double seconds = nanos / (double) TimeUnit.SECONDS.toNanos(1); // Convert to fractional seconds
            double bytesPerSecond = contentLength / seconds;
            message.append(" at ");
            format.formatRate(message, bytesPerSecond);
        }

        message.append(')').resetStyle();
        out.println(message);
    }

     */
    protected StringBuilder appendTimestamp(final StringBuilder buf) {
        final SystemHelper systemHelper = ComponentUtil.getSystemHelper();
        append(buf, "timestamp", () -> FessFunctions.formatDate(systemHelper.getCurrentTime()));
        return buf;
    }

    /**
     * Appends exception information to the buffer.
     *
     * @param buf the string buffer to append to

     *
     * @param date the date to format
     * @return formatted date string, or empty string if date is null
     */
    public static String formatDate(final Date date) {
        if (date == null) {
            return StringUtil.EMPTY;
        }
        final SimpleDateFormat sdf = new SimpleDateFormat(Constants.ISO_DATETIME_FORMAT);

                    throw new InvalidAccessTokenException("invalid_token",
                            "The token is expired(" + FessFunctions.formatDate(FessFunctions.date(expiredTime)) + ").");
                }
                stream(accessToken.getPermissions()).of(stream -> stream.forEach(permissionSet::add));

        format(builder, size, null, false);
    }

    public void format(MessageBuilder builder, long size, ScaleUnit unit) {
        format(builder, size, unit, false);
    }

    public void formatRate(MessageBuilder builder, double rate) {
        // Handle invalid rates gracefully (including negative values)
        if (Double.isNaN(rate) || Double.isInfinite(rate) || rate < 0) {
            builder.append("? B/s");

        final StringBuilder buf = new StringBuilder(1000);
        buf.append("url:").append(getUrl(keyObj));
        buf.append('\t');
        buf.append("time:").append(FessFunctions.formatDate(new Date(time)));
        return buf;
    }

    /**
     * Extracts the URL string from a crawler object for logging purposes.
     *
     * @param keyObj the crawler object to extract URL from

                                final Date dt = FessFunctions.parseDate(values[0], dateFormat);
                                if (dt != null) {
                                    dataMap.put(mapping.getValue1(), FessFunctions.formatDate(dt));
                                } else {
                                    logger.warn("Failed to parse date mapping: {}", mapping);
                                }
                            } else {

                    value = list.stream().collect(Collectors.joining("\n"));
                }
            } else if (dateFieldSet.contains(key)) {
                value = FessFunctions.formatDate((Date) value);
            } else if (integerFieldSet.contains(key) || longFieldSet.contains(key) || floatFieldSet.contains(key)
                    || doubleFieldSet.contains(key)) {
                value = value.toString();