private static function nfx( $expr ) {

			$index = 0;
			$stack = new WC_Eval_Math_Stack;
			$output = array(); // postfix form of expression, to be passed to pfx()
			$expr = trim( $expr );

			$ops   = array( '+', '-', '*', '/', '^', '_' );
			$ops_r = array( '+' => 0, '-' => 0, '*' => 0, '/' => 0, '^' => 1 ); // right-associative operator?
			$ops_p = array( '+' => 0, '-' => 0, '*' => 1, '/' => 1, '_' => 1, '^' => 2 ); // operator precedence

			$expecting_op = false; // we use this in syntax-checking the expression
			// and determining when a - is a negation
			if ( preg_match( "/[^\w\s+*^\/()\.,-]/", $expr, $matches ) ) { // make sure the characters are all good
				return self::trigger( "illegal character '{$matches[0]}'" );
			}

			while ( 1 ) { // 1 Infinite Loop ;)
				$op = substr( $expr, $index, 1 ); // get the first character at the current index
				// find out if we're currently at the beginning of a number/variable/function/parenthesis/operand
				$ex = preg_match( '/^([A-Za-z]\w*\(?|\d+(?:\.\d*)?|\.\d+|\()/', substr( $expr, $index ), $match );
				// ===============
				if ( '-' === $op and ! $expecting_op ) { // is it a negation instead of a minus?
					$stack->push( '_' ); // put a negation on the stack
					$index++;
				} elseif ( '_' === $op ) { // we have to explicitly deny this, because it's legal on the stack
					return self::trigger( "illegal character '_'" ); // but not in the input expression
					// ===============
				} elseif ( ( in_array( $op, $ops ) or $ex ) and $expecting_op ) { // are we putting an operator on the stack?
					if ( $ex ) { // are we expecting an operator but have a number/variable/function/opening parenthesis?
						$op = '*';
						$index--; // it's an implicit multiplication
					}
					// heart of the algorithm:
					while ( $stack->count > 0 and ( $o2 = $stack->last() ) and in_array( $o2, $ops ) and ( $ops_r[ $op ] ? $ops_p[ $op ] < $ops_p[ $o2 ] : $ops_p[ $op ] <= $ops_p[ $o2 ] ) ) {
						$output[] = $stack->pop(); // pop stuff off the stack into the output
					}
					// many thanks: https://en.wikipedia.org/wiki/Reverse_Polish_notation#The_algorithm_in_detail
					$stack->push( $op ); // finally put OUR operator onto the stack
					$index++;
					$expecting_op = false;
					// ===============
				} elseif ( ')' === $op && $expecting_op ) { // ready to close a parenthesis?
					while ( ( $o2 = $stack->pop() ) != '(' ) { // pop off the stack back to the last (
						if ( is_null( $o2 ) ) {
							return self::trigger( "unexpected ')'" );
						} else {
							$output[] = $o2;
						}
					}
					if ( preg_match( "/^([A-Za-z]\w*)\($/", $stack->last( 2 ), $matches ) ) { // did we just close a function?
						$fnn = $matches[1]; // get the function name
						$arg_count = $stack->pop(); // see how many arguments there were (cleverly stored on the stack, thank you)
						$output[] = $stack->pop(); // pop the function and push onto the output
						if ( in_array( $fnn, self::$fb ) ) { // check the argument count
							if ( $arg_count > 1 ) {
								return self::trigger( "too many arguments ($arg_count given, 1 expected)" );
							}
						} elseif ( array_key_exists( $fnn, self::$f ) ) {
							if ( count( self::$f[ $fnn ]['args'] ) != $arg_count ) {
								return self::trigger( "wrong number of arguments ($arg_count given, " . count( self::$f[ $fnn ]['args'] ) . " expected)" );
							}
						} else { // did we somehow push a non-function on the stack? this should never happen
							return self::trigger( "internal error" );
						}
					}
					$index++;
					// ===============
				} elseif ( ',' === $op and $expecting_op ) { // did we just finish a function argument?
					while ( ( $o2 = $stack->pop() ) != '(' ) {
						if ( is_null( $o2 ) ) {
							return self::trigger( "unexpected ','" ); // oops, never had a (
						} else {
							$output[] = $o2; // pop the argument expression stuff and push onto the output
						}
					}
					// make sure there was a function
					if ( ! preg_match( "/^([A-Za-z]\w*)\($/", $stack->last( 2 ), $matches ) ) {
						return self::trigger( "unexpected ','" );
					}
					$stack->push( $stack->pop() + 1 ); // increment the argument count
					$stack->push( '(' ); // put the ( back on, we'll need to pop back to it again
					$index++;
					$expecting_op = false;
					// ===============
				} elseif ( '(' === $op and ! $expecting_op ) {
					$stack->push( '(' ); // that was easy
					$index++;
					// ===============
				} elseif ( $ex and ! $expecting_op ) { // do we now have a function/variable/number?
					$expecting_op = true;
					$val = $match[1];
					if ( preg_match( "/^([A-Za-z]\w*)\($/", $val, $matches ) ) { // may be func, or variable w/ implicit multiplication against parentheses...
						if ( in_array( $matches[1], self::$fb ) or array_key_exists( $matches[1], self::$f ) ) { // it's a func
							$stack->push( $val );
							$stack->push( 1 );
							$stack->push( '(' );
							$expecting_op = false;
						} else { // it's a var w/ implicit multiplication
							$val = $matches[1];
							$output[] = $val;
						}
					} else { // it's a plain old var or num
						$output[] = $val;
					}
					$index += strlen( $val );
					// ===============
				} elseif ( ')' === $op ) { // miscellaneous error checking
					return self::trigger( "unexpected ')'" );
				} elseif ( in_array( $op, $ops ) and ! $expecting_op ) {
					return self::trigger( "unexpected operator '$op'" );
				} else { // I don't even want to know what you did to get here
					return self::trigger( "an unexpected error occurred" );
				}
				if ( strlen( $expr ) == $index ) {
					if ( in_array( $op, $ops ) ) { // did we end with an operator? bad.
						return self::trigger( "operator '$op' lacks operand" );
					} else {
						break;
					}
				}
				while ( substr( $expr, $index, 1 ) == ' ' ) { // step the index past whitespace (pretty much turns whitespace
					$index++;                             // into implicit multiplication if no operator is there)
				}
			}
			while ( ! is_null( $op = $stack->pop() ) ) { // pop everything off the stack and push onto output
				if ( '(' === $op ) {
					return self::trigger( "expecting ')'" ); // if there are (s on the stack, ()s were unbalanced
				}
				$output[] = $op;
			}
			return $output;
		}