Tips about @inline

General Usage
3

In fact, after some modifications (in the input arguments) I found a much higher gain:

function M_to_E(e::Number, M::Number, tol::Number = 1e-10)
    # Compute the eccentric anomaly using the Newton-Raphson method.
    # ==============================================================

    # Make sure that M is in the interval [0,2π].
    M = mod(M,2π)

    # Initial guess.
    #
    # See [1, p. 75].
    E = (M > π) ? M - e : M + e

    sin_E, cos_E = sincos(E)

    # Newton-Raphson iterations.
    while ( abs(E - e*sin_E - M) > tol )
        E = E - (E - e*sin_E - M)/(1-e*cos_E)

        sin_E, cos_E = sincos(E)
    end

    # Return the eccentric anomaly in the interval [0, 2π].
    mod(E, 2π)
end

@inline function M_to_Ein(e::Number, M::Number, tol::Number = 1e-10)
    # Compute the eccentric anomaly using the Newton-Raphson method.
    # ==============================================================

    # Make sure that M is in the interval [0,2π].
    M = mod(M,2π)

    # Initial guess.
    #
    # See [1, p. 75].
    E = (M > π) ? M - e : M + e

    sin_E, cos_E = sincos(E)

    # Newton-Raphson iterations.
    while ( abs(E - e*sin_E - M) > tol )
        E = E - (E - e*sin_E - M)/(1-e*cos_E)

        sin_E, cos_E = sincos(E)
    end

    # Return the eccentric anomaly in the interval [0, 2π].
    mod(E, 2π)
end

using BenchmarkTools

@btime M_to_E(0.005, 100)
@btime M_to_Ein(0.005, 100)

  87.117 ns (0 allocations: 0 bytes)
  63.452 ns (0 allocations: 0 bytes)

Should I open an issue or is this expected?