[Merged by Bors] - refactor(Analysis): golf Mathlib/Analysis/SpecialFunctions/Log/Monotone

[yuanyi-350]

• refactors Log/Monotone by extracting the repeated exp (1 / a) ≤ z to exp 1 ≤ z ^ a bound into a shared local helper
• reuses that helper in log_div_self_rpow_antitoneOn to shorten the final call to log_div_self_antitoneOn

Extracted from #37968

[github-actions]

PR summary ee3a5404e5

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

No declarations were harmed in the making of this PR! 🐙

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[yuanyi-350]

I ran a profiler comparison for the changed declarations in this PR.

Results (seconds):

• Real.log_div_self_rpow_antitoneOn: 0.147811 -> 0.136405 (-7.72%)

Overall:

• The changed declaration elaborates slightly faster after the refactor.

[yuanyi-350]

!bench

[leanprover-radar]

Benchmark results for 63f8ec6 against ee3a540 are in. No significant results found. @yuanyi-350

• 🟥 build//instructions: +7.4G (+0.00%)

No significant changes detected.

[themathqueen]

Thanks!

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by themathqueen.

[j-loreaux]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Build
• ci (staging) / Lint style
• ci (staging) / Post-Build Step
• ci (staging) / Post-CI job

[SnirBroshi]

FYI this PR might be reverted by #37717 (but might not be). Do you have any suggestions, perhaps these two golfs could combine to create an even better golf?

Regardless it might be interesting as a case of an LLM and a human golfing the same theorem and arriving at the same length (ignoring the double nth_rw keyhole golf) in different ways.