EQ Fee Projection

    function _getEquilibriumFee(
        uint256 idealBalance,
        uint256 beforeBalance,
        uint256 amountSD
    ) internal pure returns (uint256, uint256) {
        require(beforeBalance >= amountSD, "Interswap: not enough balance");
        uint256 afterBalance = beforeBalance.sub(amountSD);

        uint256 safeZoneMax = idealBalance.mul(DELTA_1).div(DENOMINATOR);
        uint256 safeZoneMin = idealBalance.mul(DELTA_2).div(DENOMINATOR);

        uint256 eqFee = 0;
        uint256 protocolSubsidy = 0;

        if (afterBalance >= safeZoneMax) {
            // no fee zone, protocol subsidize it.
            eqFee = amountSD.mul(PROTOCOL_SUBSIDY).div(DENOMINATOR);
            protocolSubsidy = eqFee;
        } else if (afterBalance >= safeZoneMin) {
            // safe zone
            uint256 proxyBeforeBalance = beforeBalance < safeZoneMax
                ? beforeBalance
                : safeZoneMax;
            eqFee = _getTrapezoidArea(
                LAMBDA_1,
                0,
                safeZoneMax,
                safeZoneMin,
                proxyBeforeBalance,
                afterBalance
            );
        } else {
            // danger zone
            if (beforeBalance >= safeZoneMin) {
                // across 2 or 3 zones
                // part 1
                uint256 proxyBeforeBalance = beforeBalance < safeZoneMax
                    ? beforeBalance
                    : safeZoneMax;
                eqFee = eqFee.add(
                    _getTrapezoidArea(
                        LAMBDA_1,
                        0,
                        safeZoneMax,
                        safeZoneMin,
                        proxyBeforeBalance,
                        safeZoneMin
                    )
                );
                // part 2
                eqFee = eqFee.add(
                    _getTrapezoidArea(
                        LAMBDA_2,
                        LAMBDA_1,
                        safeZoneMin,
                        0,
                        safeZoneMin,
                        afterBalance
                    )
                );
            } else {
                // only in danger zone
                // part 2 only
                eqFee = eqFee.add(
                    _getTrapezoidArea(
                        LAMBDA_2,
                        LAMBDA_1,
                        safeZoneMin,
                        0,
                        beforeBalance,
                        afterBalance
                    )
                );
            }
        }
        return (eqFee, protocolSubsidy);
    }