Þ¥bonds€¬cell_results†Ù$0df4eb50-4d19-4a68-9b65-718a1e1d86dbŠ¦queued¤logs§running¦output†¤bodyÙ)gradient (generic function with 1 method)¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÙÃJq5!°persist_js_state·has_pluto_hook_features§cell_idÙ$0df4eb50-4d19-4a68-9b65-718a1e1d86db¹depends_on_disabled_cells§runtimeÎ ’{µpublished_object_keys¸depends_on_skipped_cells§erroredÂÙ$8a05420f-092f-4fcc-a8ec-54babdcdae72Š¦queued¤logs§running¦output†¤bodyÙ”
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¤mime©text/html¬rootassigneeÀ²last_run_timestampËAÙÃJq&,0°persist_js_state·has_pluto_hook_features§cell_idÙ$8a05420f-092f-4fcc-a8ec-54babdcdae72¹depends_on_disabled_cells§runtimeÎ:_vµpublished_object_keys¸depends_on_skipped_cells§erroredÂÙ$b14e3e44-6693-11ed-1536-d1ad4b7a28fbŠ¦queued¤logs‘ˆ¤lineÿ£msg’ÚÜPrecompiling Symbolics... 1438.5 ms ? DomainSets Info Given Symbolics was explicitly requested, output will be shown live  WARNING: Method definition isapprox(IntervalSets.AbstractInterval{T} where T, IntervalSets.AbstractInterval{T} where T) in module IntervalSets at /home/runner/.julia/packages/IntervalSets/kyCuf/src/IntervalSets.jl:296 overwritten in module DomainSets at /home/runner/.julia/packages/DomainSets/aafhp/src/domains/interval.jl:52. ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation. 1796.6 ms ? Symbolics WARNING: Method definition isapprox(IntervalSets.AbstractInterval{T} where T, IntervalSets.AbstractInterval{T} where T) in module IntervalSets at /home/runner/.julia/packages/IntervalSets/kyCuf/src/IntervalSets.jl:296 overwritten in module DomainSets at /home/runner/.julia/packages/DomainSets/aafhp/src/domains/interval.jl:52. ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation. Precompiling DomainSets... Info Given DomainSets was explicitly requested, output will be shown live  WARNING: Method definition isapprox(IntervalSets.AbstractInterval{T} where T, IntervalSets.AbstractInterval{T} where T) in module IntervalSets at /home/runner/.julia/packages/IntervalSets/kyCuf/src/IntervalSets.jl:296 overwritten in module DomainSets at /home/runner/.julia/packages/DomainSets/aafhp/src/domains/interval.jl:52. ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation. 1326.5 ms ? DomainSets WARNING: Method definition isapprox(IntervalSets.AbstractInterval{T} where T, IntervalSets.AbstractInterval{T} where T) in module IntervalSets at /home/runner/.julia/packages/IntervalSets/kyCuf/src/IntervalSets.jl:296 overwritten in module DomainSets at /home/runner/.julia/packages/DomainSets/aafhp/src/domains/interval.jl:52. ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation. ªtext/plain§cell_idÙ$b14e3e44-6693-11ed-1536-d1ad4b7a28fb¦kwargs¢id´PlutoRunner_d1acb81e¤fileÙP/home/runner/.julia/packages/Pluto/6smog/src/runner/PlutoRunner/src/io/stdout.jl¥group¦stdout¥level®LogLevel(-555)§running¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÙÃJpšPô°persist_js_state·has_pluto_hook_features§cell_idÙ$b14e3e44-6693-11ed-1536-d1ad4b7a28fb¹depends_on_disabled_cells§runtimeÏÝž·Tµpublished_object_keys¸depends_on_skipped_cells§erroredÂÙ$7632c395-beab-4d6d-bf2d-d34eaecfc1c1Š¦queued¤logs§running¦output†¤body¡3¤mimeªtext/plain¬rootassignee¡N²last_run_timestampËAÙÃJpø^î°persist_js_state·has_pluto_hook_features§cell_idÙ$7632c395-beab-4d6d-bf2d-d34eaecfc1c1¹depends_on_disabled_cells§runtimeÍmäµpublished_object_keys¸depends_on_skipped_cells§erroredÂÙ$3ba5a48d-6e12-4905-8e4a-fae8eba21191Š¦queued¤logs§running¦output†¤body ¤mimeªtext/plain¬rootassigneeÀ²last_run_timestampËAÙÃJq¿°persist_js_state·has_pluto_hook_features§cell_idÙ$3ba5a48d-6e12-4905-8e4a-fae8eba21191¹depends_on_disabled_cells§runtimeÎ üŸµpublished_object_keys¸depends_on_skipped_cells§erroredÂÙ$e8f5514c-888b-4a60-b82a-e2b9535606dfŠ¦queued¤logs§running¦output†¤bodyÙÝ

$$\begin{equation} \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} \right] \end{equation}$$

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Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package ForwardDiff [f6369f11]: │  ForwardDiff [f6369f11] log: │  ├─possible versions are: 0.9.0 - 0.10.36 or uninstalled â””  └─restricted to versions 0.10.33 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. 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Downloads v1.6.0 [7b1f6079] + FileWatching v1.11.0 [9fa8497b] + Future v1.11.0 [b77e0a4c] + InteractiveUtils v1.11.0 [b27032c2] + LibCURL v0.6.4 [76f85450] + LibGit2 v1.11.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.11.0 [56ddb016] + Logging v1.11.0 [d6f4376e] + Markdown v1.11.0 [ca575930] + NetworkOptions v1.2.0 [44cfe95a] + Pkg v1.11.0 [de0858da] + Printf v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.11.0 [4607b0f0] + SuiteSparse [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [8dfed614] + Test v1.11.0 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [deac9b47] + LibCURL_jll v8.6.0+0 [e37daf67] + LibGit2_jll v1.7.2+0 [29816b5a] + LibSSH2_jll v1.11.0+1 [c8ffd9c3] + MbedTLS_jll v2.28.6+0 [14a3606d] + MozillaCACerts_jll v2023.12.12 [4536629a] + OpenBLAS_jll v0.3.27+1 [05823500] + OpenLibm_jll v0.8.1+2 [bea87d4a] + SuiteSparse_jll v7.7.0+0 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.59.0+0 [3f19e933] + p7zip_jll v17.4.0+2  Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_IKkmgj` Precompiling project... 1391.5 ms ✓ ExprTools 1697.9 ms ✓ FunctionWrappers 2133.4 ms ✓ Combinatorics 1320.7 ms ✓ ADTypes 998.7 ms ✓ UnPack 1133.6 ms ✓ IntegerMathUtils 2517.7 ms ✓ InitialValues 2365.7 ms ✓ FillArrays 1452.3 ms ✓ InverseFunctions 1801.9 ms ✓ LambertW 1140.5 ms ✓ CommonSolve 1185.9 ms ✓ ArgCheck 1242.9 ms ✓ CompositeTypes 1065.4 ms ✓ AutoHashEquals 1419.9 ms ✓ EnumX 1058.1 ms ✓ CompositionsBase 1280.5 ms ✓ IntervalSets 1135.5 ms ✓ PtrArrays 1109.7 ms ✓ DefineSingletons 1118.4 ms ✓ IfElse 1184.6 ms ✓ TermInterface 1323.9 ms ✓ Adapt 1436.3 ms ✓ ConstructionBase 1151.6 ms ✓ Bijections 1651.3 ms ✓ SuiteSparse 2570.7 ms ✓ Baselet 1219.6 ms ✓ DiffResults 1428.5 ms ✓ CommonSubexpressions 1824.7 ms ✓ GroupsCore 4245.5 ms ✓ RandomExtensions 1032.1 ms ✓ TreeViews 1319.5 ms ✓ TruncatedStacktraces 1455.8 ms ✓ SymbolicIndexingInterface 1368.2 ms ✓ Rmath_jll 1632.2 ms ✓ OpenSpecFun_jll 3316.4 ms ✓ ChainRulesCore 2300.6 ms ✓ QuadGK 1267.2 ms ✓ RuntimeGeneratedFunctions 1172.0 ms ✓ FunctionWrappersWrappers 1439.9 ms ✓ Parameters 1849.3 ms ✓ Primes 1162.4 ms ✓ FillArrays → FillArraysStatisticsExt 8046.4 ms ✓ TimerOutputs 1786.6 ms ✓ FillArrays → FillArraysSparseArraysExt 13925.8 ms ✓ MutableArithmetics 1300.9 ms ✓ InverseFunctions → InverseFunctionsDatesExt 1559.6 ms ✓ InverseFunctions → InverseFunctionsTestExt 1127.4 ms ✓ LogExpFunctions → LogExpFunctionsInverseFunctionsExt 1163.5 ms ✓ CompositionsBase → CompositionsBaseInverseFunctionsExt 1153.5 ms ✓ IntervalSets → IntervalSetsRandomExt 1419.6 ms ✓ AliasTables 1447.1 ms ✓ Adapt → AdaptStaticArraysExt 1822.0 ms ✓ ConstructionBase → ConstructionBaseStaticArraysExt 2266.6 ms ✓ PDMats 2218.1 ms ✓ ArrayInterfaceCore 2118.1 ms ✓ Rmath 1679.3 ms ✓ ChainRulesCore → ChainRulesCoreSparseArraysExt 1751.0 ms ✓ StaticArrays → StaticArraysChainRulesCoreExt 2757.2 ms ✓ LogExpFunctions → LogExpFunctionsChainRulesCoreExt 1432.4 ms ✓ IntervalSets → IntervalSetsRecipesBaseExt 1305.8 ms ✓ IntervalSets → IntervalSetsStatisticsExt 1274.3 ms ✓ ConstructionBase → ConstructionBaseIntervalSetsExt 1266.9 ms ✓ Referenceables 1134.9 ms ✓ GPUArraysCore 1927.6 ms ✓ ArrayInterface 1428.4 ms ✓ FillArrays → FillArraysPDMatsExt 2046.1 ms ✓ ZygoteRules 4612.1 ms ✓ MultivariatePolynomials 5397.9 ms ✓ StatsBase 3004.1 ms ? DomainSets 5651.8 ms ✓ SpecialFunctions 21448.7 ms ✓ AbstractAlgebra 1581.7 ms ✓ ArrayInterface → ArrayInterfaceGPUArraysCoreExt 2798.0 ms ✓ Setfield 1663.8 ms ✓ ArrayInterface → ArrayInterfaceStaticArraysCoreExt 4557.0 ms ✓ Accessors 3302.2 ms ✓ DynamicPolynomials 3860.3 ms ✓ SpecialFunctions → SpecialFunctionsChainRulesCoreExt 2287.0 ms ✓ SplittablesBase 4142.7 ms ✓ Groebner 1335.3 ms ✓ Accessors → AccessorsDatesExt 1731.4 ms ✓ Accessors → AccessorsTestExt 2792.6 ms ✓ RecursiveArrayTools 1193.9 ms ✓ Accessors → AccessorsIntervalSetsExt 1855.4 ms ✓ DiffRules 2593.3 ms ✓ HypergeometricFunctions 1721.6 ms ✓ Accessors → AccessorsStaticArraysExt 2074.6 ms ✓ BangBang 4260.6 ms ✓ StatsFuns 3538.6 ms ✓ SciMLOperators 1909.6 ms ✓ BangBang → BangBangStaticArraysExt 1146.4 ms ✓ BangBang → BangBangChainRulesCoreExt 1351.9 ms ✓ BangBang → BangBangTablesExt 8277.6 ms ✓ ForwardDiff 1547.8 ms ✓ StatsFuns → StatsFunsInverseFunctionsExt 1912.8 ms ✓ SciMLOperators → SciMLOperatorsSparseArraysExt 1652.5 ms ✓ MicroCollections 3316.1 ms ✓ StatsFuns → StatsFunsChainRulesCoreExt 1629.1 ms ✓ SciMLOperators → SciMLOperatorsStaticArraysCoreExt 2405.5 ms ✓ ForwardDiff → ForwardDiffStaticArraysExt 5440.7 ms ✓ Transducers 2132.5 ms ✓ PreallocationTools 1544.4 ms ✓ Transducers → TransducersAdaptExt 10430.5 ms ✓ Distributions 3162.2 ms ✓ LabelledArrays 1593.0 ms ✓ Transducers → TransducersReferenceablesExt 2615.6 ms ✓ Distributions → DistributionsTestExt 13756.1 ms ✓ SciMLBase 2520.7 ms ✓ Distributions → DistributionsChainRulesCoreExt 1930.3 ms ✓ ThreadsX 2615.3 ms ✓ Metatheory 10722.2 ms ✓ SymbolicUtils 1760.7 ms ? Symbolics 111 dependencies successfully precompiled in 111 seconds. 65 already precompiled. 2 dependencies failed but may be precompilable after restarting julia 2 dependencies had output during precompilation: ┌ Symbolics │ WARNING: Method definition isapprox(IntervalSets.AbstractInterval{T} where T, IntervalSets.AbstractInterval{T} where T) in module IntervalSets at /home/runner/.julia/packages/IntervalSets/kyCuf/src/IntervalSets.jl:296 overwritten in module DomainSets at /home/runner/.julia/packages/DomainSets/aafhp/src/domains/interval.jl:52. │ ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation. â””  ┌ DomainSets │ WARNING: Method definition isapprox(IntervalSets.AbstractInterval{T} where T, IntervalSets.AbstractInterval{T} where T) in module IntervalSets at /home/runner/.julia/packages/IntervalSets/kyCuf/src/IntervalSets.jl:296 overwritten in module DomainSets at /home/runner/.julia/packages/DomainSets/aafhp/src/domains/interval.jl:52. │ ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation. â”” ªnbpkg_syncÚ“ Instantiating... === ┌ Warning: The active manifest file has dependencies that were resolved with a different julia version (1.8.0). Unexpected behavior may occur. â”” @ /tmp/jl_IKkmgj/Manifest.toml:0  Installed Calculus ─────────────────────── v0.5.1 Installed AutoHashEquals ───────────────── v0.2.0  Installed RandomExtensions ─────────────── v0.4.3  Installed DiffRules ────────────────────── v1.12.2  Installed DualNumbers ──────────────────── v0.6.8  Installed DynamicPolynomials ───────────── v0.4.5  Installed FunctionWrappersWrappers ─────── v0.1.1  Installed Transducers ──────────────────── v0.4.74  Installed TreeViews ────────────────────── v0.3.0  Installed MutableArithmetics ───────────── v1.0.5  Installed GPUArraysCore ────────────────── v0.1.2  Installed ArgCheck ─────────────────────── v2.3.0  Installed Rmath ────────────────────────── v0.7.0  Installed ArrayInterfaceStaticArrays ───── v0.1.5  Installed HypergeometricFunctions ──────── v0.3.11  Installed MultivariatePolynomials ──────── v0.4.6  Installed DiffResults ──────────────────── v1.1.0  Installed Latexify ─────────────────────── v0.15.17  Installed IntegerMathUtils ─────────────── v0.1.0  Installed IntervalSets ─────────────────── v0.7.3  Installed Tables ───────────────────────── v1.10.0  Installed Referenceables ───────────────── v0.1.2  Installed DomainSets ───────────────────── v0.5.14  Installed CompositeTypes ───────────────── v0.1.3  Installed IfElse ───────────────────────── v0.1.1  Installed Setfield ─────────────────────── v1.1.1  Installed Symbolics ────────────────────── v4.13.0  Installed PDMats ───────────────────────── v0.11.16  Installed StatsFuns ────────────────────── v1.0.1  Installed TermInterface ────────────────── v0.2.3  Installed Baselet ──────────────────────── v0.1.1  Installed SciMLBase ────────────────────── v1.72.0  Installed RuntimeGeneratedFunctions ────── v0.5.5  Installed DataAPI ──────────────────────── v1.13.0  Installed Primes ───────────────────────── v0.5.3  Installed TimerOutputs ─────────────────── v0.5.22  Installed Groebner ─────────────────────── v0.2.11  Installed SymbolicUtils ────────────────── v0.19.11  Installed StaticArrays ─────────────────── v1.5.9  Installed DefineSingletons ─────────────── v0.1.2  Installed StaticArraysCore ─────────────── v1.4.0  Installed ConstructionBase ─────────────── v1.4.1  Installed LabelledArrays ───────────────── v1.12.5  Installed RecipesBase ──────────────────── v1.3.1  Installed MicroCollections ─────────────── v0.1.3  Installed LambertW ─────────────────────── v0.4.5  Installed ArrayInterfaceCore ───────────── v0.1.26  Installed InitialValues ────────────────── v0.3.1  Installed Bijections ───────────────────── v0.1.4  Installed AbstractAlgebra ──────────────── v0.27.6  Installed ArrayInterfaceStaticArraysCore ─ v0.1.3  Installed EnumX ────────────────────────── v1.0.3  Installed Combinatorics ────────────────── v1.0.2  Installed FunctionWrappers ─────────────── v1.1.3  Installed SnoopPrecompile ──────────────── v1.0.1  Installed AbstractTrees ────────────────── v0.4.3  Installed ChainRulesCore ───────────────── v1.15.6  Installed QuadGK ───────────────────────── v2.6.0  Installed RecursiveArrayTools ──────────── v2.32.1  Installed ForwardDiff ──────────────────── v0.10.33  Installed Rmath_jll ────────────────────── v0.3.0+0  Installed ArrayInterface ───────────────── v6.0.24  Installed FillArrays ───────────────────── v0.13.5  Installed ThreadsX ─────────────────────── v0.1.11  Installed SplittablesBase ──────────────── v0.1.15  Installed CommonSubexpressions ─────────── v0.3.0  Installed ZygoteRules ──────────────────── v0.2.2  Installed Metatheory ───────────────────── v1.3.5  Installed PreallocationTools ───────────── v0.4.4  Installed Parameters ───────────────────── v0.12.3  Installed UnPack ───────────────────────── v1.0.2  Installed Static ───────────────────────── v0.8.2  Installed GroupsCore ───────────────────── v0.4.0  Installed Distributions ────────────────── v0.25.78  Installed BangBang ─────────────────────── v0.3.37  Installed DensityInterface ─────────────── v0.4.0  Installed ExprTools ────────────────────── v0.1.8  Installed Compat ───────────────────────── v4.3.0  Installed CompositionsBase ─────────────── v0.1.1  Installed CommonSolve ──────────────────── v0.2.3  Installed DocStringExtensions ──────────── v0.9.2  Resolving... === ┌ Info: Operation failed. Updating registries and trying again... │  exception = │  Unsatisfiable requirements detected for package ForwardDiff [f6369f11]: │  ForwardDiff [f6369f11] log: │  ├─possible versions are: 0.9.0 - 0.10.36 or uninstalled â””  └─restricted to versions 0.10.33 by an explicit requirement — no versions left Resolving... === ┌ Warning: Operation failed. Removing Manifest and trying again... │  exception = │  Unsatisfiable requirements detected for package ForwardDiff [f6369f11]: │  ForwardDiff [f6369f11] log: │  ├─possible versions are: 0.9.0 - 0.10.36 or uninstalled │  └─restricted to versions 0.10.33 by an explicit requirement — no versions left â”” @ Pluto ~/.julia/packages/Pluto/6smog/src/packages/Packages.jl:494 Resolving... ===  Installed Adapt ───────────────────── v3.7.2 Installed RandomExtensions ────────── v0.4.4  Installed FunctionWrappersWrappers ── v0.1.3  Installed DiffRules ───────────────── v1.15.1  Installed MutableArithmetics ──────── v1.5.1  Installed Transducers ─────────────── v0.4.84  Installed Rmath ───────────────────── v0.8.0  Installed IntegerMathUtils ────────── v0.1.2  Installed IntervalSets ────────────── v0.7.10  Installed HypergeometricFunctions ─── v0.3.24  Installed GPUArraysCore ───────────── v0.1.5  Installed DynamicPolynomials ──────── v0.4.6  Installed StatsFuns ───────────────── v1.3.2  Installed CompositeTypes ──────────── v0.1.4  Installed PtrArrays ───────────────── v1.2.1  Installed Referenceables ──────────── v0.1.3  Installed Accessors ───────────────── v0.1.38  Installed MultivariatePolynomials ─── v0.4.7  Installed RuntimeGeneratedFunctions ─ v0.5.13  Installed SpecialFunctions ────────── v2.4.0  Installed SciMLOperators ──────────── v0.3.10  Installed SciMLBase ───────────────── v1.98.1  Installed Primes ──────────────────── v0.5.6  Installed TimerOutputs ────────────── v0.5.25  Installed PDMats ──────────────────── v0.11.31  Installed TruncatedStacktraces ────── v1.4.0  Installed ArrayInterfaceCore ──────── v0.1.29  Installed MicroCollections ────────── v0.2.0  Installed ConstructionBase ────────── v1.5.6  Installed ADTypes ─────────────────── v0.2.7  Installed LabelledArrays ──────────── v1.15.1  Installed EnumX ───────────────────── v1.0.4  Installed ChainRulesCore ──────────── v1.25.0  Installed Bijections ──────────────── v0.1.9  Installed LambertW ────────────────── v0.4.6  Installed ForwardDiff ─────────────── v0.10.36  Installed FillArrays ──────────────── v1.13.0  Installed AbstractAlgebra ─────────── v0.27.10  Installed QuadGK ──────────────────── v2.11.1  Installed ThreadsX ────────────────── v0.1.12  Installed SymbolicIndexingInterface ─ v0.2.2  Installed RecursiveArrayTools ─────── v2.38.10  Installed ArrayInterface ──────────── v7.7.1  Installed Rmath_jll ───────────────── v0.5.1+0  Installed ZygoteRules ─────────────── v0.2.5  Installed CommonSubexpressions ────── v0.3.1  Installed AliasTables ─────────────── v1.1.3  Installed ExprTools ───────────────── v0.1.10  Installed PreallocationTools ──────── v0.4.24  Installed BangBang ────────────────── v0.4.3  Installed Distributions ───────────── v0.25.112  Installed InverseFunctions ────────── v0.1.17  Installed CompositionsBase ────────── v0.1.2  Installed GroupsCore ──────────────── v0.4.2  Installed CommonSolve ─────────────── v0.2.4  Installed StatsBase ───────────────── v0.34.3  Updating `/tmp/jl_IKkmgj/Project.toml`  ⌅ [0c5d862f] + Symbolics v4.13.0  Updating `/tmp/jl_IKkmgj/Manifest.toml` ⌅ [47edcb42] + ADTypes v0.2.7 ⌅ [c3fe647b] + AbstractAlgebra v0.27.10 [1520ce14] + AbstractTrees v0.4.5 [7d9f7c33] + Accessors v0.1.38 ⌅ [79e6a3ab] + Adapt v3.7.2 [66dad0bd] + AliasTables v1.1.3 [dce04be8] + ArgCheck v2.3.0 ⌃ [4fba245c] + ArrayInterface v7.7.1 [30b0a656] + ArrayInterfaceCore v0.1.29 ⌅ [15f4f7f2] + AutoHashEquals v0.2.0 [198e06fe] + BangBang v0.4.3 [9718e550] + Baselet v0.1.1 [e2ed5e7c] + Bijections v0.1.9 [d360d2e6] + ChainRulesCore v1.25.0 [861a8166] + Combinatorics v1.0.2 [38540f10] + CommonSolve v0.2.4 [bbf7d656] + CommonSubexpressions v0.3.1 [34da2185] + Compat v4.16.0 [b152e2b5] + CompositeTypes v0.1.4 [a33af91c] + CompositionsBase v0.1.2 ⌅ [187b0558] + ConstructionBase v1.5.6 [9a962f9c] + DataAPI v1.16.0 [864edb3b] + DataStructures v0.18.20 [e2d170a0] + DataValueInterfaces v1.0.0 [244e2a9f] + DefineSingletons v0.1.2 [163ba53b] + DiffResults v1.1.0 [b552c78f] + DiffRules v1.15.1 [31c24e10] + Distributions v0.25.112 [ffbed154] + DocStringExtensions v0.9.3 ⌅ [5b8099bc] + DomainSets v0.5.14 ⌅ [7c1d4256] + DynamicPolynomials v0.4.6 [4e289a0a] + EnumX v1.0.4 [e2ba6199] + ExprTools v0.1.10 [1a297f60] + FillArrays v1.13.0 [59287772] + Formatting v0.4.3 [f6369f11] + ForwardDiff v0.10.36 [069b7b12] + FunctionWrappers v1.1.3 [77dc65aa] + FunctionWrappersWrappers v0.1.3 ⌃ [46192b85] + GPUArraysCore v0.1.5 ⌅ [0b43b601] + Groebner v0.2.11 ⌅ [d5909c97] + GroupsCore v0.4.2 [34004b35] + HypergeometricFunctions v0.3.24 [615f187c] + IfElse v0.1.1 [22cec73e] + InitialValues v0.3.1 [18e54dd8] + IntegerMathUtils v0.1.2 [8197267c] + IntervalSets v0.7.10 [3587e190] + InverseFunctions v0.1.17 [92d709cd] + IrrationalConstants v0.2.2 [82899510] + IteratorInterfaceExtensions v1.0.0 [692b3bcd] + JLLWrappers v1.6.1 [b964fa9f] + LaTeXStrings v1.3.1 ⌃ [2ee39098] + LabelledArrays v1.15.1 ⌅ [984bce1d] + LambertW v0.4.6 ⌅ [23fbe1c1] + Latexify v0.15.21 [2ab3a3ac] + LogExpFunctions v0.3.28 [1914dd2f] + MacroTools v0.5.13 ⌅ [e9d8d322] + Metatheory v1.3.5 [128add7d] + MicroCollections v0.2.0 [e1d29d7a] + Missings v1.2.0 ⌅ [102ac46a] + MultivariatePolynomials v0.4.7 [d8a4904e] + MutableArithmetics v1.5.1 [77ba4419] + NaNMath v1.0.2 [bac558e1] + OrderedCollections v1.6.3 [90014a1f] + PDMats v0.11.31 [d96e819e] + Parameters v0.12.3 [d236fae5] + PreallocationTools v0.4.24 [aea7be01] + PrecompileTools v1.2.1 [21216c6a] + Preferences v1.4.3 [27ebfcd6] + Primes v0.5.6 [43287f4e] + PtrArrays v1.2.1 [1fd47b50] + QuadGK v2.11.1 [fb686558] + RandomExtensions v0.4.4 [3cdcf5f2] + RecipesBase v1.3.4 ⌅ [731186ca] + RecursiveArrayTools v2.38.10 [189a3867] + Reexport v1.2.2 [42d2dcc6] + Referenceables v0.1.3 [ae029012] + Requires v1.3.0 [79098fc4] + Rmath v0.8.0 [7e49a35a] + RuntimeGeneratedFunctions v0.5.13 ⌅ [0bca4576] + SciMLBase v1.98.1 [c0aeaf25] + SciMLOperators v0.3.10 [efcf1570] + Setfield v1.1.1 [66db9d55] + SnoopPrecompile v1.0.3 [a2af1166] + SortingAlgorithms v1.2.1 [276daf66] + SpecialFunctions v2.4.0 [171d559e] + SplittablesBase v0.1.15 [90137ffa] + StaticArrays v1.9.7 [1e83bf80] + StaticArraysCore v1.4.3 [10745b16] + Statistics v1.11.1 [82ae8749] + StatsAPI v1.7.0 [2913bbd2] + StatsBase v0.34.3 [4c63d2b9] + StatsFuns v1.3.2 ⌅ [2efcf032] + SymbolicIndexingInterface v0.2.2 ⌅ [d1185830] + SymbolicUtils v0.19.11 ⌅ [0c5d862f] + Symbolics v4.13.0 [3783bdb8] + TableTraits v1.0.1 [bd369af6] + Tables v1.12.0 ⌅ [8ea1fca8] + TermInterface v0.2.3 [ac1d9e8a] + ThreadsX v0.1.12 [a759f4b9] + TimerOutputs v0.5.25 [28d57a85] + Transducers v0.4.84 [a2a6695c] + TreeViews v0.3.0 [781d530d] + TruncatedStacktraces v1.4.0 [3a884ed6] + UnPack v1.0.2 [700de1a5] + ZygoteRules v0.2.5 [efe28fd5] + OpenSpecFun_jll v0.5.5+0 [f50d1b31] + Rmath_jll v0.5.1+0 [0dad84c5] + ArgTools v1.1.2 [56f22d72] + Artifacts v1.11.0 [2a0f44e3] + Base64 v1.11.0 [ade2ca70] + Dates v1.11.0 [8ba89e20] + Distributed v1.11.0 [f43a241f] + Downloads v1.6.0 [7b1f6079] + FileWatching v1.11.0 [9fa8497b] + Future v1.11.0 [b77e0a4c] + InteractiveUtils v1.11.0 [b27032c2] + LibCURL v0.6.4 [76f85450] + LibGit2 v1.11.0 [8f399da3] + Libdl v1.11.0 [37e2e46d] + LinearAlgebra v1.11.0 [56ddb016] + Logging v1.11.0 [d6f4376e] + Markdown v1.11.0 [ca575930] + NetworkOptions v1.2.0 [44cfe95a] + Pkg v1.11.0 [de0858da] + Printf v1.11.0 [9a3f8284] + Random v1.11.0 [ea8e919c] + SHA v0.7.0 [9e88b42a] + Serialization v1.11.0 [6462fe0b] + Sockets v1.11.0 [2f01184e] + SparseArrays v1.11.0 [4607b0f0] + SuiteSparse [fa267f1f] + TOML v1.0.3 [a4e569a6] + Tar v1.10.0 [8dfed614] + Test v1.11.0 [cf7118a7] + UUIDs v1.11.0 [4ec0a83e] + Unicode v1.11.0 [e66e0078] + CompilerSupportLibraries_jll v1.1.1+0 [deac9b47] + LibCURL_jll v8.6.0+0 [e37daf67] + LibGit2_jll v1.7.2+0 [29816b5a] + LibSSH2_jll v1.11.0+1 [c8ffd9c3] + MbedTLS_jll v2.28.6+0 [14a3606d] + MozillaCACerts_jll v2023.12.12 [4536629a] + OpenBLAS_jll v0.3.27+1 [05823500] + OpenLibm_jll v0.8.1+2 [bea87d4a] + SuiteSparse_jll v7.7.0+0 [83775a58] + Zlib_jll v1.2.13+1 [8e850b90] + libblastrampoline_jll v5.11.0+0 [8e850ede] + nghttp2_jll v1.59.0+0 [3f19e933] + p7zip_jll v17.4.0+2  Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m` Instantiating... === Precompiling... ===  Activating project at `/tmp/jl_IKkmgj` Precompiling project... 1391.5 ms ✓ ExprTools 1697.9 ms ✓ FunctionWrappers 2133.4 ms ✓ Combinatorics 1320.7 ms ✓ ADTypes 998.7 ms ✓ UnPack 1133.6 ms ✓ IntegerMathUtils 2517.7 ms ✓ InitialValues 2365.7 ms ✓ FillArrays 1452.3 ms ✓ InverseFunctions 1801.9 ms ✓ LambertW 1140.5 ms ✓ CommonSolve 1185.9 ms ✓ ArgCheck 1242.9 ms ✓ CompositeTypes 1065.4 ms ✓ AutoHashEquals 1419.9 ms ✓ EnumX 1058.1 ms ✓ CompositionsBase 1280.5 ms ✓ IntervalSets 1135.5 ms ✓ PtrArrays 1109.7 ms ✓ DefineSingletons 1118.4 ms ✓ IfElse 1184.6 ms ✓ TermInterface 1323.9 ms ✓ Adapt 1436.3 ms ✓ ConstructionBase 1151.6 ms ✓ Bijections 1651.3 ms ✓ SuiteSparse 2570.7 ms ✓ Baselet 1219.6 ms ✓ DiffResults 1428.5 ms ✓ CommonSubexpressions 1824.7 ms ✓ GroupsCore 4245.5 ms ✓ RandomExtensions 1032.1 ms ✓ TreeViews 1319.5 ms ✓ TruncatedStacktraces 1455.8 ms ✓ SymbolicIndexingInterface 1368.2 ms ✓ Rmath_jll 1632.2 ms ✓ OpenSpecFun_jll 3316.4 ms ✓ ChainRulesCore 2300.6 ms ✓ QuadGK 1267.2 ms ✓ RuntimeGeneratedFunctions 1172.0 ms ✓ FunctionWrappersWrappers 1439.9 ms ✓ Parameters 1849.3 ms ✓ Primes 1162.4 ms ✓ FillArrays → FillArraysStatisticsExt 8046.4 ms ✓ TimerOutputs 1786.6 ms ✓ FillArrays → FillArraysSparseArraysExt 13925.8 ms ✓ MutableArithmetics 1300.9 ms ✓ InverseFunctions → InverseFunctionsDatesExt 1559.6 ms ✓ InverseFunctions → InverseFunctionsTestExt 1127.4 ms ✓ LogExpFunctions → LogExpFunctionsInverseFunctionsExt 1163.5 ms ✓ CompositionsBase → CompositionsBaseInverseFunctionsExt 1153.5 ms ✓ IntervalSets → IntervalSetsRandomExt 1419.6 ms ✓ AliasTables 1447.1 ms ✓ Adapt → AdaptStaticArraysExt 1822.0 ms ✓ ConstructionBase → ConstructionBaseStaticArraysExt 2266.6 ms ✓ PDMats 2218.1 ms ✓ ArrayInterfaceCore 2118.1 ms ✓ Rmath 1679.3 ms ✓ ChainRulesCore → ChainRulesCoreSparseArraysExt 1751.0 ms ✓ StaticArrays → StaticArraysChainRulesCoreExt 2757.2 ms ✓ LogExpFunctions → LogExpFunctionsChainRulesCoreExt 1432.4 ms ✓ IntervalSets → IntervalSetsRecipesBaseExt 1305.8 ms ✓ IntervalSets → IntervalSetsStatisticsExt 1274.3 ms ✓ ConstructionBase → ConstructionBaseIntervalSetsExt 1266.9 ms ✓ Referenceables 1134.9 ms ✓ GPUArraysCore 1927.6 ms ✓ ArrayInterface 1428.4 ms ✓ FillArrays → FillArraysPDMatsExt 2046.1 ms ✓ ZygoteRules 4612.1 ms ✓ MultivariatePolynomials 5397.9 ms ✓ StatsBase 3004.1 ms ? DomainSets 5651.8 ms ✓ SpecialFunctions 21448.7 ms ✓ AbstractAlgebra 1581.7 ms ✓ ArrayInterface → ArrayInterfaceGPUArraysCoreExt 2798.0 ms ✓ Setfield 1663.8 ms ✓ ArrayInterface → ArrayInterfaceStaticArraysCoreExt 4557.0 ms ✓ Accessors 3302.2 ms ✓ DynamicPolynomials 3860.3 ms ✓ SpecialFunctions → SpecialFunctionsChainRulesCoreExt 2287.0 ms ✓ SplittablesBase 4142.7 ms ✓ Groebner 1335.3 ms ✓ Accessors → AccessorsDatesExt 1731.4 ms ✓ Accessors → AccessorsTestExt 2792.6 ms ✓ RecursiveArrayTools 1193.9 ms ✓ Accessors → AccessorsIntervalSetsExt 1855.4 ms ✓ DiffRules 2593.3 ms ✓ HypergeometricFunctions 1721.6 ms ✓ Accessors → AccessorsStaticArraysExt 2074.6 ms ✓ BangBang 4260.6 ms ✓ StatsFuns 3538.6 ms ✓ SciMLOperators 1909.6 ms ✓ BangBang → BangBangStaticArraysExt 1146.4 ms ✓ BangBang → BangBangChainRulesCoreExt 1351.9 ms ✓ BangBang → BangBangTablesExt 8277.6 ms ✓ ForwardDiff 1547.8 ms ✓ StatsFuns → StatsFunsInverseFunctionsExt 1912.8 ms ✓ SciMLOperators → SciMLOperatorsSparseArraysExt 1652.5 ms ✓ MicroCollections 3316.1 ms ✓ StatsFuns → StatsFunsChainRulesCoreExt 1629.1 ms ✓ SciMLOperators → SciMLOperatorsStaticArraysCoreExt 2405.5 ms ✓ ForwardDiff → ForwardDiffStaticArraysExt 5440.7 ms ✓ Transducers 2132.5 ms ✓ PreallocationTools 1544.4 ms ✓ Transducers → TransducersAdaptExt 10430.5 ms ✓ Distributions 3162.2 ms ✓ LabelledArrays 1593.0 ms ✓ Transducers → TransducersReferenceablesExt 2615.6 ms ✓ Distributions → DistributionsTestExt 13756.1 ms ✓ SciMLBase 2520.7 ms ✓ Distributions → DistributionsChainRulesCoreExt 1930.3 ms ✓ ThreadsX 2615.3 ms ✓ Metatheory 10722.2 ms ✓ SymbolicUtils 1760.7 ms ? Symbolics 111 dependencies successfully precompiled in 111 seconds. 65 already precompiled. 2 dependencies failed but may be precompilable after restarting julia 2 dependencies had output during precompilation: ┌ Symbolics │ WARNING: Method definition isapprox(IntervalSets.AbstractInterval{T} where T, IntervalSets.AbstractInterval{T} where T) in module IntervalSets at /home/runner/.julia/packages/IntervalSets/kyCuf/src/IntervalSets.jl:296 overwritten in module DomainSets at /home/runner/.julia/packages/DomainSets/aafhp/src/domains/interval.jl:52. │ ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation. â””  ┌ DomainSets │ WARNING: Method definition isapprox(IntervalSets.AbstractInterval{T} where T, IntervalSets.AbstractInterval{T} where T) in module IntervalSets at /home/runner/.julia/packages/IntervalSets/kyCuf/src/IntervalSets.jl:296 overwritten in module DomainSets at /home/runner/.julia/packages/DomainSets/aafhp/src/domains/interval.jl:52. │ ERROR: Method overwriting is not permitted during Module precompilation. Use `__precompile__(false)` to opt-out of precompilation. â”” §enabled÷restart_recommended_msgÀ´restart_required_msgÀ­busy_packages¶waiting_for_permissionÂÙ,waiting_for_permission_but_probably_disabled«cell_inputs†Ù$0df4eb50-4d19-4a68-9b65-718a1e1d86db„§cell_idÙ$0df4eb50-4d19-4a68-9b65-718a1e1d86db¤codeÙˆfunction gradient(f, X) vars = [X...] XX = reshape(vars, size(X)...) ∇ = Symbolics.gradient(f(XX), vars) reshape(∇, size(X)) end¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÂÙ$8a05420f-092f-4fcc-a8ec-54babdcdae72„§cell_idÙ$8a05420f-092f-4fcc-a8ec-54babdcdae72¤codeÙH""" Sums the trace of \$X\$. """ f(X) = sum(X[i,i] for i in 1:size(X,1))¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÂÙ$b14e3e44-6693-11ed-1536-d1ad4b7a28fb„§cell_idÙ$b14e3e44-6693-11ed-1536-d1ad4b7a28fb¤code¯using Symbolics¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÂÙ$7632c395-beab-4d6d-bf2d-d34eaecfc1c1„§cell_idÙ$7632c395-beab-4d6d-bf2d-d34eaecfc1c1¤code¥N = 3¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÃÙ$3ba5a48d-6e12-4905-8e4a-fae8eba21191„§cell_idÙ$3ba5a48d-6e12-4905-8e4a-fae8eba21191¤code¶@variables X[1:N,1:N];¨metadataƒ©show_logsèdisabled®skip_as_script«code_foldedÂÙ$e8f5514c-888b-4a60-b82a-e2b9535606df„§cell_idÙ$e8f5514c-888b-4a60-b82a-e2b9535606df¤code®gradient(f, X)¨metadataƒ©show_logsèdisabled®skip_as_script«code_folded«notebook_idÙ$bf2fb68e-8a37-11ef-22fb-cbb0b43beb42«in_temp_dir¨metadata€