 0,
-					ops: 0,
-					monomial: true,
-					sum_of_monomials: true,
-					monic: false,
-					factorized: true
-				})
-			},
-			EquationLanguage::Unknown => {
-				FactorizationCost::Polynomial(PolyStat {
-					degree: 1,
-					factors: 1,
-					ops: 0,
-					monomial: true,
-					sum_of_monomials: true,
-					monic: true,
-					factorized: true
-				})
-			},
-			_ => FactorizationCost::UnwantedOps,
-		}
-	}
-}

src/lib.rs

@@ -1,3 +1,5 @@
 pub mod language;
 pub mod normal_form;
 pub mod parse;
+pub mod factorization;
+pub mod output;

src/main.rs

@@ -1,24 +1,36 @@
-use egg::{Extractor, Pattern, RecExpr, Runner};
-use solveq::language::{RULES, EquationLanguage, PlusTimesCostFn, FactorizationCostFn};
-use solveq::normal_form::analyze3;
+use egg::{AstSize, Extractor, Id, Pattern, PatternAst, RecExpr, Runner, Searcher};
+use solveq::factorization::{FactorizationCost, FactorizationCostFn};
+use solveq::language::{ConstantFold, EquationLanguage, Rational, RULES, EGraph};
+use solveq::normal_form::extract_normal_form;
 use solveq::parse::parse_equation;
+use solveq::output::print_term;
 
 static TEST_EQUATIONS: &[&str] = &[
-	"(x + 50) * 10 - 150 - 100",
-	"(x - 2) * (x + 2) - 0",
-	"x ^ 2 - 4",
-	"x ^ 2 - 2 - 0",
-	"x ^ 2 - (2 * x + 15)",
-	"(x ^ 2 - 2 * x - 15) * (x + 5) - 0",
-	"x ^ 3 + 3 * x ^ 2 - 25 * x - 75 - 0",
+	"(x + 50) * 10 - 150 = 100",
+	"(x - 2) * (x + 2) = 0",
+	"x ^ 2 = 4",
+	"x ^ 2 - 2 = 0",
+	"x ^ 2 = 2 * x + 15",
+	"(x ^ 2 - 2 * x - 15) * (x + 5) = 0",
+	"x ^ 3 + 3 * x ^ 2 - 25 * x - 75 = 0",
 ];
 
-fn main() {
-	for eq in TEST_EQUATIONS {
-		let start = parse_equation(*eq).unwrap();
 
-	//	println!("{:?}", &start);
-	// do transformation to left - right = 0
+fn main() {
+	//	let expr: RecExpr<EquationLanguage> = "(+ (* x (+ x -2)) -15)".parse().unwrap();
+//	let expr: RecExpr<EquationLanguage> = "(* (+ (* x (+ x -2)) -15) (+ x 5))".parse().unwrap();
+//	println!("{:?}", get_expression_cost(&expr));
+
+	for eq in TEST_EQUATIONS {
+		println!("Equation: {}", *eq);
+
+		let mut start = parse_equation(*eq).unwrap();
+		let root_id = Id::from(start.as_ref().len()-1);
+		let EquationLanguage::Equals([left, right]) = start[root_id]
+		else { panic!("Not an equation without an equals sign!"); };
+		start[root_id] = EquationLanguage::Sub([left, right]);
+
+		println!("Parsed: {}", &start);
 
 		let mut runner = Runner::default()
 			.with_explanations_enabled()
@@ -29,198 +41,68 @@ fn main() {
 
 		let (best_cost, best_expr) = extractor.find_best(runner.roots[0]);
 
-		println!("{}", start);
-		println!("{:?} {:?}", best_cost, <RecExpr<EquationLanguage> as AsRef<[EquationLanguage]>>::as_ref(&best_expr));
+//		println!("Best expresssion: {} {:?}", best_expr, best_cost);
+//		println!("{}", runner.explain_equivalence(&start, &best_expr).get_flat_string());
+
+		let Some(factorization) = extract_normal_form(&runner.egraph, runner.roots[0]) else {
+			panic!("Couldn't factorize polynomial!");
+		};
+		println!("Factorized normal form: {}", factorization);
+
+		/*
+		get_expression_cost("(* x (+ x -2))", &runner.egraph);
+		get_expression_cost("-15", &runner.egraph);
+		get_expression_cost("(+ (* x (+ x -2)) -15)", &runner.egraph);
+		*/
+
+//		let factorization = extract_factorization(&best_expr);
 
 
-		println!("");
-	}
+		let mut solutions: Vec<String> = Vec::new();
+		for poly in &factorization.polynomials {
+			if poly.len() == 2 { // linear factor
+				let Rational { num, denom } = &poly[0];
+				solutions.push(format!("x = {}", Rational { num: -*num, denom: *denom }));
+			} else if poly.len() == 3 { // quadratic factor
+				let Rational { num: num0, denom: denom0 } = &poly[0];
+				let Rational { num: num1, denom: denom1 } = &poly[1];
 
-//	let root = runner.roots[0];
-//		let egraph = &runner.egraph;
-//	let pattern: Pattern<EquationLanguage> = "(+ (* ?a (* x x)) ?c)".parse().unwrap();
-//	let matches = pattern.search(&egraph);
+				let sol1 = format!("- ({num1})/(2 * ({denom1})) + ((({num1})/(2 * ({denom1}))) ^ 2 - ({num0}) / ({denom0})) ^ (1/2)");
+				let sol2 = format!("- ({num1})/(2 * ({denom1})) - ((({num1})/(2 * ({denom1}))) ^ 2 - ({num0}) / ({denom0})) ^ (1/2)");
 
+				let expr = parse_equation(&sol1).unwrap();
+				let runner = Runner::default()
+					.with_expr(&expr)
+					.run(&*RULES);
+				let extractor = Extractor::new(&runner.egraph, AstSize);
+				let (_, simplified_expr) = extractor.find_best(runner.roots[0]);
+				solutions.push(format!("x = {}", print_term(&simplified_expr)));
 
-
-//	println!("{:?}", egraph.classes().count());
-
-	// Analyze
-//	analyze3(egraph, runner.roots[0]);
-
-	/*
-	for class in egraph.classes() {
-		if monic_nonconst_polynomial(egraph, class.id).is_some() {
-			let (_, best_expr) = extractor.find_best(class.id);
-			println!("Monomial: {}", best_expr);
-		}
-	}
-
-	println!("{:?}", &matches);
-	*/
-
-
-//	println!("{}", runner.explain_equivalence(&start, &best_expr).get_flat_string());
-}
-
-
-/*
-fn power_of_x(egraph: &EGraph, eclass: Id) -> Option<usize> {
-	for n in &egraph[eclass].nodes {
-		match *n {
-			EquationLanguage::Unknown => { return Some(1) },
-			EquationLanguage::Mul([a,b]) => {
-				let Some(left) = power_of_x(egraph, a) else { continue };
-				let Some(right) = power_of_x(egraph, b) else { continue };
-				return Some(left + right);
-			},
-			_ => {}
-		}
-	}
-	None
-}
-
-fn monomial(egraph: &EGraph, eclass: Id) -> Option<(usize, Rational)> {
-	if let Some(deg) = power_of_x(egraph, eclass) {
-		return Some((deg, RATIONAL_ONE.clone()));
-	}
-
-	for n in &egraph[eclass].nodes {
-		match *n {
-			EquationLanguage::Mul([a,b]) => {
-				let Some(coeff) = egraph[a].data.clone() else { continue };
-				let Some(deg) = power_of_x(egraph, b) else { continue };
-				return Some((deg, coeff));
-			},
-			_ => {}
-		}
-	}
-	None
-}
-
-
-// this is either a power_of_x, or a sum of this and a monomial
-fn monic_nonconst_polynomial(egraph: &EGraph, eclass: Id) -> Option<Vec<Rational>> {
-	let mut result: Vec<Rational> = Vec::new();
-
-	if let Some(deg) = power_of_x(egraph, eclass) {
-		result.resize(deg - 1, RATIONAL_ZERO);
-		result.push(RATIONAL_ONE.clone());
-		return Some(result);
-	}
-
-	for n in &egraph[eclass].nodes {
-		match *n {
-			EquationLanguage::Add([a,b]) => {
-				let Some(mut leading) = monic_nonconst_polynomial(egraph, a)
-				else { continue };
-				let Some(addon) = monomial(egraph, b)
-				else { continue };
-
-				if leading.len() <= addon.0 || leading[addon.0] != RATIONAL_ZERO {
-					continue;
-				}
-
-				leading[addon.0] = addon.1.clone();
-				return Some(leading);
-			},
-			_ => {},
-		}
-	}
-	None
-}
-
-*/
-
-
-/*
-fn analyze(egraph: &EGraph, _id: Id) {
-	let mut types: HashMap<Id, SpecialTerm> = HashMap::new();
-	let mut todo: VecDeque<Id> = VecDeque::new();
-	//	todo.push_back(runner.roots[0]);
-	for cls in egraph.classes() {
-		todo.push_back(cls.id);
-	}
-
-	'todo: while todo.len() > 0 {
-		let id = todo.pop_front().unwrap();
-		if types.contains_key(&id) {
-			continue 'todo;
-		}
-
-		if let Some(c) = &egraph[id].data {
-			types.insert(id, SpecialTerm::Constant(c.clone()));
-			continue 'todo;
-		}
-
-		'nodes: for n in &egraph[id].nodes {
-			match *n {
-				EquationLanguage::Unknown => {
-					types.insert(id, SpecialTerm::PowerOfX(1));
-					continue 'todo;
-				},
-				EquationLanguage::Mul([a,b]) => {
-					if !types.contains_key(&a) {
-						todo.push_back(a);
-						todo.push_back(id);
-						continue 'nodes;
-					}
-
-					if !types.contains_key(&b) {
-						todo.push_back(b);
-						todo.push_back(id);
-						continue 'nodes;
-					}
-
-					match (&types[&a], &types[&b]) {
-						(SpecialTerm::PowerOfX(dega), SpecialTerm::PowerOfX(degb)) => {
-							types.insert(id, SpecialTerm::PowerOfX(*dega + *degb));
-						},
-						(SpecialTerm::Constant(coeff), SpecialTerm::PowerOfX(deg)) => {
-							types.insert(id, SpecialTerm::Monomial(*deg, coeff.clone()));
-						},
-						_ => { continue 'nodes; },
-					}
-					continue 'todo;
-				},
-				EquationLanguage::Add([a,b]) => {
-					if !types.contains_key(&a) {
-						todo.push_front(a);
-						todo.push_back(id);
-						continue 'todo;
-					}
-
-					if !types.contains_key(&b) {
-						todo.push_front(b);
-						todo.push_back(id);
-						continue 'todo;
-					}
-
-					match (&types[&a], &types[&b]) {
-						(SpecialTerm::MonicNonconstPoly(poly), SpecialTerm::Monomial(deg, coeff)) => {
-							if poly.len() <= *deg || poly[*deg] != RATIONAL_ZERO {
-								continue 'nodes;
-							}
-
-							let mut poly = poly.clone();
-							poly[*deg] = coeff.clone();
-							types.insert(id, SpecialTerm::MonicNonconstPoly(poly));
-						},
-						_ => { continue 'nodes; },
-					}
-					continue 'todo;
-				},
-				_ => {},
+				let expr = parse_equation(&sol2).unwrap();
+				let runner = Runner::default()
+					.with_expr(&expr)
+					.run(&*RULES);
+				let extractor = Extractor::new(&runner.egraph, AstSize);
+				let (_, simplified_expr) = extractor.find_best(runner.roots[0]);
+				solutions.push(format!("x = {}", print_term(&simplified_expr)));
 			}
 		}
 
-		types.insert(id, SpecialTerm::Other);
-	}
-
-	for (id, ty) in &types {
-		if !matches!(ty, &SpecialTerm::Other) {
-			println!("{:?}", &ty);
-		}
+		println!("Solutions: {{ {} }}", solutions.join(", "));
+		println!("");
 	}
 }
-*/
+
+fn get_expression_cost(expr: &str, egraph: &EGraph) {
+//    let mut egraph = EGraph::new(ConstantFold::default());
+	//    let id = egraph.add_expr(expr);
+	let pattern: Pattern<EquationLanguage> = expr.parse().unwrap();
+	let matches = pattern.search(egraph);
+	for m in matches {
+		let extractor = Extractor::new(&egraph, FactorizationCostFn);
+		let (cost, _) = extractor.find_best(m.eclass);
+
+		println!("expr: {}, id: {}, cost: {:?}", expr, m.eclass, cost);
+	}
+//    cost
+}

src/normal_form.rs

@@ -1,6 +1,6 @@
 use crate::language::{EGraph, EquationLanguage, Rational, RATIONAL_ONE, RATIONAL_ZERO};
-use std::collections::HashMap;
-use egg::Id;
+use std::{collections::HashMap, fmt};
+use egg::{AstSize, Extractor, Id};
 
 #[derive(Debug,Clone)]
 pub enum SpecialTerm {
@@ -12,36 +12,281 @@ pub enum SpecialTerm {
 	Other,
 }
 
-fn search_for<F, T>(egraph: &EGraph, f: F) -> HashMap<Id, T>
+#[derive(Debug,Clone)]
+pub struct Factorization {
+	pub constant_factor: Rational,
+	pub polynomials: Vec<Vec<Rational>>,
+}
+
+// this is a property of an eclass, not a particular expression
+#[derive(Debug,Clone)]
+struct PolyStats {
+	degree: usize,
+	monomial: bool,
+	monic: bool,
+}
+
+fn gather_poly_stats(egraph: &EGraph) -> HashMap<Id, PolyStats> {
+	walk_egraph(egraph, |_id, node, stats: &HashMap<Id, PolyStats>| {
+		let x = |i: &Id| stats.get(&egraph.find(*i));
+		Some(match node {
+			EquationLanguage::Unknown => PolyStats {
+				degree: 1,
+				monomial: true,
+				monic: true,
+			},
+			EquationLanguage::Num(c) => PolyStats {
+				degree: 0,
+				monomial: true,
+				monic: c == &RATIONAL_ONE,
+			},
+			EquationLanguage::Mul([a,b]) => {
+				// if both aren't monic we can't tell, the leading coefficients could cancel
+				// but there should be an alternative representative with one of them monic
+				if !x(a)?.monic && !x(b)?.monic {
+					return None;
+				}
+
+				PolyStats {
+					degree: x(a)?.degree + x(b)?.degree,
+					monomial: x(a)?.monomial && x(b)?.monomial,
+					monic: x(a)?.monic && x(b)?.monic,
+				}
+			},
+			EquationLanguage::Add([a,b]) => {
+				// in this case, there should also be a simplified representative which
+				// has only a single leading term
+				if x(a)?.degree == x(b)?.degree {
+					return None;
+				}
+
+				PolyStats {
+					degree: usize::max(x(a)?.degree, x(b)?.degree),
+					monomial: false,
+					monic: if x(a)?.degree > x(b)?.degree { x(a)?.monic } else { x(b)?.monic },
+				}
+			},
+			_ => { return None; }
+		})
+	})
+}
+
+pub fn extract_normal_form(egraph: &EGraph, eclass: Id) -> Option<Factorization> {
+	let eclass = egraph.find(eclass); // get the canonical eclass
+
+	let stats = gather_poly_stats(egraph);
+
+	let Some(factorization) = find_general_factorization(egraph, &stats, eclass) else { return None; };
+
+	let mut result = Vec::new();
+	let mut coeff: Option<Rational> = None;
+
+	for factor in factorization {
+		let extracted = extract_polynomial(egraph, &stats, factor)?;
+//		println!("Extracted: {:?}", extracted);
+
+		if extracted.len() == 1 {
+			coeff = Some(extracted[0].clone());
+		} else {
+			result.push(extracted);
+		}
+	}
+
+	Some(Factorization {
+		constant_factor: coeff.unwrap_or_else(||RATIONAL_ONE.clone()),
+		polynomials: result
+	})
+}
+
+// a polynomial should be either of:
+// - a monomial: then we know the degree and we try to parse it as a product of a constant and a monic monomial
+//               or just a constant
+// - a sum of a monomial of highest degree, and a polynomial of lower degree, recursively walk these
+fn extract_polynomial(egraph: &EGraph, stats: &HashMap<Id, PolyStats>, id: Id) -> Option<Vec<Rational>> {
+	let st = &stats[&id];
+
+	if st.monomial {
+		let (deg, coeff) = extract_monomial(egraph, stats, id)?;
+
+		let mut result = vec![RATIONAL_ZERO; deg];
+		result.push(coeff);
+		return Some(result);
+	} else {
+		for node in &egraph[id].nodes {
+			match node {
+				EquationLanguage::Add([a,b]) => {
+					let a = egraph.find(*a);
+					let b = egraph.find(*b);
+					let Some(stata) = &stats.get(&a) else { continue };
+					let Some(statb) = &stats.get(&b) else { continue };
+
+					if stata.degree == st.degree && stata.monomial && statb.degree < st.degree {
+						let (leading_deg, leading_coeff) = extract_monomial(egraph, stats, a)?;
+						let mut remainder = extract_polynomial(egraph, stats, b)?;
+
+						assert!(leading_deg >= remainder.len());
+
+						remainder.resize(leading_deg, RATIONAL_ZERO.clone());
+						remainder.push(leading_coeff);
+						return Some(remainder);
+					}
+				},
+				_ => {}
+			}
+		}
+	}
+
+	None
+}
+
+// a monomial is either a power of x, a constant, or a product of a constant and power of x
+fn extract_monomial(egraph: &EGraph, stats: &HashMap<Id, PolyStats>, id: Id) -> Option<(usize, Rational)> {
+	let extractor = Extractor::new(egraph, AstSize);
+	let (_, expr) = extractor.find_best(id);
+//	println!("Extract Monomial: {}", expr);
+
+	let st = &stats[&id];
+
+	assert!(st.monomial);
+
+	// monic + monomial = power of x
+	if st.monic {
+		return Some((st.degree, RATIONAL_ONE.clone()));
+	}
+
+	for node in &egraph[id].nodes {
+		match node {
+			EquationLanguage::Mul([a,b]) => {
+				let a = egraph.find(*a);
+				let b = egraph.find(*b);
+				let Some(statb) = stats.get(&b) else { continue };
+
+				// a should be a constant
+				let Some(coeff) = egraph[a].data.clone() else { continue };
+
+				// b should be monic and nonconstant (hence a power of x)
+				if statb.degree == 0 || !statb.monic {
+					continue;
+				}
+
+				assert_eq!(st.degree, statb.degree);
+
+				return Some((st.degree, coeff));
+			},
+			EquationLanguage::Num(c) => { // a constant is also a monomial
+				return Some((0, c.clone()));
+			},
+			_ => {},
+		}
+	}
+
+	None
+}
+
+// like find_monic_factorization, but with the option of having a constant factor
+fn find_general_factorization(egraph: &EGraph, stats: &HashMap<Id, PolyStats>, id: Id) -> Option<Vec<Id>> {
+	let st = stats.get(&id)?;
+
+	if st.monic {
+		return find_monic_factorization(egraph, stats, id);
+	} else {
+		for node in &egraph[id].nodes {
+			match node {
+				EquationLanguage::Mul([a,b]) => {
+					let a = egraph.find(*a);
+					let b = egraph.find(*b);
+					let Some(stata) = stats.get(&a) else { continue };
+					let Some(statb) = stats.get(&b) else { continue };
+
+					// a is constant, b is monic and nonconstant
+					if stata.degree == 0 && statb.degree > 0 && statb.monic {
+						let mut fac = find_monic_factorization(egraph, stats, b)?;
+						fac.push(a);
+						return Some(fac);
+					}
+				},
+				_ => {}
+			}
+		}
+	}
+	None
+}
+
+// this assumes `id` to be canonical
+fn find_monic_factorization(egraph: &EGraph, stats: &HashMap<Id, PolyStats>, id: Id) -> Option<Vec<Id>> {
+	// we want the polynomial to be nonconstant and monic
+	if ! stats.get(&id).is_some_and(|x|x.monic && x.degree > 0) {
+		return None;
+	}
+
+	// now the whole thing is a monic nonconst poly, so would be a valid factorization,
+	// but we want to go as deep as possible
+//	println!("{:?}", stats[&id]);
+
+	// check if it is the product of two nonconstant monic polynomials
+	for node in &egraph[id].nodes {
+		match node {
+			EquationLanguage::Mul([a,b]) => {
+				let a = egraph.find(*a);
+				let b = egraph.find(*b);
+				let Some(stata) = stats.get(&a) else { continue };
+				let Some(statb) = stats.get(&b) else { continue };
+
+				if stata.degree == 0 || statb.degree == 0 || !stata.monic || !statb.monic {
+					continue;
+				}
+
+//				println!("stats = {:?}, stats a = {:?}, stats b = {:?}", stats[&id], stata, statb);
+
+				let Some(mut faca) = find_monic_factorization(egraph, stats, a) else { continue };
+				let Some(facb) = find_monic_factorization(egraph, stats, b) else { continue };
+
+				faca.extend_from_slice(&facb);
+				return Some(faca);
+			},
+			_ => {}
+		}
+	}
+
+	// at this point we know the current polynomial is monic, but we didn't find a further factorization
+	// so just return it as a single factor
+	Some(vec![id])
+}
+
+fn walk_egraph<F, T>(egraph: &EGraph, f: F) -> HashMap<Id, T>
 where
 	F: Fn(Id, &EquationLanguage, &HashMap<Id, T>) -> Option<T> {
 
 	let mut result: HashMap<Id, T> = HashMap::new();
 	let mut modifications: usize = 1;
 
+//	println!("{:?}", egraph[canonical]);
+
 	while modifications > 0 {
 		modifications = 0;
 
-		for cls in egraph.classes() {
+		'next_class: for cls in egraph.classes() {
 			let id = cls.id;
 			if result.contains_key(&id) {
-				continue;
+				continue 'next_class;
 			}
 
 			for node in &cls.nodes {
 				if let Some(x) = f(id, node, &result) {
 					result.insert(id, x);
 					modifications += 1;
+					continue 'next_class;
 				}
 			}
 		}
 
-		println!("{} modifications!", modifications);
+//		println!("{} modifications!", modifications);
 	}
 
 	result
 }
 
+/*
 pub fn analyze3(egraph: &EGraph, eclass: Id) {
 	let constants = search_for(egraph, |id, _, _|
 		egraph[id].data.as_ref().map(|c|c.clone())
@@ -227,3 +472,28 @@ pub fn analyze2(egraph: &EGraph) -> HashMap<Id, SpecialTerm> {
 
 	types
 }
+*/
+
+impl fmt::Display for Factorization {
+	fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+		if self.constant_factor != RATIONAL_ONE {
+			write!(f, "{}", self.constant_factor)?;
+		}
+
+		for poly in &self.polynomials {
+			write!(f, "(")?;
+			for (deg, coeff) in poly.iter().enumerate() {
+				if deg == 0 {
+					write!(f, "{}", coeff)?;
+				} else if deg == 1 {
+					write!(f, " + {}x", coeff)?;
+				} else {
+					write!(f, " + {}x^{}", coeff, deg)?;
+				}
+			}
+			write!(f, ")")?;
+		}
+
+		Ok(())
+	}
+}

src/output.rs

@@ -0,0 +1,66 @@
+use egg::{RecExpr, Id};
+use crate::language::EquationLanguage;
+
+// there is already a Display implementation generated by define_langauge!
+// but we want an alternative string conversion
+pub fn print_term(expr: &RecExpr<EquationLanguage>) -> String {
+	let root_id = Id::from(expr.as_ref().len()-1);
+	print_term_inner(expr, root_id).0
+}
+
+// the second result is the precedence of the top level op: 1 = '+-', 2 = '*/', 3 = '^', 4 = primitive
+fn print_term_inner(expr: &RecExpr<EquationLanguage>, id: Id) -> (String, usize) {
+	match &expr[id] {
+		EquationLanguage::Num(c) => {
+			(format!("{}", c), if c.denom == 1 { 4 } else { 2 })
+		},
+		EquationLanguage::Neg([a]) => {
+			(print_unary(expr, *a, "-", 1), 1)
+		},
+		EquationLanguage::Add([a,b]) => {
+			(print_binary(expr, *a, *b, "+", 1), 1)
+		},
+		EquationLanguage::Sub([a,b]) => {
+			(print_binary(expr, *a, *b, "-", 1), 1)
+		},
+		EquationLanguage::Mul([a,b]) => {
+			(print_binary(expr, *a, *b, "*", 2), 2)
+		},
+		EquationLanguage::Div([a,b]) => {
+			(print_binary(expr, *a, *b, "/", 2), 2)
+		},
+		EquationLanguage::Power([a,b]) => {
+			(print_binary(expr, *a, *b, "^", 3), 3)
+		},
+		_ => unimplemented!()
+	}
+}
+
+fn print_unary(expr: &RecExpr<EquationLanguage>, a: Id, op: &str, precedence: usize) -> String {
+	let (astr, aprec) = print_term_inner(expr, a);
+
+	if aprec > precedence {
+		format!("{}{}", op, astr)
+	} else {
+		format!("{}({})", op, astr)
+	}
+}
+
+fn print_binary(expr: &RecExpr<EquationLanguage>, a: Id, b: Id, op: &str, precedence: usize) -> String {
+	let (astr, aprec) = print_term_inner(expr, a);
+	let (bstr, bprec) = print_term_inner(expr, b);
+
+	if aprec > precedence {
+		if bprec > precedence {
+			format!("{} {} {}", astr, op, bstr)
+		} else {
+			format!("{} {} ({})", astr, op, bstr)
+		}
+	} else {
+		if bprec > precedence {
+			format!("({}) {} {}", astr, op, bstr)
+		} else {
+			format!("({}) {} ({})", astr, op, bstr)
+		}
+	}
+}

src/parse.rs

@@ -26,15 +26,15 @@ fn parse_equation_inner(input: &str, expr: &mut RecExpr<EquationLanguage>) -> Re
 		}
 
 		match c {
-			'^' if precedence > 3 => {
+			'^' if precedence >= 3 => {
 				operator_position = Some(i);
 				precedence = 3;
 			},
-			'*' | '/' if precedence > 2 => {
+			'*' | '/' if precedence >= 2 => {
 				operator_position = Some(i);
 				precedence = 2;
 			},
-			'-' | '+' if precedence > 1 => {
+			'-' | '+' if precedence >= 1 => {
 				operator_position = Some(i);
 				precedence = 1;
 			},