diff --git a/src/kibit/rules/arithmetic.clj b/src/kibit/rules/arithmetic.clj
index c4d8b69..456104a 100644
--- a/src/kibit/rules/arithmetic.clj
+++ b/src/kibit/rules/arithmetic.clj
@@ -7,5 +7,29 @@
   [(- ?x 1) (dec ?x)]
 
   [(* ?x (* . ?xs)) (* ?x . ?xs)]
-  [(+ ?x (+ . ?xs)) (+ ?x . ?xs)])
+  [(+ ?x (+ . ?xs)) (+ ?x . ?xs)]
+
+  ;;trivial identites
+  [(+ ?x 0) ?x]
+  [(- ?x 0) ?x]
+  [(* ?x 1) ?x]
+  [(/ ?x 1) ?x]
+  [(* ?x 0) 0]
+
+  ;;Math/pow
+  [(* ?x ?x) (Math/pow ?x 2) ]
+  [(* ?x ?x ?x) (Math/pow ?x 3) ]
+  [(* ?x ?x ?x ?x) (Math/pow ?x 4) ]
+  [(* ?x ?x ?x ?x ?x) (Math/pow ?x 5) ]
+
+  ;;Math/hypot
+  [(Math/sqrt (+ (Math/pow ?x 2) (Math/pow ?y 2))) (Math/hypot ?x ?y)]
+
+  ;;Math/expm1
+  [(dec (Math/exp ?x)) (Math/expm1 ?x)]
+
+  ;;ugly rounding tricks
+  [(long (+ ?x 0.5)) (Math/round ?x)]
+)
+
 
diff --git a/test/kibit/test/arithmetic.clj b/test/kibit/test/arithmetic.clj
index ab76034..c7c3fc8 100644
--- a/test/kibit/test/arithmetic.clj
+++ b/test/kibit/test/arithmetic.clj
@@ -9,4 +9,28 @@
     '(inc num) '(+ 1 num)
     '(dec num) '(- num 1)
     '(* x y z) '(* x (* y z))
-    '(+ x y z) '(+ x (+ y z))))
+    '(+ x y z) '(+ x (+ y z))
+
+    ;;hypot
+    '(Math/hypot x y) '(Math/sqrt (+ (Math/pow x 2) (Math/pow y 2)))
+    '(Math/hypot x y) '(Math/sqrt (+ (* x x) (* y y)))
+
+    ;;special exponential form
+    '(Math/expm1 x) '(- (Math/exp x) 1)
+    '(Math/expm1 x) '(dec (Math/exp x))
+
+    ;;not that ugly rounding trick, thank you
+    '(Math/round x) '(long (+ x 0.5))
+
+    ;;trivial identities
+    'x '(+ x 0) 
+    'x '(- x 0)
+    'x '(* x 1) 
+    'x '(/ x 1) 
+    '0 '(* x 0)
+    
+    ;;pow
+    '(Math/pow x 5) '(* x x x x x) 
+    '(Math/pow x 4) '(* x x x x) 
+    '(Math/pow x 3) '(* x x x) 
+    '(Math/pow x 2) '(* x x)))