CalcParser.php

<?php
class CalcParser
{
    public function parse($str)
    {
        $result = $this->PlusMinus($str);
        if (!empty($result->rest)) {
            echo "Error: can't parse all.<br />";
            echo "rest: " . $result->rest;
        }
        return $result->acc;
    }

    private function plusMinus($str)
    {
        $current = $this->mulDiv($str);
        $acc = $current->acc;

        while (strlen($current->rest) > 0) {
            if (!($current->rest[0] == '+' || $current->rest[0] == '-')) {
                break;
            }
            $sign = $current->rest[0];
            $next = substr($current->rest, 1);

            $current = $this->mulDiv($next);
            if ($sign == '+') {
                $acc += $current->acc;
            } else {
                $acc -= $current->acc;
            }
            $current->acc = $acc;
        }
        return new Result($current->acc, $current->rest);
    }

    private function mulDiv($str)
    {
        $current = $this->pow($str);
        $acc = $current->acc;
        while (true) {
            if (strlen($current->rest) == 0) {
                return $current;
            } else {
                $sign = $current->rest[0];
                $next = substr($current->rest, 1);
                $right = $this->pow($next);
                if ($sign == '*') {
                    $acc *= $right->acc;
                } elseif ($sign == '/') {
                    $acc /= $right->acc;
                } else {
                    return $current;
                }
                $current = new Result($acc, $right->rest);
            }
        }
    }

    private function pow($str)
    {
        $current = $this->bracket($str);
        $acc = $current->acc;
        while (true) {
            if (strlen($current->rest) == 0) {
                return $current;
            } else {
                $sign = $current->rest[0];
                $next = substr($current->rest, 1);
                $right = $this->bracket($next);
                if ($sign == '^') {
                    $acc = pow($acc, $right->acc);
                } else {
                    return $current;
                }
                $current = new Result($acc, $right->rest);
            }
        }
    }

    private function bracket($str)
    {
        if ($str[0] == '(') {
            $result = $this->plusMinus(substr($str, 1));
            if (!empty($result->rest) && $result->rest[0] == ')') {
                $result->rest = substr($result->rest, 1);
            } else {
                echo "Error: bracket is not closed";
            }
            return $result;
        }
        return $this->extraFunctions($str);
    }

    private function extraFunctions($str)
    {
        $funct = '';
        $i = 0;
        while ($i < strlen($str) && ctype_alpha($str[$i])) {
            $funct .= $str[$i];
            $i++;
        }
        if (!empty($funct)) {
            if (strlen($str) > $i && $str[$i] == "(") {
                $result = $this->bracket(substr($str, strlen($funct)));
                return $this->processFunction($funct, $result);
            } else {
                echo "Error: undefined function";
            }
        }
        return $this->num($str);
    }

    private function processFunction($funct, $result)
    {
        switch ($funct) {
            case "sin" :
                return new Result(sin(deg2rad($result->acc)), $result->rest);
                break;
            case "cos" :
                return new Result(cos(deg2rad($result->acc)), $result->rest);
                break;
            case "tan" :
                return new Result(tan(deg2rad($result->acc)), $result->rest);
                break;
            case "sqrt" :
                return new Result(sqrt($result->acc), $result->rest);
                break;
            default:
                echo "Error: undefined function";
        }
        return $result;
    }

    private function num($str)
    {
        $i = 0;
        $dot_cnt = 0;
        $negative = false;
        if ($str[0] == '-') {
            $negative = true;
            $str = substr($str, 1);
        }
        while ($i < strlen($str) && (is_numeric($str[$i]) || $str[$i] == '.')) {
            if ($str[$i] == '.' && ++$dot_cnt > 1) {
                throw new Exception("Number has two dots in a row '" . substr($str, 0, $i + 1) + "'");
            }
            $i++;
        }

        $part = substr($str, 0, $i);
        if ($negative) {
            $part *= -1;
        }
        $restPart = substr($str, $i);

        return new Result($part, $restPart);
    }
}

index.php

<?php
include "CalcParser.php";
include "Result.php";

$calc = new CalcParser();
$str = "2+2*2-cos(15+45)+2^(3+2)";
try {
    echo "Result: {$calc->parse($str)}";
} catch(Exception $e) {
    echo "Error while parsing '{$str}' with message: " . $e->getMessage();
}

Result.php

<?php
class Result
{
    public $acc;
    public $rest;

    public function result($part, $str)
    {
        $this->acc = $part;
        $this->rest = $str;
    }
}