std bench improvement proposal (#873)

- removed usage of a new external command `math significant-digits`
- rounded precision to 4th digit including (max relative error of 0.05%)
- in `--pretty` I replaced abs `stddev` with relative `coefficient of
variation` (CV)

@amtoine, would you please take a look into my new variant once again? 
Maybe this time it will be good enough? 

<img width="804" alt="image"
src="https://github.com/nushell/nu_scripts/assets/4896754/49e62609-4301-4d5c-b1f5-d2c3355cb33e">

stdlib-candidate/std-rfc/bench.nu

@@ -1,16 +1,12 @@
 # A proposal for improving the original `std bench` command by @amtoine
 # https://github.com/nushell/nushell/blob/31f3d2f6642b585f0d88192724723bf0ce330ecf/crates/nu-std/std/mod.nu#L134
 
-use ./math
-
-# convert an integer amount of nanoseconds to a real duration
-def "from ns" [
- --sign-digits: int = 4 # a number of first non-zero digits to keep (default 4; set 0 to disable rounding)
-] {
- if $sign_digits == 0 {} else {
- math significant-digits $sign_digits
+# round an integer amount of nanoseconds to 4th digit and convert to a real duration
+def "from ns" [] {
+ if $in == 0 {0} else { #math log errors on 0
+ math round -p (3 - ($in | math log 10 | math floor)) # rounds to 4th digit including, with maximum realtive err 0.05%
+ | math round # second math round as a fix for `> 123456 | math round -p -5` = 99999.99999999999
  }
- | $"($in)ns"
  | into duration
 }
 
@@ -42,26 +38,26 @@ def "from ns" [
 #
 # get a pretty benchmark report
 # > bench {1 + 2} --pretty
-# 922ns +/- 2µs 40ns
+# 716ns ± 76.67%
 #
 # measure the performance of simple addition with 1ms delay and output each timing
-# > bench {sleep 1ms; 1 + 2} --rounds 2 --list-timings | table -e
-# ╭───────┬─────────────────────╮
-# │ mean │ 1ms 272µs  │
-# │ min │ 1ms 259µs  │
-# │ max │ 1ms 285µs  │
-# │ std │ 13µs 370ns  │
-# │ │ ╭─────────────────╮ │
-# │ times │ │ 1ms 285µs 791ns │ │
-# │ │ │  1ms 259µs 42ns │ │
-# │ │ ╰─────────────────╯ │
-# ╰───────┴─────────────────────╯
+# > bench {sleep 1ms; 1 + 2} --rounds 2 --timings | table -e
+# ╭───────┬───────────────╮
+# │ mean │ 1ms 272µs │
+# │ min │ 1ms 259µs │
+# │ max │ 1ms 285µs │
+# │ std │ 13µs 370ns │
+# │ │ ╭───────────╮ │
+# │ times │ │ 1ms 285µs │ │
+# │ │ │ 1ms 259µs │ │
+# │ │ ╰───────────╯ │
+# ╰───────┴───────────────╯
 export def main [
  code: closure # the piece of `nushell` code to measure the performance of
  --rounds (-n): int = 50 # the number of benchmark rounds (hopefully the more rounds the less variance)
  --verbose (-v) # be more verbose (namely prints the progress)
  --pretty # shows the results in human-readable format: "<mean> +/- <stddev>"
- --list-timings # list all rounds' timings in a `times` field
+ --timings (-t) # list all rounds' timings in a `times` field
 ] {
  let times = seq 1 $rounds
  | each {|i|
@@ -72,16 +68,16 @@ export def main [
  if $verbose { print $"($rounds) / ($rounds)" }
 
  {
- mean: ($times | math avg | from ns --sign-digits 4)
- min: ($times | math min | from ns --sign-digits 4)
- max: ($times | math max | from ns --sign-digits 4)
- std: ($times | math stddev | from ns --sign-digits 4)
+ mean: ($times | math avg | from ns)
+ min: ($times | math min | from ns)
+ max: ($times | math max | from ns)
+ std: ($times | math stddev | from ns)
  }
  | if $pretty {
- $"($in.mean) +/- ($in.std)"
+ $"($in.mean) ± (($in.std / $in.mean) * 100 | math round -p 2)%"
  } else {
- if $list_timings {
- merge { times: ($times | each { from ns --sign-digits 0 }) }
+ if $timings {
+ merge { times: ($times | each { from ns }) }
  } else {}
  }
 }

stdlib-candidate/tests/bench.nu

@@ -2,11 +2,11 @@ use std assert
 use ../std-rfc bench
 
 export def "test bench-timings" [] {
- let $test = bench {1 + 2} --rounds 3 --list-timings | get times | length
+ let $test = bench {1 + 2} --rounds 3 --timings | get times | length
  assert equal $test 3
 }
 
 export def "test bench-pretty" [] {
- let $test = (bench {1 + 2} --rounds 3 --pretty) =~ '\d.* \+/- \d'
+ let $test = (bench {1 + 2} --rounds 3 --pretty) =~ '\d.* ± \d'
  assert equal $test true
 }