diff --git a/LICENSE b/LICENSE
index d212a13..85c56fb 100644
--- a/LICENSE
+++ b/LICENSE
@@ -1,4 +1,4 @@
-Copyright (c) 2015 Patrick Roberts
+Copyright (c) 2016 Patrick Roberts
 
 Permission is hereby granted, free of charge, to any person
 obtaining a copy of this software and associated documentation
diff --git a/README.md b/README.md
index 5ee40db..3649a1d 100644
--- a/README.md
+++ b/README.md
@@ -180,7 +180,7 @@ input.addEventListener('change', function () {
 
 Note that the compiler creates a function rather than evaluating the
 expression that is compiled immediately. The function returned is
-high-performace, since it caches all real-values in the expression
+high-performace, since it caches all constant expressions in the string
 so that they don't need to be re-evaluated with each call.
 
 The following is an example where the compiler provides parameters
@@ -1076,3 +1076,27 @@ __Arguments__
 * `string` - A human-readable `String` of a math expression to be compiled.
 * `params` - An optional `Array[String]` of human-readable parameters to parse.
 * `skipFormat` - An optional `Boolean` to determine whether to skip pre-formatting.
+
+## License
+
+Copyright (c) 2016 Patrick Roberts
+
+Permission is hereby granted, free of charge, to any person
+obtaining a copy of this software and associated documentation
+files (the "Software"), to deal in the Software without restriction,
+including without limitation the rights to use, copy, modify,
+merge, publish, distribute, sublicense, and/or sell copies of the
+Software, and to permit persons to whom the Software is furnished
+to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
+OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
+HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
+OTHER DEALINGS IN THE SOFTWARE.
diff --git a/bower.json b/bower.json
index 88e0b07..16ee682 100644
--- a/bower.json
+++ b/bower.json
@@ -1,7 +1,7 @@
 {
   "name": "complex-js",
   "description": "Complex math for the browser and Node.js",
-  "version": "3.1.3",
+  "version": "3.2.0",
   "authors": [
     "Patrick Roberts"
   ],
diff --git a/lib/complex.js b/lib/complex.js
index f8cb149..0fa67a4 100644
--- a/lib/complex.js
+++ b/lib/complex.js
@@ -1,5 +1,5 @@
 /**
- * Copyright (c) 2015 Patrick Roberts
+ * Copyright (c) 2016 Patrick Roberts
  *
  * Permission is hereby granted, free of charge, to any person
  * obtaining a copy of this software and associated documentation
@@ -180,13 +180,13 @@
 
   if(Math.sinh === undefined) {
     Math.sinh = function(x) {
-      return (-Math.exp(-x) + Math.exp(x)) / 2;
+      return (Math.exp(x) - Math.exp(-x)) / 2;
     };
   }
 
   if(Math.cosh === undefined) {
     Math.cosh = function(x) {
-      return (Math.exp(-x) + Math.exp(x)) / 2;
+      return (Math.exp(x) + Math.exp(-x)) / 2;
     };
   }
 
@@ -210,6 +210,8 @@
    */
 
   function Complex(r, i, m, t) {
+    i = i || 0;
+
     if(!(this instanceof Complex)) {
       return new Complex(r, i, m, t);
     }
@@ -1254,7 +1256,7 @@
         throw new SyntaxError('"' + arg + '" is an invalid variable name.');
       }
 
-      return name.toLowerCase();
+      return name;
     });
 
     for(i = 0; i < args.length; i++) {
@@ -1454,7 +1456,19 @@
           // ignores extraneous grouping
           str += (func === '(' ? '' : func);
           i += match.length;
-          str += compile(exp.substring(i, j), vars, namespace) + (func === '(' ? '' : ')');
+          // efficiently compiles subgroup by first assuming a constant expression
+          try {
+            var ns = new Namespace();
+            var body = compile(exp.substring(i, j), [], ns, true);
+            var comp = (new Function('', 'var C=this.Complex;return ' + body + ';')).bind(ns)();
+            str += 'this[' + namespace.push(comp) + ']';
+          // then compiling with specified variables if that fails
+          } catch(e) {
+            str += compile(exp.substring(i, j), vars, namespace, true);
+          } finally {
+            str += (func === '(' ? '' : ')');
+          }
+
           i = (exp[j] === ')' ? j + 1 : j);
           findOper = true;
         }
@@ -1495,7 +1509,19 @@
 
         str += oper;
         i += match.length;
-        str += compile(exp.substring(i, j), vars, namespace) + ')';
+        // efficiently compiles subgroup by first assuming a constant expression
+        try {
+          var ns = new Namespace();
+          var body = compile(exp.substring(i, j), [], ns, true);
+          var comp = (new Function('', 'var C=this.Complex;return ' + body + ';')).bind(ns)();
+          str += 'this[' + namespace.push(comp) + ']';
+        // then compiling with specified variables if that fails
+        } catch(e) {
+          str += compile(exp.substring(i, j), vars, namespace, true);
+        } finally {
+          str += ')';
+        }
+
         i = (exp[j] === ')' ? j + 1 : j);
         findOper = true;
       // no identifiable expressions left to parse
@@ -1522,11 +1548,10 @@
     if(typeof args === 'boolean') {
       skipFormat = args;
       args = [];
-    } else if(!(typeof args === 'object' && args !== null && args.constructor === Array)) {
+    } else if(!Array.isArray(args)) {
       args = [];
     }
-    // make everything lowercase because it's easier
-    str = str.toLowerCase();
+
     // default is to format the human-readable string
     if(!skipFormat) {
       str = Complex.formatFunction(str);
@@ -1538,11 +1563,12 @@
       // create namespace to bind to function
       namespace = new Namespace(),
       // compile function body from string given valid arguments and namespace to cache parsed numerical constants
-      body = compile(str, vars, namespace),
+      body = compile('(' + str + ')', vars, namespace),
       // convert compiled variable names map to array for function arguments
       params = args.map(function(arg) {
         return vars[arg];
       }).join(',');
+
     // the constructed function being returned
     return (new Function(params, 'var C=this.Complex;return ' + body + ';')).bind(namespace);
   };
diff --git a/lib/complex.min.js b/lib/complex.min.js
index 7140d47..6d78fb2 100644
--- a/lib/complex.min.js
+++ b/lib/complex.min.js
@@ -1 +1 @@
-/* Copyright (c) 2015 Patrick Roberts */!function(t){"use strict";function r(t){return t>=0?t-t%1:t-(1+t%1)%1}function n(t){return t>=0?t+(1-t%1)%1:t-t%1}function e(t){return r(t+.5)}function i(t){return t-t%1}function o(t){return t%1}function a(t,r,n,e){return this instanceof a?(this.m="number"==typeof n?w.abs(n):w.sqrt(t*t+r*r),this.t="number"==typeof e?n>=0?e:e+b:w.atan2(r,t),this.t=(this.t%(2*b)+2*b)%(2*b),this.t-=this.t>b?2*b:0,this.r=t,void(this.i=r)):new a(t,r,n,e)}function c(t,r,n){var e;return q.test(t)?S.test(n.slice(r))?t:t.charAt(0).replace(x,c)+"*"+t.charAt(1).replace(x,c):O.test(t)?"(":I.test(t)?")":(e=t.search(T),t.charAt(-1!==e?e:"*"))}function s(t){var r,n,e,i=/[^a-z]+/gi,o="abcdefghijklmnopqrstuvwxyz",a=o.length,c={},s="";for(t=t.map(function(t){var r=t.replace(i,"");if(t!==r)throw new SyntaxError('"'+t+'" is an invalid variable name.');return r.toLowerCase()}),r=0;r<t.length;r++){if(c[t[r]])throw new ReferenceError("May not have duplicate parameter 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a.replace(h,A)},G.prototype=[],G.prototype.push=function(){return Array.prototype.push.apply(this,arguments)-1},G.prototype.Complex=z,z.parseFunction=function(a,b,c){"boolean"==typeof b?(c=b,b=[]):Array.isArray(b)||(b=[]),c||(a=z.formatFunction(a));var d=B(b),e=new G,f=H("("+a+")",d,e),g=b.map(function(a){return d[a]}).join(",");return new Function(g,"var C=this.Complex;return "+f+";").bind(e)},"undefined"!=typeof module&&null!==module&&module.exports?module.exports=z:"function"==typeof define&&define.amd?define([],function(){return z}):a.Complex=z}("undefined"==typeof global?this:global);
\ No newline at end of file
diff --git a/package.json b/package.json
index 8a15a65..59a8de2 100644
--- a/package.json
+++ b/package.json
@@ -7,7 +7,7 @@
 	],
 	"author": "Patrick Roberts",
 	"main": "./index",
-	"version": "3.1.2",
+	"version": "3.2.0",
 	"repository": {
 		"type": "git",
 		"url": "https://github.com/patrickroberts/complex-js.git"