Types error: invalid operands to binary expression ('double' and 'state_type')

Reproduce the provided C++ example and inspect boost/numeric/odeint/algebra/default_operations.hpp around line 443, especially the controlled-step error expression. Trace the types of m_eps_abs, m_eps_rel, and get_unit_value(...) to determine whether the formula supports vector_space_algebra. Done means the example no longer requires scalar-plus-state_type solely to satisfy the error estimate, with the behavior verified.

I defined new state type as

struct state_type { double x; };

and vector space operators

state_type operator * (const state_type &a, double k) { return {a.x * k}; }
state_type operator * (double k, const state_type &a) { return {a.x * k}; }
state_type operator + (const state_type &a, const state_type &b) { return {a.x + b.x}; }
state_type operator - (const state_type &a, const state_type &b) { return {a.x - b.x}; }
state_type operator / (const state_type &a, const state_type &b) { return {a.x / b.x}; }
state_type abs(state_type const& v) { return {fabs(v.x)}; }

The main function is

int main()
{
    state_type x0 {1.};
    double t0 = 0, t1 = 1, dt = 1e-3;
    using Stepper = runge_kutta_dopri5<state_type, double, state_type, double, vector_space_algebra>;
    auto f = [](state_type const& x, state_type& dx, double t) {
        dx = x;
    };
    integrate_adaptive(make_controlled<Stepper>(1e-10, 1e-10), f, x0, t0, t1, dt);
}

During compilation I am getting the error

/usr/include/boost/numeric/odeint/algebra/default_operations.hpp:443:76: error: invalid operands to binary expression ('double' and 'state_type')
[build] set_unit_value( t3 , abs( get_unit_value( t3 ) ) / ( m_eps_abs + m_eps_rel * ( m_a_x * abs( get_unit_value( t1 ) ) + m_a_dxdt * abs( get_unit_value( t2 ) ) ) ) );

If I add the requested operator

state_type operator + (double k, const state_type &a) { return {a.x + k}; }

the compilation works well. It seems that the formula

set_unit_value( t3 , abs( get_unit_value( t3 ) ) / ( m_eps_abs + m_eps_rel * ( m_a_x * abs( get_unit_value( t1 ) ) + m_a_dxdt * abs( get_unit_value( t2 ) ) ) ) );

is wrong, or type of m_eps_abs is wrong. In a vector space there must not be operator + between elements of state_type and and coefficients. Moreover the operator / between state_type elements is questionable.