Trying to make sense of the InnoDB log file stats
37000 tables, itself, is really bad.  Each table is implemented as 1 to 3 files on disk.  This leads to a burden on the OS.  Also, there are various caches (controlled by multiple settings, such as table_open_cache) that could overflow, and probably run inefficiently if made large.

0.56 log i/o's/second sounds trivial.  A spinning drive can (Rule of Thumb) do 10 IOPs.  So the log I/O is only 5% of the available bandwidth.  (Better on SSDs.)

It is very rare that a performance problem is traced to a poorly sized log file (either too large or too small).  (Or maybe I am too dumb in this area?)


Innodb_os_log_written / (Uptime / 3600) / innodb_log_files_in_group / innodb_log_file_size
I recommend 0.2 to 2.5.  It means "Minutes between InnoDB log rotations".
Innodb_log_waits / Innodb_log_writes
I recommend 0 to 0.1%.  If out of range, Increase innodb_log_buffer_size.
innodb_log_files_in_group should be 2.  Larger values are possible but they have been tentatively linked to bad performance.


If you would like further tuning and performance critique, see this .

Analysis of VARIABLES and GLOBAL STATUS

The Important Issues

Apropros the original question:  ( Uptime / 60 * innodb_log_file_size / Innodb_os_log_written ) = 144 minutes.  This is reasonably close to the optimal of 1 hour so that I suggest that your log settings are fine.
(One must stray quite far from the optimal to get into trouble.)

innodb_buffer_pool_size = 87G is probably OK for 126G of RAM, despite what the analysis below says. 

innodb_log_buffer_size -- increase from 8M to, say, 100M.
This may be one of the more important recommendations, but I can't say how important.

Your code seems to be deleting almost as fast as it inserts; what is going on?
In particular, using MySQL as a "queue" has various problems.

Innodb_row_lock_time_avg = 23s -- This is extremely high, and it worries me, but I don't know what to recommend.

Max_used_connections = 158 while max_connections = 1000.
I recommend lowering `max_connections to 500 as a way of preventing a burst of connections from blowing out RAM.

What framework are you using?  It is doing some things, such as SHOW CREATE TABLE and SHOW VARIABLES, that unnecessarily burden the processing.

Suggest increasing bulk_insert_buffer_size from 8M to 32M since you have so much RAM.

Here comes another "more important" recommendation:
161 tmp tables created per second!  Let's look at some of the slower queries.
By adding composite indexes and/or reformulating the queries, performance
may be significantly improved.
See my comments on using the Slowlog to identify such queries in http://mysql.rjweb.org/doc.php/mysql_analysis .
(If you like, start a new Q&amp;A to discuss one of the queries.)

Currently max_tmp_tables = 32 and tmp_table_size = 1G.  It might be better to have max_tmp_tables = 100 and tmp_table_size = 100M.  (Even better would be to work on avoiding some of the tmp tables.)

Of those tmp tables, 1.1/sec are on disk.  This is in spite of the huge values for tmp_table_size and max_heap_table_size of 1GB each.  (Becuase you have so much RAM, I do not have a good argument for lowering those values.)

8.8% of SELECTs are "full joins".  And 146 full table scans/sec.  This may or may not be significant.  I'll wait until such shows up in the slowlog.  When a table has just a few rows; the alarming metrics don't matter.  When a table has lots of rows, they beg for better indexing, etc.

Do you use Cursors in your Stored Routines?

(Some STATUS values confirm that table_open_cache = 20000 is probably OK.)

Be aware that init_connect = SET NAMES utf8 is ignore when connecting as root (or other SUPER user).

innodb_large_prefix is removed (as obsolete) in 5.7.7.  You should remove it when you upgrade.

Why are you running with tx_isolation = READ-COMMITTED?

Details and other observations

mysqld has been running 15 days.  Percona 5.6.32.  126GB of RAM.

( table_open_cache ) = 20,000 -- Number of table descriptors to cache 
-- Several hundred is usually good.  (We have alredy discussed this.)

( innodb_buffer_pool_size / innodb_buffer_pool_instances ) = 87040M / 16 = 5440MB -- Size of each buffer_pool instance.
-- An instance should be at least 1GB. In very large RAM, have 16 instances.

( innodb_max_dirty_pages_pct ) = 60 -- When buffer_pool starts flushing to disk 
-- Are you experimenting?

( Innodb_os_log_written ) = 324,963,533,824 / 1314928 = 247134 /sec -- This is an indicator of how busy InnoDB is.
-- Very busy InnoDB.

( Innodb_log_waits / Innodb_log_writes ) = 15,857 / 216746 = 7.3% -- Frequency of needing to wait to write to log
-- Increase innodb_log_buffer_size.

( Innodb_rows_deleted / Innodb_rows_inserted ) = 116,716,394 / 143158563 = 0.815 -- Churn
-- "Don't queue it, just do it." (If MySQL is being used as a queue.)

( Innodb_row_lock_time_avg ) = 23,465 -- Avg time to lock a row (millisec)

( max_tmp_tables * tmp_table_size / _ram ) = 32 * 1024M / 129024M = 25.4% -- Pct of RAM potentially consumed by tmp tables
-- Swapping is bad; decrease max_tmp_tables and/or tmp_table_size. Or lower innodb_buffer_pool_size.

( (Com_show_create_table + Com_show_fields) / Questions ) = (468502 + 509251) / 40574407 = 2.4% -- Naughty framework -- spending a lot of effort rediscovering the schema.
-- Complain to the 3rd party vendor.

( bulk_insert_buffer_size / _ram ) = 8M / 129024M = 0.01% -- Buffer for multi-row INSERTs and LOAD DATA
-- Too big could threaten RAM size. Too small could hinder such operations.

( (Queries-Questions)/Queries ) = (348646859-40574407)/348646859 = 88.4% -- Fraction of queries that are inside Stored Routines.
-- (Not bad if high; but it impacts the validity of some other conclusions.)

( Created_tmp_tables ) = 212,256,483 / 1314928 = 161 /sec -- Frequency of creating "temp" tables as part of complex SELECTs. 

( Created_tmp_disk_tables ) = 1,461,983 / 1314928 = 1.1 /sec -- Frequency of creating disk "temp" tables as part of complex SELECTs
-- increase tmp_table_size and max_heap_table_size. 
Check the rules for temp tables on when MEMORY is used instead of MyISAM. Perhaps minor schema or query changes can avoid MyISAM.
Better indexes and reformulation of queries are more likely to help.

( tmp_table_size ) = 1024M -- Limit on size of MEMORY temp tables used to support a SELECT 
-- Decrease tmp_table_size to avoid running out of RAM. Perhaps no more than 64M.

( Select_full_join ) = 1,396,307 / 1314928 = 1.1 /sec -- joins without index
-- Add suitable index(es) to tables used in JOINs.

( Select_full_join / Com_select ) = 1,396,307 / 15893105 = 8.8% -- % of selects that are indexless join
-- Add suitable index(es) to tables used in JOINs.

( Select_scan ) = 192,567,904 / 1314928 = 146 /sec -- full table scans 
-- Add indexes / optimize queries (unless they are tiny tables)

( Select_scan / Com_select ) = 192,567,904 / 15893105 = 1211.6% -- % of selects doing full table scan. (May be fooled by Stored Routines.)
-- Add indexes / optimize queries

( ( Com_stmt_prepare - Com_stmt_close ) / ( Com_stmt_prepare + Com_stmt_close ) ) = ( 374362 - 360454 ) / ( 374362 + 360454 ) = 1.9% -- Are you closing your prepared statements?
-- Add Closes.

( Connections ) = 7,761,574 / 1314928 = 5.9 /sec -- Connections 
-- Increase wait_timeout; use pooling?

Extremes The following are noted, mostly without comment:

Abnormally small:

Com_commit = 0.95 /HR
Com_kill = 0.0027 /HR
Com_show_collations = 0.0082 /HR
Com_show_events = 0.0082 /HR
Com_show_processlist = 0.025 /HR
Innodb_log_writes / Innodb_log_write_requests = 0.02%
Key_blocks_unused = 3,946
Threads_connected = 0.0055 /HR
innodb_lru_scan_depth / innodb_io_capacity = 0.0341
key_buffer_size / _ram = 0.01%
query_cache_limit = 131,072


Abnormally large:

Com_create_procedure = 0.84 /HR
Com_drop_procedure = 0.84 /HR
Com_show_create_table = 0.36 /sec
Com_show_table_status = 0.35 /sec
Com_show_tables = 0.38 /sec
Com_unlock_tables = 0.35 /sec
Handler_delete = 88 /sec
Handler_read_first = 156 /sec
Innodb_buffer_pool_pages_data = 5.12e+6
Innodb_buffer_pool_pages_misc = 438,469
Innodb_buffer_pool_pages_total = 5.57e+6
Innodb_dblwr_pages_written / Innodb_dblwr_writes = 93.1
Innodb_ibuf_merged_delete_marks = 243 /sec
Innodb_ibuf_merges = 2.5 /sec
Innodb_log_write_requests = 673 /sec
Innodb_rows_deleted = 89 /sec
Open_table_definitions = 20,252
Open_tables = 20,000
binlog_cache_size = 1.05e+6
group_concat_max_len = 3.36e+7
innodb_io_capacity = 30,000
innodb_io_capacity_max = 60,000
innodb_open_files = 20,000
max_heap_table_size = 1024MB
min(max_heap_table_size, tmp_table_size) = 1024MB
performance_schema_max_cond_instances = 44,100
performance_schema_max_statement_classes = 181
table_definition_cache = 20,000


Abnormal strings:

Compression = ON
block_encryption_mode = aes-256-cbc
init_connect = SET NAMES utf8
innodb_file_format = Barracuda
innodb_file_format_max = Barracuda
innodb_force_load_corrupted = OFF
innodb_large_prefix = ON
innodb_numa_interleave = ON
locked_in_memory = ON
optimizer_trace = enabled=off,one_line=off
optimizer_trace_features = greedy_search=on, range_optimizer=on, dynamic_range=on, repeated_subselect=on
secure_file_priv = /tmp/
slave_rows_search_algorithms = TABLE_SCAN,INDEX_SCAN
tx_isolation = READ-COMMITTED