┌ Warning: Module Groebner with build ID fafbfcfd-e38f-37d1-0000-0c1083141a1f is missing from the cache.
│ This may mean Groebner [0b43b601-686d-58a3-8a1c-6623616c7cd4] does not support precompilation but is imported by a module that does.
└ @ Base loading.jl:1793
┌ Warning: Module Symbolics with build ID fafbfcfd-011a-198d-0000-0c25e359d248 is missing from the cache.
│ This may mean Symbolics [0c5d862f-8b57-4792-8d23-62f2024744c7] does not support precompilation but is imported by a module that does.
└ @ Base loading.jl:1793
WARNING: using OrdinaryDiffEq.isconstant in module ModelingToolkit conflicts with an existing identifier.
WARNING: using OrdinaryDiffEq.islinear in module ModelingToolkit conflicts with an existing identifier.
┌ Error: Error during loading of extension SparseDiffToolsSymbolicsExt of SparseDiffTools, use `Base.retry_load_extensions()` to retry.
│   exception =
│    1-element ExceptionStack:
│    Declaring __precompile__(false) is not allowed in files that are being precompiled.
│    Stacktrace:
│      [1] _require(pkg::Base.PkgId, env::Nothing)
│        @ Base ./loading.jl:1825
│      [2] _require_prelocked(uuidkey::Base.PkgId, env::Nothing)
│        @ Base ./loading.jl:1660
│      [3] _require_prelocked(uuidkey::Base.PkgId)
│        @ Base ./loading.jl:1658
│      [4] run_extension_callbacks(extid::Base.ExtensionId)
│        @ Base ./loading.jl:1255
│      [5] run_extension_callbacks(pkgid::Base.PkgId)
│        @ Base ./loading.jl:1290
│      [6] run_package_callbacks(modkey::Base.PkgId)
│        @ Base ./loading.jl:1124
│      [7] _tryrequire_from_serialized(modkey::Base.PkgId, path::String, ocachepath::String, sourcepath::String, depmods::Vector{Any})
│        @ Base ./loading.jl:1398
│      [8] _require_search_from_serialized(pkg::Base.PkgId, sourcepath::String, build_id::UInt128)
│        @ Base ./loading.jl:1494
│      [9] _require(pkg::Base.PkgId, env::String)
│        @ Base ./loading.jl:1783
│     [10] _require_prelocked(uuidkey::Base.PkgId, env::String)
│        @ Base ./loading.jl:1660
│     [11] macro expansion
│        @ ./loading.jl:1648 [inlined]
│     [12] macro expansion
│        @ ./lock.jl:267 [inlined]
│     [13] require(into::Module, mod::Symbol)
│        @ Base ./loading.jl:1611
│     [14] include(mod::Module, _path::String)
│        @ Base ./Base.jl:457
│     [15] include(x::String)
│        @ ModelingToolkit ~/.julia/packages/ModelingToolkit/okjHa/src/ModelingToolkit.jl:4
│     [16] top-level scope
│        @ ~/.julia/packages/ModelingToolkit/okjHa/src/ModelingToolkit.jl:124
│     [17] include
│        @ ./Base.jl:457 [inlined]
│     [18] include_package_for_output(pkg::Base.PkgId, input::String, depot_path::Vector{String}, dl_load_path::Vector{String}, load_path::Vector{String}, concrete_deps::Vector{Pair{Base.PkgId, UInt128}}, source::String)
│        @ Base ./loading.jl:2049
│     [19] top-level scope
│        @ stdin:3
│     [20] eval
│        @ ./boot.jl:370 [inlined]
│     [21] include_string(mapexpr::typeof(identity), mod::Module, code::String, filename::String)
│        @ Base ./loading.jl:1903
│     [22] include_string
│        @ ./loading.jl:1913 [inlined]
│     [23] exec_options(opts::Base.JLOptions)
│        @ Base ./client.jl:305
│     [24] _start()
│        @ Base ./client.jl:522
└ @ Base loading.jl:1261
WARNING: using OrdinaryDiffEq.islinear in module ModelingToolkit conflicts with an existing identifier.
WARNING: using OrdinaryDiffEq.isconstant in module ModelingToolkit conflicts with an existing identifier.
┌ Info: 
└   FUNCTION_NAME = "find_identifiable_functions"
┌ Info: 
└   PROBLEM_NAME = "SEIR_1_io"
┌ Info: 
└   KWARGS = (with_states = true, strategy = (:normalforms, 2))
┌ Info: 
└   GLOBAL_ID = Symbol("(:normalforms, 2)_with_states")
┌ Warning: The call to compilecache failed to create a usable precompiled cache file for ModelingToolkit [961ee093-0014-501f-94e3-6117800e7a78]
│   exception = Required dependency Symbolics [0c5d862f-8b57-4792-8d23-62f2024744c7] failed to load from a cache file.
└ @ Base loading.jl:1818
[ Info: Summary of the model:
[ Info: State variables: S, E, I, R, Q
[ Info: Parameters: beta, gamma, v, psi
[ Info: Inputs: 
[ Info: Outputs: y1
[ Info: Summary of the model:
[ Info: State variables: x1, x2
[ Info: Parameters: a, b, d, c
[ Info: Inputs: 
[ Info: Outputs: y
[ Info: Computing IO-equations
┌ Info: Computed in 10.580514418 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 10.580514418
[ Info: Computing Wronskians
┌ Info: Computed in 11.512913351 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 11.512913351
[ Info: Dimensions of the Wronskians [15]
┌ Info: Ranks of the Wronskians computed in 0.033978314 seconds
│   :rank_time = :rank_time
└   rank_times = 0.033978314

⌜ # Computing specializations..  	 Time: 0:00:10[K
✓ # Computing specializations..  	 Time: 0:00:10[K

⌜ # Computing specializations..  	 Time: 0:00:04[K
✓ # Computing specializations..  	 Time: 0:00:04[K
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 4 for num. and 2 for den.
└ Points used: 48.
[ Info: Groebner basis computed in 13.316464652 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 4.620160681 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 8 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 4 fractions 4 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 5.702402407 seconds. Result: true
[ Info: Out of 18 initial generators there are 4 indepdendent
[ Info: The ranking of the new set of generators is 690
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 4 for num. and 2 for den.
└ Points used: 48.
[ Info: Groebner basis computed in 5.28268861 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 1.467603715 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 4 for num. and 3 for den.
│ Maximal number of interpolated terms are: 4 for num. and 3 for den.
└ Points used: 72.
[ Info: Groebner basis computed in 0.047463799 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.004834266 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 15 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (9 in total): Nemo.QQMPolyRingElem[beta, gamma, v, psi, S, E, I, R, Q]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 35
┌ Info: Final cleaning and simplification of generators. 
└ Out of 15 fractions 13 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 2.312039813 seconds. Result: true
[ Info: Out of 9 initial generators there are 8 indepdendent
[ Info: The ranking of the new set of generators is 59150
[ Info: The search for identifiable functions concluded in 76.810540272 seconds
[ Info: Processing SEIR_1_io
┌ Info: Averaging over 1 runs.
│ Using keyword arguments:
│ NamedTuple{(:with_states, :strategy), Tuple{Bool, Tuple{Symbol, Int64}}}
│ (with_states = true, strategy = (:normalforms, 2))
└ ID: (:normalforms, 2)_with_states
[ Info: Computing IO-equations
┌ Info: Computed in 0.013821427 seconds
│   :ioeq_time = :ioeq_time
└   ioeq_time = 0.013821427
[ Info: Computing Wronskians
┌ Info: Computed in 0.012568032 seconds
│   :wrnsk_time = :wrnsk_time
└   wrnsk_time = 0.012568032
[ Info: Dimensions of the Wronskians [15]
┌ Info: Ranks of the Wronskians computed in 3.8253e-5 seconds
│   :rank_time = :rank_time
└   rank_times = 3.8253e-5
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 4 for num. and 2 for den.
└ Points used: 48.
[ Info: Groebner basis computed in 0.023285556 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.063337333 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 8 rational functions
┌ Info: Final cleaning and simplification of generators. 
└ Out of 4 fractions 4 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.002686253 seconds. Result: true
[ Info: Out of 18 initial generators there are 4 indepdendent
[ Info: The ranking of the new set of generators is 690
[ Info: Simplifying identifiable functions
┌ Info: Computing parametric Groebner basis up to degrees (2, 2)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 2 for num. and 2 for den.
│ Maximal number of interpolated terms are: 4 for num. and 2 for den.
└ Points used: 48.
[ Info: Groebner basis computed in 0.031627232 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.003128036 seconds. Result: false
┌ Info: Computing parametric Groebner basis up to degrees (4, 4)
│ Ordering, input / target: degrevlex / InputOrdering
│ Rational interpolator: VanDerHoevenLecerf
│ Polynomial interpolator: PrimesBenOrTiwari
│ Estimate degrees: true
└ Assess correctness: false
┌ Info: Basis interpolated exponents summary:
│ Maximal interpolated degrees are: 4 for num. and 3 for den.
│ Maximal number of interpolated terms are: 4 for num. and 3 for den.
└ Points used: 72.
[ Info: Groebner basis computed in 0.092174798 seconds
[ Info: Checking two-sided inclusion modulo a prime
[ Info: Inclusion checked in 0.004175772 seconds. Result: true
[ Info: The coefficients of the Groebner basis are presented by 15 rational functions
┌ Info: Computing normal forms (probabilistic)
│ Variables (9 in total): Nemo.QQMPolyRingElem[beta, gamma, v, psi, S, E, I, R, Q]
│ Up to degree: 2
└ Modulo: Finite field of characteristic 1073741827
[ Info: Used specialization points: 35
┌ Info: Final cleaning and simplification of generators. 
└ Out of 15 fractions 13 are syntactically unique.
[ Info: Checking inclusion with probability 0.995
[ Info: Inclusion checked in 0.040439877 seconds. Result: true
[ Info: Out of 9 initial generators there are 8 indepdendent
[ Info: The ranking of the new set of generators is 59150
[ Info: The search for identifiable functions concluded in 0.554938256 seconds
┌ Info: Result is
│   result =
│    8-element Vector{AbstractAlgebra.Generic.Frac{Nemo.QQMPolyRingElem}}:
│     Q
│     gamma
│     I*psi
│     beta*I
│     beta*gamma - beta*v
│     v*psi - v - psi
│     (gamma*S)//(I*gamma*psi - I*gamma - I*psi)
└     (I*gamma*psi - I*psi + gamma*E)//(I*gamma*psi - I*gamma - I*psi)
