Test failure in `LinearAlgebra/lapack.jl` in comparing `LAPACK.sytri!` to `inv` for an almost-symmetric matrix

[jishnub]

In the aarch64-apple-darwin job https://buildkite.com/julialang/julia-master/builds/41270#0192a51c-3afb-4a6f-a53f-3c3b9f537ed4, there is

The global RNG seed was 0xf3fab14bb37f52ec47cdcf1f85e908bd.
Error in testset LinearAlgebra/lapack:
Test Failed at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-HL2F7YQ3XH.0/build/default-honeycrisp-HL2F7YQ3XH-0/julialang/julia-master/julia-d3cd3f4a3a/share/julia/stdlib/v1.12/LinearAlgebra/test/lapack.jl:441
  Expression: ≈(triu(inv(A)), triu(LAPACK.sytri!('U', B, ipiv)), rtol = eps(cond(A)))
   Evaluated: Float32[1.1648309 0.25645927 … -0.82741505 0.3340336; 0.0 -0.6714291 … 0.5142702 -0.2888328; … ; 0.0 0.0 … 0.086971946 0.14950116; 0.0 0.0 … 0.0 0.38216618] ≈ Float32[1.164831 0.25645974 … -0.82741505 0.3340336; 0.0 -0.6714287 … 0.5142697 -0.2888328; … ; 0.0 0.0 … 0.08697438 0.1495005; 0.0 0.0 … 0.0 0.3821662] (rtol=1.9073486e-6)
ERROR: LoadError: Test run finished with errors
in expression starting at /Users/julia/.julia/scratchspaces/a66863c6-20e8-4ff4-8a62-49f30b1f605e/agent-cache/default-honeycrisp-HL2F7YQ3XH.0/build/default-honeycrisp-HL2F7YQ3XH-0/julialang/julia-master/julia-d3cd3f4a3a/share/julia/test/runtests.jl:100
ERROR: A test has failed. Please submit a bug report (https://github.com/JuliaLang/julia/issues)
including error messages above and the output of versioninfo():
Julia Version 1.12.0-DEV.1426
Commit d3cd3f4a3aa (2024-10-19 14:08 UTC)
Build Info:
  Official https://julialang.org release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 8 × Apple M2
  WORD_SIZE: 64
  LLVM: libLLVM-18.1.7 (ORCJIT, apple-m2)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)
Environment:
  JULIA_INSTALL_DIR = julia-d3cd3f4a3a
  JULIA_SHELL = /bin/bash
  JULIA_CPU_TARGET = generic;apple-m1,clone_all
  JULIA_TEST_MAXRSS_MB = 3800
  JULIA_CMD_FOR_TESTS = julia-d3cd3f4a3a/bin/julia .buildkite/utilities/timeout.jl julia-d3cd3f4a3a/bin/julia
  JULIA_TEST_VERBOSE_LOGS_DIR = /private/var/tmp/agent-tempdirs/default-honeycrisp-HL2F7YQ3XH.0/tmp/jl_JXug2a
  JULIA_IMAGE_THREADS = 4
  JULIA_BINARYDIST_FILENAME = julia-d3cd3f4a3a-macaarch64
  JULIA_CPU_THREADS = 4
  JULIA_NUM_THREADS = 1
  JULIA_VERSION = 1.12.0-DEV
  JULIA_TEST_IS_BASE_CI = true

Unfortunately, I am not being able to replicate it locally using the same seed but on a different platform (x86_64-linux-gnu). The issue seems to be related to floating-point accuracy.