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
+# round an integer amount of nanoseconds to 4th digit and convert to a real duration
-
+def "from ns" [] {
-# convert an integer amount of nanoseconds to a real duration
+    if $in == 0 {0} else { #math log errors on 0
-def "from ns" [
+        math round -p (3 - ($in | math log 10 | math floor)) # rounds to 4th digit including, with maximum realtive err 0.05%
-    --sign-digits: int = 4 # a number of first non-zero digits to keep (default 4; set 0 to disable rounding)
+        | math round # second math round as a fix for `> 123456 | math round -p -5` = 99999.99999999999
-] {
-    if $sign_digits == 0 {} else {
-        math significant-digits $sign_digits
     }
-    | $"($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
+#     > bench {sleep 1ms; 1 + 2} --rounds 2 --timings | table -e
-#     ╭───────┬─────────────────────╮
+#     ╭───────┬───────────────╮
-#     │ mean  │ 1ms 272µs           │
+#     │ mean  │ 1ms 272µs     │
-#     │ min   │ 1ms 259µs           │
+#     │ min   │ 1ms 259µs     │
-#     │ max   │ 1ms 285µs           │
+#     │ max   │ 1ms 285µs     │
-#     │ std   │ 13µs 370ns          │
+#     │ std   │ 13µs 370ns    │
-#     │       │ ╭─────────────────╮ │
+#     │       │ ╭───────────╮ │
-#     │ times │ │ 1ms 285µs 791ns │ │
+#     │ times │ │ 1ms 285µs │ │
-#     │       │ │  1ms 259µs 42ns │ │
+#     │       │ │ 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: ($times | math avg | from ns --sign-digits 4)
+        mean: ($times | math avg | from ns)
-        min: ($times | math min | from ns --sign-digits 4)
+        min: ($times | math min | from ns)
-        max: ($times | math max | from ns --sign-digits 4)
+        max: ($times | math max | from ns)
-        std: ($times | math stddev | from ns --sign-digits 4)
+        std: ($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 {
+        if $timings {
-            merge { times: ($times | each { from ns --sign-digits 0 }) }
+            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
 }