#262 - Add 'Log' simplification rules

sys27 · May 16, 2020 · 4833368 · 4833368
1 parent 16d0867
commit 4833368
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Showing 3 changed files with 91 additions and 2 deletions.
diff --git a/xFunc.Maths/Analyzers/Simplifier.cs b/xFunc.Maths/Analyzers/Simplifier.cs
@@ -379,7 +379,13 @@ public virtual IExpression Analyze(Div exp)
         [ExcludeFromCodeCoverage]
         public virtual IExpression Analyze(Exp exp)
         {
-            return AnalyzeUnary(exp);
+            exp = AnalyzeUnary(exp);
+
+            // exp(ln(y)) -> y
+            if (exp.Argument is Ln ln)
+                return ln.Argument;
+
+            return exp;
         }
 
         /// <summary>
@@ -681,7 +687,18 @@ public virtual IExpression Analyze(Pow exp)
             if (exp.Right.Equals(one))
                 return exp.Left;
 
-            return exp;
+            return (exp.Left, exp.Right) switch
+            {
+                // x ^ log(x, y) -> y
+                (var left, Log log) when left.Equals(log.Left) => log.Right,
+                // e ^ ln(y) -> y
+                (Variable variable, Ln ln) when variable.Name == "e" => ln.Argument,
+                // 10 ^ lg(y) -> y
+                (Number number, Lg lg) when MathExtensions.Equals(number.Value, 10) => lg.Argument,
+                // 2 ^ lb(y) -> y
+                (Number number, Lb lb) when MathExtensions.Equals(number.Value, 2) => lb.Argument,
+                _ => exp,
+            };
         }
 
         /// <summary>

diff --git a/xFunc.Maths/MathExtensions.cs b/xFunc.Maths/MathExtensions.cs
@@ -16,6 +16,7 @@
 using System;
 using System.Globalization;
 using System.Numerics;
+using System.Runtime.CompilerServices;
 using xFunc.Maths.Expressions;
 using xFunc.Maths.Resources;
 
@@ -406,5 +407,15 @@ public static double Not(this double value)
 
             return ~(int)value;
         }
+
+        /// <summary>
+        /// Determines whether the specified number is equal to the current number.
+        /// </summary>
+        /// <param name="left">The current number.</param>
+        /// <param name="right">The number to compare with the current number.</param>
+        /// <returns><c>true</c> if the specified number is equal to the current number; otherwise, <c>false</c>.</returns>
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static bool Equals(double left, double right) =>
+            left.Equals(right) || Math.Abs(left - right) < Epsilon;
     }
 }
diff --git a/xFunc.Tests/Analyzers/SimplifierTest.cs b/xFunc.Tests/Analyzers/SimplifierTest.cs
@@ -947,6 +947,50 @@ public void PowerOne()
             SimpleTest(pow, expected);
         }
 
+        [Fact]
+        public void PowLog()
+        {
+            var pow = new Pow(
+                new Number(30),
+                new Log(new Number(30), new Variable("x")));
+            var expected = new Variable("x");
+
+            SimpleTest(pow, expected);
+        }
+
+        [Fact]
+        public void PowLg()
+        {
+            var pow = new Pow(
+                new Number(10),
+                new Lg(new Variable("x")));
+            var expected = new Variable("x");
+
+            SimpleTest(pow, expected);
+        }
+
+        [Fact]
+        public void PowLn()
+        {
+            var pow = new Pow(
+                new Variable("e"),
+                new Ln(new Variable("x")));
+            var expected = new Variable("x");
+
+            SimpleTest(pow, expected);
+        }
+
+        [Fact]
+        public void PowLb()
+        {
+            var pow = new Pow(
+                new Number(2),
+                new Lb(new Variable("x")));
+            var expected = new Variable("x");
+
+            SimpleTest(pow, expected);
+        }
+
         [Fact]
         public void RootOne()
         {
@@ -964,6 +1008,23 @@ public void Root()
             SimpleTest(root, root);
         }
 
+        [Fact]
+        public void Exp()
+        {
+            var exp = new Exp(new Number(30));
+
+            SimpleTest(exp, exp);
+        }
+
+        [Fact]
+        public void ExpLn()
+        {
+            var exp = new Exp(new Ln(new Number(30)));
+            var expected = new Number(30);
+
+            SimpleTest(exp, expected);
+        }
+
         [Fact]
         public void Log()
         {