mathjs/lib/cjs/function/algebra/simplify.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

"use strict";

var _interopRequireDefault = require("@babel/runtime/helpers/interopRequireDefault");

Object.defineProperty(exports, "__esModule", {
  value: true
});
exports.createSimplify = void 0;

var _typeof2 = _interopRequireDefault(require("@babel/runtime/helpers/typeof"));

var _is = require("../../utils/is.js");

var _factory = require("../../utils/factory.js");

var _util = require("./simplify/util.js");

var _simplifyCore = require("./simplify/simplifyCore.js");

var _simplifyConstant = require("./simplify/simplifyConstant.js");

var _resolve = require("./simplify/resolve.js");

var _object = require("../../utils/object.js");

var _map = require("../../utils/map.js");

var name = 'simplify';
var dependencies = ['config', 'typed', 'parse', 'add', 'subtract', 'multiply', 'divide', 'pow', 'isZero', 'equal', '?fraction', '?bignumber', 'mathWithTransform', 'ConstantNode', 'FunctionNode', 'OperatorNode', 'ParenthesisNode', 'SymbolNode'];
var createSimplify = /* #__PURE__ */(0, _factory.factory)(name, dependencies, function (_ref) {
  var config = _ref.config,
      typed = _ref.typed,
      parse = _ref.parse,
      add = _ref.add,
      subtract = _ref.subtract,
      multiply = _ref.multiply,
      divide = _ref.divide,
      pow = _ref.pow,
      isZero = _ref.isZero,
      equal = _ref.equal,
      fraction = _ref.fraction,
      bignumber = _ref.bignumber,
      mathWithTransform = _ref.mathWithTransform,
      ConstantNode = _ref.ConstantNode,
      FunctionNode = _ref.FunctionNode,
      OperatorNode = _ref.OperatorNode,
      ParenthesisNode = _ref.ParenthesisNode,
      SymbolNode = _ref.SymbolNode;
  var simplifyConstant = (0, _simplifyConstant.createSimplifyConstant)({
    typed: typed,
    config: config,
    mathWithTransform: mathWithTransform,
    fraction: fraction,
    bignumber: bignumber,
    ConstantNode: ConstantNode,
    OperatorNode: OperatorNode,
    FunctionNode: FunctionNode,
    SymbolNode: SymbolNode
  });
  var simplifyCore = (0, _simplifyCore.createSimplifyCore)({
    equal: equal,
    isZero: isZero,
    add: add,
    subtract: subtract,
    multiply: multiply,
    divide: divide,
    pow: pow,
    ConstantNode: ConstantNode,
    OperatorNode: OperatorNode,
    FunctionNode: FunctionNode,
    ParenthesisNode: ParenthesisNode
  });
  var resolve = (0, _resolve.createResolve)({
    parse: parse,
    FunctionNode: FunctionNode,
    OperatorNode: OperatorNode,
    ParenthesisNode: ParenthesisNode
  });

  var _createUtil = (0, _util.createUtil)({
    FunctionNode: FunctionNode,
    OperatorNode: OperatorNode,
    SymbolNode: SymbolNode
  }),
      isCommutative = _createUtil.isCommutative,
      isAssociative = _createUtil.isAssociative,
      flatten = _createUtil.flatten,
      unflattenr = _createUtil.unflattenr,
      unflattenl = _createUtil.unflattenl,
      createMakeNodeFunction = _createUtil.createMakeNodeFunction;
  /**
   * Simplify an expression tree.
   *
   * A list of rules are applied to an expression, repeating over the list until
   * no further changes are made.
   * It's possible to pass a custom set of rules to the function as second
   * argument. A rule can be specified as an object, string, or function:
   *
   *     const rules = [
   *       { l: 'n1*n3 + n2*n3', r: '(n1+n2)*n3' },
   *       'n1*n3 + n2*n3 -> (n1+n2)*n3',
   *       function (node) {
   *         // ... return a new node or return the node unchanged
   *         return node
   *       }
   *     ]
   *
   * String and object rules consist of a left and right pattern. The left is
   * used to match against the expression and the right determines what matches
   * are replaced with. The main difference between a pattern and a normal
   * expression is that variables starting with the following characters are
   * interpreted as wildcards:
   *
   * - 'n' - matches any Node
   * - 'c' - matches any ConstantNode
   * - 'v' - matches any Node that is not a ConstantNode
   *
   * The default list of rules is exposed on the function as `simplify.rules`
   * and can be used as a basis to built a set of custom rules.
   *
   * For more details on the theory, see:
   *
   * - [Strategies for simplifying math expressions (Stackoverflow)](https://stackoverflow.com/questions/7540227/strategies-for-simplifying-math-expressions)
   * - [Symbolic computation - Simplification (Wikipedia)](https://en.wikipedia.org/wiki/Symbolic_computation#Simplification)
   *
   *  An optional `options` argument can be passed as last argument of `simplify`.
   *  There is currently one option available:
   *  - `exactFractions`: a boolean which is `true` by default.
   *  - `fractionsLimit`: when `exactFractions` is true, a fraction will be returned
   *    only when both numerator and denominator are smaller than `fractionsLimit`.
   *    Default value is 10000.
   *
   * Syntax:
   *
   *     simplify(expr)
   *     simplify(expr, rules)
   *     simplify(expr, rules)
   *     simplify(expr, rules, scope)
   *     simplify(expr, rules, scope, options)
   *     simplify(expr, scope)
   *     simplify(expr, scope, options)
   *
   * Examples:
   *
   *     math.simplify('2 * 1 * x ^ (2 - 1)')      // Node "2 * x"
   *     math.simplify('2 * 3 * x', {x: 4})        // Node "24"
   *     const f = math.parse('2 * 1 * x ^ (2 - 1)')
   *     math.simplify(f)                          // Node "2 * x"
   *     math.simplify('0.4 * x', {}, {exactFractions: true})  // Node "x * 2 / 5"
   *     math.simplify('0.4 * x', {}, {exactFractions: false}) // Node "0.4 * x"
   *
   * See also:
   *
   *     derivative, parse, evaluate, rationalize
   *
   * @param {Node | string} expr
   *            The expression to be simplified
   * @param {Array<{l:string, r: string} | string | function>} [rules]
   *            Optional list with custom rules
   * @return {Node} Returns the simplified form of `expr`
   */


  var simplify = typed('simplify', {
    string: function string(expr) {
      return this(parse(expr), this.rules, (0, _map.createEmptyMap)(), {});
    },
    'string, Map | Object': function stringMapObject(expr, scope) {
      return this(parse(expr), this.rules, scope, {});
    },
    'string, Map | Object, Object': function stringMapObjectObject(expr, scope, options) {
      return this(parse(expr), this.rules, scope, options);
    },
    'string, Array': function stringArray(expr, rules) {
      return this(parse(expr), rules, (0, _map.createEmptyMap)(), {});
    },
    'string, Array, Map | Object': function stringArrayMapObject(expr, rules, scope) {
      return this(parse(expr), rules, scope, {});
    },
    'string, Array, Map | Object, Object': function stringArrayMapObjectObject(expr, rules, scope, options) {
      return this(parse(expr), rules, scope, options);
    },
    'Node, Map | Object': function NodeMapObject(expr, scope) {
      return this(expr, this.rules, scope, {});
    },
    'Node, Map | Object, Object': function NodeMapObjectObject(expr, scope, options) {
      return this(expr, this.rules, scope, options);
    },
    Node: function Node(expr) {
      return this(expr, this.rules, (0, _map.createEmptyMap)(), {});
    },
    'Node, Array': function NodeArray(expr, rules) {
      return this(expr, rules, (0, _map.createEmptyMap)(), {});
    },
    'Node, Array, Map | Object': function NodeArrayMapObject(expr, rules, scope) {
      return this(expr, rules, scope, {});
    },
    'Node, Array, Object, Object': function NodeArrayObjectObject(expr, rules, scope, options) {
      return this(expr, rules, (0, _map.createMap)(scope), options);
    },
    'Node, Array, Map, Object': function NodeArrayMapObject(expr, rules, scope, options) {
      rules = _buildRules(rules);
      var res = resolve(expr, scope);
      res = removeParens(res);
      var visited = {};
      var str = res.toString({
        parenthesis: 'all'
      });

      while (!visited[str]) {
        visited[str] = true;
        _lastsym = 0; // counter for placeholder symbols

        for (var i = 0; i < rules.length; i++) {
          if (typeof rules[i] === 'function') {
            res = rules[i](res, options);
          } else {
            flatten(res);
            res = applyRule(res, rules[i]);
          }

          unflattenl(res); // using left-heavy binary tree here since custom rule functions may expect it
        }

        str = res.toString({
          parenthesis: 'all'
        });
      }

      return res;
    }
  });
  simplify.simplifyCore = simplifyCore;
  simplify.resolve = resolve;

  function removeParens(node) {
    return node.transform(function (node, path, parent) {
      return (0, _is.isParenthesisNode)(node) ? removeParens(node.content) : node;
    });
  } // All constants that are allowed in rules


  var SUPPORTED_CONSTANTS = {
    "true": true,
    "false": true,
    e: true,
    i: true,
    Infinity: true,
    LN2: true,
    LN10: true,
    LOG2E: true,
    LOG10E: true,
    NaN: true,
    phi: true,
    pi: true,
    SQRT1_2: true,
    SQRT2: true,
    tau: true // null: false,
    // undefined: false,
    // version: false,

  }; // Array of strings, used to build the ruleSet.
  // Each l (left side) and r (right side) are parsed by
  // the expression parser into a node tree.
  // Left hand sides are matched to subtrees within the
  // expression to be parsed and replaced with the right
  // hand side.
  // TODO: Add support for constraints on constants (either in the form of a '=' expression or a callback [callback allows things like comparing symbols alphabetically])
  // To evaluate lhs constants for rhs constants, use: { l: 'c1+c2', r: 'c3', evaluate: 'c3 = c1 + c2' }. Multiple assignments are separated by ';' in block format.
  // It is possible to get into an infinite loop with conflicting rules

  simplify.rules = [simplifyCore, // { l: 'n+0', r: 'n' },     // simplifyCore
  // { l: 'n^0', r: '1' },     // simplifyCore
  // { l: '0*n', r: '0' },     // simplifyCore
  // { l: 'n/n', r: '1'},      // simplifyCore
  // { l: 'n^1', r: 'n' },     // simplifyCore
  // { l: '+n1', r:'n1' },     // simplifyCore
  // { l: 'n--n1', r:'n+n1' }, // simplifyCore
  {
    l: 'log(e)',
    r: '1'
  }, // temporary rules
  {
    l: 'n-n1',
    r: 'n+-n1'
  }, // temporarily replace 'subtract' so we can further flatten the 'add' operator
  {
    l: '-(c*v)',
    r: '(-c) * v'
  }, // make non-constant terms positive
  {
    l: '-v',
    r: '(-1) * v'
  }, {
    l: 'n/n1^n2',
    r: 'n*n1^-n2'
  }, // temporarily replace 'divide' so we can further flatten the 'multiply' operator
  {
    l: 'n/n1',
    r: 'n*n1^-1'
  }, // expand nested exponentiation
  {
    l: '(n ^ n1) ^ n2',
    r: 'n ^ (n1 * n2)'
  }, // collect like factors
  {
    l: 'n*n',
    r: 'n^2'
  }, {
    l: 'n * n^n1',
    r: 'n^(n1+1)'
  }, {
    l: 'n^n1 * n^n2',
    r: 'n^(n1+n2)'
  }, // collect like terms
  {
    l: 'n+n',
    r: '2*n'
  }, {
    l: 'n+-n',
    r: '0'
  }, {
    l: 'n1*n2 + n2',
    r: '(n1+1)*n2'
  }, {
    l: 'n1*n3 + n2*n3',
    r: '(n1+n2)*n3'
  }, // remove parenthesis in the case of negating a quantitiy
  {
    l: 'n1 + -1 * (n2 + n3)',
    r: 'n1 + -1 * n2 + -1 * n3'
  }, simplifyConstant, {
    l: '(-n)*n1',
    r: '-(n*n1)'
  }, // make factors positive (and undo 'make non-constant terms positive')
  // ordering of constants
  {
    l: 'c+v',
    r: 'v+c',
    context: {
      add: {
        commutative: false
      }
    }
  }, {
    l: 'v*c',
    r: 'c*v',
    context: {
      multiply: {
        commutative: false
      }
    }
  }, // undo temporary rules
  // { l: '(-1) * n', r: '-n' }, // #811 added test which proved this is redundant
  {
    l: 'n+-n1',
    r: 'n-n1'
  }, // undo replace 'subtract'
  {
    l: 'n*(n1^-1)',
    r: 'n/n1'
  }, // undo replace 'divide'
  {
    l: 'n*n1^-n2',
    r: 'n/n1^n2'
  }, {
    l: 'n1^-1',
    r: '1/n1'
  }, {
    l: 'n*(n1/n2)',
    r: '(n*n1)/n2'
  }, // '*' before '/'
  {
    l: 'n-(n1+n2)',
    r: 'n-n1-n2'
  }, // '-' before '+'
  // { l: '(n1/n2)/n3', r: 'n1/(n2*n3)' },
  // { l: '(n*n1)/(n*n2)', r: 'n1/n2' },
  {
    l: '1*n',
    r: 'n'
  }, // this pattern can be produced by simplifyConstant
  {
    l: 'n1/(n2/n3)',
    r: '(n1*n3)/n2'
  }];
  /**
   * Parse the string array of rules into nodes
   *
   * Example syntax for rules:
   *
   * Position constants to the left in a product:
   * { l: 'n1 * c1', r: 'c1 * n1' }
   * n1 is any Node, and c1 is a ConstantNode.
   *
   * Apply difference of squares formula:
   * { l: '(n1 - n2) * (n1 + n2)', r: 'n1^2 - n2^2' }
   * n1, n2 mean any Node.
   *
   * Short hand notation:
   * 'n1 * c1 -> c1 * n1'
   */

  function _buildRules(rules) {
    // Array of rules to be used to simplify expressions
    var ruleSet = [];

    for (var i = 0; i < rules.length; i++) {
      var rule = rules[i];
      var newRule = void 0;
      var ruleType = (0, _typeof2["default"])(rule);

      switch (ruleType) {
        case 'string':
          {
            var lr = rule.split('->');

            if (lr.length === 2) {
              rule = {
                l: lr[0],
                r: lr[1]
              };
            } else {
              throw SyntaxError('Could not parse rule: ' + rule);
            }
          }

        /* falls through */

        case 'object':
          newRule = {
            l: removeParens(parse(rule.l)),
            r: removeParens(parse(rule.r))
          };

          if (rule.context) {
            newRule.evaluate = rule.context;
          }

          if (rule.evaluate) {
            newRule.evaluate = parse(rule.evaluate);
          }

          if (isAssociative(newRule.l)) {
            var makeNode = createMakeNodeFunction(newRule.l);

            var expandsym = _getExpandPlaceholderSymbol();

            newRule.expanded = {};
            newRule.expanded.l = makeNode([newRule.l.clone(), expandsym]); // Push the expandsym into the deepest possible branch.
            // This helps to match the newRule against nodes returned from getSplits() later on.

            flatten(newRule.expanded.l);
            unflattenr(newRule.expanded.l);
            newRule.expanded.r = makeNode([newRule.r, expandsym]);
          }

          break;

        case 'function':
          newRule = rule;
          break;

        default:
          throw TypeError('Unsupported type of rule: ' + ruleType);
      } // console.log('Adding rule: ' + rules[i])
      // console.log(newRule)


      ruleSet.push(newRule);
    }

    return ruleSet;
  }

  var _lastsym = 0;

  function _getExpandPlaceholderSymbol() {
    return new SymbolNode('_p' + _lastsym++);
  }
  /**
   * Returns a simplfied form of node, or the original node if no simplification was possible.
   *
   * @param  {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node
   * @return {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} The simplified form of `expr`, or the original node if no simplification was possible.
   */


  var applyRule = typed('applyRule', {
    'Node, Object': function NodeObject(node, rule) {
      // console.log('Entering applyRule(' + node.toString() + ')')
      // Do not clone node unless we find a match
      var res = node; // First replace our child nodes with their simplified versions
      // If a child could not be simplified, the assignments will have
      // no effect since the node is returned unchanged

      if (res instanceof OperatorNode || res instanceof FunctionNode) {
        if (res.args) {
          for (var i = 0; i < res.args.length; i++) {
            res.args[i] = applyRule(res.args[i], rule);
          }
        }
      } else if (res instanceof ParenthesisNode) {
        if (res.content) {
          res.content = applyRule(res.content, rule);
        }
      } // Try to match a rule against this node


      var repl = rule.r;

      var matches = _ruleMatch(rule.l, res)[0]; // If the rule is associative operator, we can try matching it while allowing additional terms.
      // This allows us to match rules like 'n+n' to the expression '(1+x)+x' or even 'x+1+x' if the operator is commutative.


      if (!matches && rule.expanded) {
        repl = rule.expanded.r;
        matches = _ruleMatch(rule.expanded.l, res)[0];
      }

      if (matches) {
        // const before = res.toString({parenthesis: 'all'})
        // Create a new node by cloning the rhs of the matched rule
        // we keep any implicit multiplication state if relevant
        var implicit = res.implicit;
        res = repl.clone();

        if (implicit && 'implicit' in repl) {
          res.implicit = true;
        } // Replace placeholders with their respective nodes without traversing deeper into the replaced nodes


        res = res.transform(function (node) {
          if (node.isSymbolNode && (0, _object.hasOwnProperty)(matches.placeholders, node.name)) {
            return matches.placeholders[node.name].clone();
          } else {
            return node;
          }
        }); // const after = res.toString({parenthesis: 'all'})
        // console.log('Simplified ' + before + ' to ' + after)
      }

      return res;
    }
  });
  /**
   * Get (binary) combinations of a flattened binary node
   * e.g. +(node1, node2, node3) -> [
   *        +(node1,  +(node2, node3)),
   *        +(node2,  +(node1, node3)),
   *        +(node3,  +(node1, node2))]
   *
   */

  function getSplits(node, context) {
    var res = [];
    var right, rightArgs;
    var makeNode = createMakeNodeFunction(node);

    if (isCommutative(node, context)) {
      for (var i = 0; i < node.args.length; i++) {
        rightArgs = node.args.slice(0);
        rightArgs.splice(i, 1);
        right = rightArgs.length === 1 ? rightArgs[0] : makeNode(rightArgs);
        res.push(makeNode([node.args[i], right]));
      }
    } else {
      rightArgs = node.args.slice(1);
      right = rightArgs.length === 1 ? rightArgs[0] : makeNode(rightArgs);
      res.push(makeNode([node.args[0], right]));
    }

    return res;
  }
  /**
   * Returns the set union of two match-placeholders or null if there is a conflict.
   */


  function mergeMatch(match1, match2) {
    var res = {
      placeholders: {}
    }; // Some matches may not have placeholders; this is OK

    if (!match1.placeholders && !match2.placeholders) {
      return res;
    } else if (!match1.placeholders) {
      return match2;
    } else if (!match2.placeholders) {
      return match1;
    } // Placeholders with the same key must match exactly


    for (var key in match1.placeholders) {
      if ((0, _object.hasOwnProperty)(match1.placeholders, key)) {
        res.placeholders[key] = match1.placeholders[key];

        if ((0, _object.hasOwnProperty)(match2.placeholders, key)) {
          if (!_exactMatch(match1.placeholders[key], match2.placeholders[key])) {
            return null;
          }
        }
      }
    }

    for (var _key in match2.placeholders) {
      if ((0, _object.hasOwnProperty)(match2.placeholders, _key)) {
        res.placeholders[_key] = match2.placeholders[_key];
      }
    }

    return res;
  }
  /**
   * Combine two lists of matches by applying mergeMatch to the cartesian product of two lists of matches.
   * Each list represents matches found in one child of a node.
   */


  function combineChildMatches(list1, list2) {
    var res = [];

    if (list1.length === 0 || list2.length === 0) {
      return res;
    }

    var merged;

    for (var i1 = 0; i1 < list1.length; i1++) {
      for (var i2 = 0; i2 < list2.length; i2++) {
        merged = mergeMatch(list1[i1], list2[i2]);

        if (merged) {
          res.push(merged);
        }
      }
    }

    return res;
  }
  /**
   * Combine multiple lists of matches by applying mergeMatch to the cartesian product of two lists of matches.
   * Each list represents matches found in one child of a node.
   * Returns a list of unique matches.
   */


  function mergeChildMatches(childMatches) {
    if (childMatches.length === 0) {
      return childMatches;
    }

    var sets = childMatches.reduce(combineChildMatches);
    var uniqueSets = [];
    var unique = {};

    for (var i = 0; i < sets.length; i++) {
      var s = JSON.stringify(sets[i]);

      if (!unique[s]) {
        unique[s] = true;
        uniqueSets.push(sets[i]);
      }
    }

    return uniqueSets;
  }
  /**
   * Determines whether node matches rule.
   *
   * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} rule
   * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} node
   * @return {Object} Information about the match, if it exists.
   */


  function _ruleMatch(rule, node, isSplit) {
    //    console.log('Entering _ruleMatch(' + JSON.stringify(rule) + ', ' + JSON.stringify(node) + ')')
    //    console.log('rule = ' + rule)
    //    console.log('node = ' + node)
    //    console.log('Entering _ruleMatch(' + rule.toString() + ', ' + node.toString() + ')')
    var res = [{
      placeholders: {}
    }];

    if (rule instanceof OperatorNode && node instanceof OperatorNode || rule instanceof FunctionNode && node instanceof FunctionNode) {
      // If the rule is an OperatorNode or a FunctionNode, then node must match exactly
      if (rule instanceof OperatorNode) {
        if (rule.op !== node.op || rule.fn !== node.fn) {
          return [];
        }
      } else if (rule instanceof FunctionNode) {
        if (rule.name !== node.name) {
          return [];
        }
      } // rule and node match. Search the children of rule and node.


      if (node.args.length === 1 && rule.args.length === 1 || !isAssociative(node) && node.args.length === rule.args.length || isSplit) {
        // Expect non-associative operators to match exactly
        var childMatches = [];

        for (var i = 0; i < rule.args.length; i++) {
          var childMatch = _ruleMatch(rule.args[i], node.args[i]);

          if (childMatch.length === 0) {
            // Child did not match, so stop searching immediately
            return [];
          } // The child matched, so add the information returned from the child to our result


          childMatches.push(childMatch);
        }

        res = mergeChildMatches(childMatches);
      } else if (node.args.length >= 2 && rule.args.length === 2) {
        // node is flattened, rule is not
        // Associative operators/functions can be split in different ways so we check if the rule matches each
        // them and return their union.
        var splits = getSplits(node, rule.context);
        var splitMatches = [];

        for (var _i = 0; _i < splits.length; _i++) {
          var matchSet = _ruleMatch(rule, splits[_i], true); // recursing at the same tree depth here


          splitMatches = splitMatches.concat(matchSet);
        }

        return splitMatches;
      } else if (rule.args.length > 2) {
        throw Error('Unexpected non-binary associative function: ' + rule.toString());
      } else {
        // Incorrect number of arguments in rule and node, so no match
        return [];
      }
    } else if (rule instanceof SymbolNode) {
      // If the rule is a SymbolNode, then it carries a special meaning
      // according to the first character of the symbol node name.
      // c.* matches a ConstantNode
      // n.* matches any node
      if (rule.name.length === 0) {
        throw new Error('Symbol in rule has 0 length...!?');
      }

      if (SUPPORTED_CONSTANTS[rule.name]) {
        // built-in constant must match exactly
        if (rule.name !== node.name) {
          return [];
        }
      } else if (rule.name[0] === 'n' || rule.name.substring(0, 2) === '_p') {
        // rule matches _anything_, so assign this node to the rule.name placeholder
        // Assign node to the rule.name placeholder.
        // Our parent will check for matches among placeholders.
        res[0].placeholders[rule.name] = node;
      } else if (rule.name[0] === 'v') {
        // rule matches any variable thing (not a ConstantNode)
        if (!(0, _is.isConstantNode)(node)) {
          res[0].placeholders[rule.name] = node;
        } else {
          // Mis-match: rule was expecting something other than a ConstantNode
          return [];
        }
      } else if (rule.name[0] === 'c') {
        // rule matches any ConstantNode
        if (node instanceof ConstantNode) {
          res[0].placeholders[rule.name] = node;
        } else {
          // Mis-match: rule was expecting a ConstantNode
          return [];
        }
      } else {
        throw new Error('Invalid symbol in rule: ' + rule.name);
      }
    } else if (rule instanceof ConstantNode) {
      // Literal constant must match exactly
      if (!equal(rule.value, node.value)) {
        return [];
      }
    } else {
      // Some other node was encountered which we aren't prepared for, so no match
      return [];
    } // It's a match!
    // console.log('_ruleMatch(' + rule.toString() + ', ' + node.toString() + ') found a match')


    return res;
  }
  /**
   * Determines whether p and q (and all their children nodes) are identical.
   *
   * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} p
   * @param {ConstantNode | SymbolNode | ParenthesisNode | FunctionNode | OperatorNode} q
   * @return {Object} Information about the match, if it exists.
   */


  function _exactMatch(p, q) {
    if (p instanceof ConstantNode && q instanceof ConstantNode) {
      if (!equal(p.value, q.value)) {
        return false;
      }
    } else if (p instanceof SymbolNode && q instanceof SymbolNode) {
      if (p.name !== q.name) {
        return false;
      }
    } else if (p instanceof OperatorNode && q instanceof OperatorNode || p instanceof FunctionNode && q instanceof FunctionNode) {
      if (p instanceof OperatorNode) {
        if (p.op !== q.op || p.fn !== q.fn) {
          return false;
        }
      } else if (p instanceof FunctionNode) {
        if (p.name !== q.name) {
          return false;
        }
      }

      if (p.args.length !== q.args.length) {
        return false;
      }

      for (var i = 0; i < p.args.length; i++) {
        if (!_exactMatch(p.args[i], q.args[i])) {
          return false;
        }
      }
    } else {
      return false;
    }

    return true;
  }

  return simplify;
});
exports.createSimplify = createSimplify;