bool CustomIntegratorUtilities::usesVariable(const Lepton::ExpressionTreeNode& node, const string& variable) {
    const Lepton::Operation& op = node.getOperation();
    if (op.getId() == Lepton::Operation::VARIABLE && op.getName() == variable)
        return true;
    for (int i = 0; i < (int) node.getChildren().size(); i++)
        if (usesVariable(node.getChildren()[i], variable))
            return true;
    return false;
}
void CustomIntegratorUtilities::validateDerivatives(const Lepton::ExpressionTreeNode& node, const vector<string>& derivNames) {
    const Lepton::Operation& op = node.getOperation();
    if (op.getId() == Lepton::Operation::CUSTOM && op.getName() == "deriv") {
        const Lepton::Operation& child = node.getChildren()[0].getOperation();
        if (child.getId() != Lepton::Operation::VARIABLE || find(derivNames.begin(), derivNames.end(), child.getName()) == derivNames.end())
            throw OpenMMException("The first argument to deriv() must be an energy variable");
        if (node.getChildren()[1].getOperation().getId() != Lepton::Operation::VARIABLE)
            throw OpenMMException("The second argument to deriv() must be a context parameter");
    }
    else {
        for (int i = 0; i < node.getChildren().size(); i++)
            validateDerivatives(node.getChildren()[i], derivNames);
    }
}