#region License Information /* HeuristicLab * Copyright (C) Heuristic and Evolutionary Algorithms Laboratory (HEAL) * * This file is part of HeuristicLab. * * HeuristicLab is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * HeuristicLab is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with HeuristicLab. If not, see . */ #endregion using System; using System.Globalization; using HeuristicLab.Encodings.SymbolicExpressionTreeEncoding; using Microsoft.VisualStudio.TestTools.UnitTesting; namespace HeuristicLab.Problems.DataAnalysis.Symbolic.Tests { [TestClass()] public class SymbolicDataAnalysisExpressionTreeSimplifierTest { [TestMethod] [TestCategory("Problems.DataAnalysis")] [TestProperty("Time", "short")] public void SimplifierAxiomsTest() { SymbolicExpressionImporter importer = new SymbolicExpressionImporter(); SymbolicExpressionTreeStringFormatter formatter = new SymbolicExpressionTreeStringFormatter(); #region single argument arithmetics AssertEqualAfterSimplification("(+ 1.0)", "1.0"); AssertEqualAfterSimplification("(- 1.0)", "-1.0"); AssertEqualAfterSimplification("(- (variable 2.0 a))", "(variable -2.0 a)"); AssertEqualAfterSimplification("(* 2.0)", "2.0"); AssertEqualAfterSimplification("(* (variable 2.0 a))", "(variable 2.0 a)"); AssertEqualAfterSimplification("(/ 2.0)", "0.5"); AssertEqualAfterSimplification("(/ (variable 2.0 a))", "(/ 1.0 (variable 2.0 a))"); #endregion #region aggregation of constants into factors AssertEqualAfterSimplification("(* 2.0 (variable 2.0 a))", "(variable 4.0 a)"); AssertEqualAfterSimplification("(/ (variable 2.0 a) 2.0)", "(variable 1.0 a)"); AssertEqualAfterSimplification("(/ (variable 2.0 a) (* 2.0 2.0))", "(variable 0.5 a)"); #endregion #region constant and variable folding AssertEqualAfterSimplification("(+ 1.0 2.0)", "3.0"); AssertEqualAfterSimplification("(+ (variable 2.0 a) (variable 2.0 a))", "(variable 4.0 a)"); AssertEqualAfterSimplification("(- (variable 2.0 a) (variable 1.0 a))", "(variable 1.0 a)"); AssertEqualAfterSimplification("(* (variable 2.0 a) (variable 2.0 a))", "(* (* (variable 1.0 a) (variable 1.0 a)) 4.0)"); AssertEqualAfterSimplification("(/ (variable 1.0 a) (variable 2.0 a))", "0.5"); #endregion #region logarithm rules // cancellation AssertEqualAfterSimplification("(log (exp (variable 2.0 a)))", "(variable 2.0 a)"); // must not transform logs in this way as we do not know wether both variables are positive AssertEqualAfterSimplification("(log (* (variable 1.0 a) (variable 1.0 b)))", "(log (* (variable 1.0 a) (variable 1.0 b)))"); // must not transform logs in this way as we do not know wether both variables are positive AssertEqualAfterSimplification("(log (/ (variable 1.0 a) (variable 1.0 b)))", "(log (/ (variable 1.0 a) (variable 1.0 b)))"); #endregion #region exponentiation rules // cancellation AssertEqualAfterSimplification("(exp (log (variable 2.0 a)))", "(variable 2.0 a)"); // exp transformation AssertEqualAfterSimplification("(exp (+ (variable 2.0 a) (variable 3.0 b)))", "(* (exp (variable 2.0 a)) (exp (variable 3.0 b)))"); // exp transformation AssertEqualAfterSimplification("(exp (- (variable 2.0 a) (variable 3.0 b)))", "(* (exp (variable 2.0 a)) (exp (variable -3.0 b)))"); // exp transformation AssertEqualAfterSimplification("(exp (- (variable 2.0 a) (* (variable 3.0 b) (variable 4.0 c))))", "(* (exp (variable 2.0 a)) (exp (* (variable 1.0 b) (variable 1.0 c) -12.0)))"); // exp transformation AssertEqualAfterSimplification("(exp (- (variable 2.0 a) (* (variable 3.0 b) (cos (variable 4.0 c)))))", "(* (exp (variable 2.0 a)) (exp (* (variable 1.0 b) (cos (variable 4.0 c)) -3.0)))"); #endregion #region power rules // cancellation AssertEqualAfterSimplification("(pow (variable 2.0 a) 0.0)", "1.0"); // fixed point AssertEqualAfterSimplification("(pow (variable 2.0 a) 1.0)", "(variable 2.0 a)"); // inversion fixed point AssertEqualAfterSimplification("(pow (variable 2.0 a) -1.0)", "(/ 1.0 (variable 2.0 a))"); // inversion AssertEqualAfterSimplification("(pow (variable 2.0 a) -2.0)", "(/ 1.0 (pow (variable 2.0 a) 2.0))"); // constant folding AssertEqualAfterSimplification("(pow 3.0 2.0)", "9.0"); #endregion #region root rules // cancellation AssertEqualAfterSimplification("(root (variable 2.0 a) 0.0)", "1.0"); // fixed point AssertEqualAfterSimplification("(root (variable 2.0 a) 1.0)", "(variable 2.0 a)"); // inversion fixed point AssertEqualAfterSimplification("(root (variable 2.0 a) -1.0)", "(/ 1.0 (variable 2.0 a))"); // inversion AssertEqualAfterSimplification("(root (variable 2.0 a) -2.0)", "(/ 1.0 (root (variable 2.0 a) 2.0))"); // constant folding AssertEqualAfterSimplification("(root 9.0 2.0)", "3.0"); #endregion #region boolean operations // always true and AssertEqualAfterSimplification("(and 1.0 2.0)", "1.0"); // always false and AssertEqualAfterSimplification("(and 1.0 -2.0)", "-1.0"); // always true or AssertEqualAfterSimplification("(or -1.0 2.0)", "1.0"); // always false or AssertEqualAfterSimplification("(or -1.0 -2.0)", "-1.0"); // constant not AssertEqualAfterSimplification("(not -2.0)", "1.0"); // constant not AssertEqualAfterSimplification("(not 2.0)", "-1.0"); // constant not AssertEqualAfterSimplification("(not 0.0)", "1.0"); // nested nots AssertEqualAfterSimplification("(not (not 1.0))", "1.0"); // not of non-Boolean argument AssertEqualAfterSimplification("(not (variable 1.0 a))", "(not (> (variable 1.0 a) 0.0))"); // not Boolean argument AssertEqualAfterSimplification("(not (and (> (variable 1.0 a) 0.0) (> (variable 1.0 a) 0.0)))", "(not (and (> (variable 1.0 a) 0.0) (> (variable 1.0 a) 0.0)))"); #endregion #region conditionals // always false AssertEqualAfterSimplification("(if -1.0 (variable 2.0 a) (variable 3.0 a))", "(variable 3.0 a)"); // always true AssertEqualAfterSimplification("(if 1.0 (variable 2.0 a) (variable 3.0 a))", "(variable 2.0 a)"); // always false (0.0) AssertEqualAfterSimplification("(if 0.0 (variable 2.0 a) (variable 3.0 a))", "(variable 3.0 a)"); // complex constant condition (always false) AssertEqualAfterSimplification("(if (* 1.0 -2.0) (variable 2.0 a) (variable 3.0 a))", "(variable 3.0 a)"); // complex constant condition (always false) AssertEqualAfterSimplification("(if (/ (variable 1.0 a) (variable -2.0 a)) (variable 2.0 a) (variable 3.0 a))", "(variable 3.0 a)"); // insertion of relational operator AssertEqualAfterSimplification("(if (variable 1.0 a) (variable 2.0 a) (variable 3.0 a))", "(if (> (variable 1.0 a) 0.0) (variable 2.0 a) (variable 3.0 a))"); #endregion #region factor variables AssertEqualAfterSimplification("(factor a 1.0)", "(factor a 1.0)"); // factor folding AssertEqualAfterSimplification("(+ (factor a 1.0 1.0) (factor a 2.0 3.0))", "(factor a 3.0 4.0)"); AssertEqualAfterSimplification("(- (factor a 1.0 1.0) (factor a 2.0 3.0))", "(factor a -1.0 -2.0)"); AssertEqualAfterSimplification("(* (factor a 2.0 2.0) (factor a 2.0 3.0))", "(factor a 4.0 6.0)"); AssertEqualAfterSimplification("(/ (factor a 2.0 5.0))", "(factor a 0.5 0.2)"); AssertEqualAfterSimplification("(/ (factor a 4.0 6.0) (factor a 2.0 3.0))", "(factor a 2.0 2.0)"); AssertEqualAfterSimplification("(+ 3.0 (factor a 4.0 6.0))", "(factor a 7.0 9.0)"); AssertEqualAfterSimplification("(+ (factor a 4.0 6.0) 3.0)", "(factor a 7.0 9.0)"); AssertEqualAfterSimplification("(- 3.0 (factor a 4.0 6.0))", "(factor a -1.0 -3.0)"); AssertEqualAfterSimplification("(- (factor a 4.0 6.0) 3.0)", "(factor a 1.0 3.0)"); AssertEqualAfterSimplification("(* 2.0 (factor a 4.0 6.0))", "(factor a 8.0 12.0)"); AssertEqualAfterSimplification("(* (factor a 4.0 6.0) 2.0)", "(factor a 8.0 12.0)"); AssertEqualAfterSimplification("(* (factor a 4.0 6.0) (variable 2.0 a))", "(* (factor a 8.0 12.0) (variable 1.0 a))"); // not possible (a is used as factor and double variable) interpreter will fail AssertEqualAfterSimplification( "(log (factor a 10.0 100.0))", string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1})", Math.Log(10.0), Math.Log(100.0))); AssertEqualAfterSimplification( "(exp (factor a 2.0 3.0))", string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1})", Math.Exp(2.0), Math.Exp(3.0))); AssertEqualAfterSimplification("(sqrt (factor a 9.0 16.0))", "(factor a 3.0 4.0))"); AssertEqualAfterSimplification("(sqr (factor a 2.0 3.0))", "(factor a 4.0 9.0))"); AssertEqualAfterSimplification("(root (factor a 8.0 27.0) 3)", "(factor a 2.0 3.0))"); AssertEqualAfterSimplification("(pow (factor a 2.0 3.0) 3)", "(factor a 8.0 27.0))"); AssertEqualAfterSimplification("(sin (factor a 1.0 2.0) )", string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1}))", Math.Sin(1.0), Math.Sin(2.0))); AssertEqualAfterSimplification("(cos (factor a 1.0 2.0) )", string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1}))", Math.Cos(1.0), Math.Cos(2.0))); AssertEqualAfterSimplification("(tan (factor a 1.0 2.0) )", string.Format(CultureInfo.InvariantCulture, "(factor a {0} {1}))", Math.Tan(1.0), Math.Tan(2.0))); AssertEqualAfterSimplification("(binfactor a val 1.0)", "(binfactor a val 1.0)"); // binfactor folding AssertEqualAfterSimplification("(+ (binfactor a val 1.0) (binfactor a val 2.0))", "(binfactor a val 3.0)"); AssertEqualAfterSimplification("(+ (binfactor a val0 1.0) (binfactor a val1 2.0))", "(+ (binfactor a val0 1.0) (binfactor a val1 2.0))"); // cannot be simplified (different vals) AssertEqualAfterSimplification("(+ (binfactor a val 1.0) (binfactor b val 2.0))", "(+ (binfactor a val 1.0) (binfactor b val 2.0))"); // cannot be simplified (different vars) AssertEqualAfterSimplification("(- (binfactor a val 1.0) (binfactor a val 2.0))", "(binfactor a val -1.0)"); AssertEqualAfterSimplification("(* (binfactor a val 2.0) (binfactor a val 3.0))", "(binfactor a val 6.0)"); AssertEqualAfterSimplification("(/ (binfactor a val 6.0) (binfactor a val 3.0))", "(/ (binfactor a val 6.0) (binfactor a val 3.0))"); // not allowed! 0/0 for other values than 'val' AssertEqualAfterSimplification("(/ (binfactor a val 4.0))", "(/ 1.0 (binfactor a val 4.0))"); // not allowed! AssertEqualAfterSimplification("(+ 3.0 (binfactor a val 4.0 ))", "(+ (binfactor a val 4.0 ) 3.0))"); // not allowed AssertEqualAfterSimplification("(- 3.0 (binfactor a val 4.0 ))", "(+ (binfactor a val -4.0 ) 3.0)"); AssertEqualAfterSimplification("(+ (binfactor a val 4.0 ) 3.0)", "(+ (binfactor a val 4.0 ) 3.0)"); // not allowed AssertEqualAfterSimplification("(- (binfactor a val 4.0 ) 3.0)", "(+ (binfactor a val 4.0 ) -3.0)"); AssertEqualAfterSimplification("(* 2.0 (binfactor a val 4.0))", "(binfactor a val 8.0 )"); AssertEqualAfterSimplification("(* (binfactor a val 4.0) 2.0)", "(binfactor a val 8.0 )"); AssertEqualAfterSimplification("(* (binfactor a val 4.0) (variable 2.0 a))", "(* (binfactor a val 1.0) (variable 1.0 a) 8.0)"); // not possible (a is used as factor and double variable) interpreter will fail AssertEqualAfterSimplification("(log (binfactor a val 10.0))", "(log (binfactor a val 10.0))"); // not allowed (log(0)) // exp( binfactor w val=a) = if(val=a) exp(w) else exp(0) = binfactor( (exp(w) - 1) val a) + 1 AssertEqualAfterSimplification("(exp (binfactor a val 3.0))", string.Format(CultureInfo.InvariantCulture, "(+ (binfactor a val {0}) 1.0)", Math.Exp(3.0) - 1) ); AssertEqualAfterSimplification("(sqrt (binfactor a val 16.0))", "(binfactor a val 4.0))"); // sqrt(0) = 0 AssertEqualAfterSimplification("(sqr (binfactor a val 3.0))", "(binfactor a val 9.0))"); // 0*0 = 0 AssertEqualAfterSimplification("(root (binfactor a val 27.0) 3)", "(binfactor a val 3.0))"); AssertEqualAfterSimplification("(pow (binfactor a val 3.0) 3)", "(binfactor a val 27.0))"); AssertEqualAfterSimplification("(sin (binfactor a val 2.0) )", string.Format(CultureInfo.InvariantCulture, "(binfactor a val {0}))", Math.Sin(2.0))); // sin(0) = 0 AssertEqualAfterSimplification("(cos (binfactor a val 2.0) )", string.Format(CultureInfo.InvariantCulture, "(+ (binfactor a val {0}) 1.0)", Math.Cos(2.0) - 1)); // cos(0) = 1 AssertEqualAfterSimplification("(tan (binfactor a val 2.0) )", string.Format(CultureInfo.InvariantCulture, "(binfactor a val {0}))", Math.Tan(2.0))); // tan(0) = 0 // combination of factor and binfactor AssertEqualAfterSimplification("(+ (binfactor a x0 2.0) (factor a 2.0 3.0))", "(factor a 4.0 3.0)"); AssertEqualAfterSimplification("(+ (factor a 2.0 3.0) (binfactor a x0 2.0))", "(factor a 4.0 3.0)"); AssertEqualAfterSimplification("(* (binfactor a x1 2.0) (factor a 2.0 3.0))", "(binfactor a x1 6.0)"); // all other values have weight zero in binfactor AssertEqualAfterSimplification("(* (factor a 2.0 3.0) (binfactor a x1 2.0))", "(binfactor a x1 6.0)"); // all other values have weight zero in binfactor AssertEqualAfterSimplification("(/ (binfactor a x0 2.0) (factor a 2.0 3.0))", "(binfactor a x0 1.0)"); AssertEqualAfterSimplification("(/ (factor a 2.0 3.0) (binfactor a x0 2.0))", string.Format(CultureInfo.InvariantCulture, "(factor a 1.0 {0})", 3.0 / 0.0)); AssertEqualAfterSimplification("(- (binfactor a x0 2.0) (factor a 2.0 3.0))", "(factor a 0.0 -3.0)"); AssertEqualAfterSimplification("(- (factor a 2.0 3.0) (binfactor a x0 2.0))", "(factor a 0.0 3.0)"); #endregion #region abs AssertEqualAfterSimplification("(abs 2.0)", "2.0"); AssertEqualAfterSimplification("(abs -2.0)", "2.0"); // constant folding AssertEqualAfterSimplification("(abs (exp (variable 2.0 x)))", "(exp (variable 2.0 x)))"); // exp is always positive AssertEqualAfterSimplification("(abs (exp (variable 2.0 x)))", "(exp (variable 2.0 x)))"); // exp is always positive AssertEqualAfterSimplification("(abs (sqr (variable 2.0 a)))", "(sqr (variable 2.0 a))"); // sqr is always positive AssertEqualAfterSimplification("(abs (sqrt (variable 2.0 a)))", "(sqrt (variable 2.0 a))"); // sqrt is always positive (for our cases) AssertEqualAfterSimplification("(abs (cuberoot (variable 2.0 a)))", "(cuberoot (variable 2.0 a))"); // cuberoot is always positive (for our cases) AssertEqualAfterSimplification("(* (abs (variable 2.0 x)) 2.0)", "(abs (variable 4.0 x))"); // can multiply positive constants into abs AssertEqualAfterSimplification("(* (abs (variable 2.0 x)) -2.0)", "(* (abs (variable 4.0 x)) -1.0)"); // for negative constants keep the sign AssertEqualAfterSimplification("(abs (* (variable 1.0 a) (variable 2.0 b)))", "(* (abs (variable 1.0 a)) (abs (variable 1.0 b)) 2.0))"); AssertEqualAfterSimplification("(abs (/ (variable 1.0 a) (variable 2.0 b)))", "(/ (abs (variable 1.0 a)) (abs (variable 2.0 b))))"); #endregion #region square and sqrt AssertEqualAfterSimplification("(sqr (sqrt (variable 2.0 x)))", "(variable 2.0 x)"); AssertEqualAfterSimplification("(sqrt (sqr (variable 2.0 x)))", "(variable 2.0 x)"); AssertEqualAfterSimplification("(sqr (abs (variable 2.0 a)))", "(sqr (variable 2.0 a))"); AssertEqualAfterSimplification("(sqr (exp (variable 2.0 x)))", "(exp (variable 4.0 x))"); AssertEqualAfterSimplification("(sqr (* (variable 2.0 a) (variable 3.0 b) (variable 4.0 c)))", "(* (sqr (variable 1.0 a)) (sqr (variable 1.0 b)) (sqr (variable 1.0 c)) 576)"); // 2²*3²*4² #endregion #region cube and cuberoot AssertEqualAfterSimplification("(cube (cuberoot (variable 2.0 x)))", "(variable 2.0 x)"); AssertEqualAfterSimplification("(cuberoot (cube (variable 2.0 x)))", "(variable 2.0 x)"); AssertEqualAfterSimplification("(cube (exp (variable 2.0 x)))", "(exp (variable 6.0 x))"); AssertEqualAfterSimplification("(sqr (cube (variable 2.0 x)))", "(pow (variable 2.0 x) 6)"); AssertEqualAfterSimplification("(cube (sqr (variable 2.0 x)))", "(pow (variable 2.0 x) 6)"); #endregion #region AQ AssertEqualAfterSimplification("(* (aq (variable 1.0 x) (variable 1.0 y)) 2.0)", "(aq (variable 2.0 x) (variable 1.0 y))"); AssertEqualAfterSimplification("(/ (aq (variable 1.0 x) (variable 1.0 y)) 2.0)", "(aq (variable 0.5 x) (variable 1.0 y))"); #endregion #region do not drop subtrees with small weights AssertEqualAfterSimplification("(* 1e-14 (variable 1.0 a))", "(variable 1e-14 a)"); AssertEqualAfterSimplification("(+ 1e-14 (variable 1.0 a))", "(+ 1e-14 (variable 1.0 a))"); // a scenario where a term with small weight can have large effect AssertEqualAfterSimplification("(+ (* 1e-14 (pow (variable 1.0 a) 10)) 1.0)", "(+ (* 1e-14 (pow (variable 1.0 a) 10)) 1.0)"); // a test case (from ticket #2985) AssertEqualAfterSimplification("(+ 5.9323E-002 (* 5.5606E-016 (exp (variable 3.5861E+001 a))))", "(+ 5.9323E-002 (* 5.5606E-016 (exp (variable 3.5861E+001 a))))"); #endregion } private void AssertEqualAfterSimplification(string original, string expected) { var formatter = new SymbolicExpressionTreeStringFormatter(); var importer = new SymbolicExpressionImporter(); var actualTree = TreeSimplifier.Simplify(importer.Import(original)); var expectedTree = importer.Import(expected); Assert.AreEqual(formatter.Format(expectedTree), formatter.Format(actualTree)); } } }