From 712dfe8a117207f1d70e0e14f9d6e7ee62c8eadd Mon Sep 17 00:00:00 2001
From: tomsmeding <tom.smeding@gmail.com>
Date: Sat, 18 Jun 2016 13:10:24 +0200
Subject: More patterns

---
 simplify.hs | 36 +++++++++++++++++++++++++++++++++++-
 1 file changed, 35 insertions(+), 1 deletion(-)

diff --git a/simplify.hs b/simplify.hs
index f2eaa28..f0fcd6e 100644
--- a/simplify.hs
+++ b/simplify.hs
@@ -137,6 +137,17 @@ canonicaliseOrder node = case node of
 
 patterndb :: [(AST,AST)]
 patterndb = [
+        (Reciprocal $ Product [Reciprocal (CaptureTerm "x"),Capture "rest"],  -- 1/(1/x * [rest]) -> x * 1/[rest]
+         Product [Capture "x",Reciprocal $ Capture "rest"]),
+
+        (Product [CaptureTerm "x",Reciprocal (CaptureTerm "x"),Capture "rest"],  -- x * 1/x * [rest] -> [rest]
+         Capture "rest"),
+
+        (Product [CaptureTerm "x",  -- x * 1/(x*[rrest]) * [rest] -> [rest] * 1/[rrest]
+                  Reciprocal (Product [CaptureTerm "x",Capture "rrest"]),
+                  Capture "rest"],
+         Product [Capture "rest",Reciprocal (Capture "rrest")]),
+
         (Sum [CaptureTerm "x",CaptureTerm "x",Capture "rest"],  -- x + x + [rest] -> 2*x + [rest]
          Sum [Product [Number 2,Capture "x"],Capture "rest"]),
 
@@ -179,6 +190,15 @@ patterndb = [
         (Apply "pow" [CaptureTerm "x",Number 1],  -- x^1 -> x
          Capture "x"),
 
+        (Product [Number 0,Capture "rest"],  -- 0*[rest] -> 0
+         Number 0),
+
+        (Product [Number 1,Capture "rest"],  -- 1*[rest] -> [rest]
+         Capture "rest"),
+
+
+        (Apply "d" [CaptureConstr "n" (Number undefined),Capture "x"], -- d(n,x) -> 0
+         Number 0),
 
         (Apply "d" [CaptureConstr "x" (Variable undefined),CaptureTerm "x"],  -- d(x,x) -> 1
          Number 1),
@@ -188,7 +208,21 @@ patterndb = [
          Product [Capture "n",Apply "pow" [Capture "x",Sum [Capture "n",Number (-1)]]]),
 
         (Apply "d" [Sum [CaptureTerm "a",Capture "b"],CaptureTerm "x"],  -- d(a+[b],x) -> d(a,x) + d([b],x)
-         Sum [Apply "d" [Capture "a",Capture "x"],Apply "d" [Capture "b",Capture "x"]])
+         Sum [Apply "d" [Capture "a",Capture "x"],Apply "d" [Capture "b",Capture "x"]]),
+
+        (Apply "d" [Product [CaptureTerm "a",Capture "b"],Capture "x"],  -- d(ab,x) -> d(a,x)*b + a*d(b,x)
+         Sum [Product [Apply "d" [Capture "a",Capture "x"],Capture "b"],
+              Product [Capture "a",Apply "d" [Capture "b",Capture "x"]]]),
+
+        (Apply "d" [Apply "pow" [CaptureConstr "a" (Variable undefined),  -- d(a^expr,x) -> a^expr * ln(a) * d(expr,x)
+                                 Capture "expr"],
+                    Capture "x"],
+         Product [Apply "pow" [Capture "a",Capture "expr"],
+                  Apply "ln" [Capture "a"],
+                  Apply "d" [Capture "expr",Capture "x"]]),
+
+        (Apply "d" [Apply "ln" [Capture "args"],Capture "x"],  -- d(ln([args]),x) -> 1/[args]*d([args],x)
+         Product [Reciprocal (Capture "args"),Apply "d" [Capture "args",Capture "x"]])
     ]
 
 astChildMap :: AST -> (AST -> AST) -> AST
-- 
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