chore: update time_test.sh

bin/time_test.sh

@@ -9,6 +9,7 @@ domain=$1
 key=$2
 count=$3
 total_time=0
+times=()
 
 for ((i=1; i<=count; i++)); do
   result=$(curl -o /dev/null -s -w %{time_total}\\n \
@@ -17,9 +18,19 @@ for ((i=1; i<=count; i++)); do
            -H "Authorization: Bearer $key" \
            -d '{"prompt": "hi!", "max_tokens": 1}')
   echo "$result"
-  total_time=$(echo "$total_time + $result" | bc)
+  total_time=$(bc <<< "$total_time + $result")
+  times+=("$result")
 done
 
-average_time=$(echo "scale=3; $total_time / $count" | bc)
-echo "Average time: $average_time"
+average_time=$(echo "scale=4; $total_time / $count" | bc)
 
+sum_of_squares=0
+for time in "${times[@]}"; do
+  difference=$(echo "scale=4; $time - $average_time" | bc)
+  square=$(echo "scale=4; $difference * $difference" | bc)
+  sum_of_squares=$(echo "scale=4; $sum_of_squares + $square" | bc)
+done
+
+standard_deviation=$(echo "scale=4; sqrt($sum_of_squares / $count)" | bc)
+
+echo "Average time: $average_time±$standard_deviation"