How to extract multiple values from a file in a single pass?

sed -n '/^Max/ { s/^.*=\s*//;h; };
        /^Time/{ s/^.*=\s*//;G; s/\n/ /;p; }' infile

• match-run syntax /.../{ ... }:
  commands within {...} will only run on the lines that matched with regex/pattern within /.../;

• s/^.*=\s*//:
  deletes everything up-to last = and whitespaces \s* also if there was any.

• h:
  copy the result into hold-space

• G:
  append the hold-space to pattern-space with embedded newline

• s/\n/ /:
  replace that embedded newline with space in the pattern-space

• p:
  print pattern-space; you can use P command here instead too.

  0.000001 3.0355
  0.000013 4.3644
  0.000025 3.7319
  1.32125 7.0695
  

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A similar approach proposed by @stevesliva that is used s//<replace>/ which is shorthand to do substitution on the last match:

sed -n '/^Max.*=\s*/ { s///;h; };
        /^Time.*=\s*/{ s///;G; s/\n/ /;p; }' infile

I can't guarantee it will be faster, but you could do something like this in awk:

awk -F' = ' '$1=="Max value of omega" {omega = $2} $1=="Time" {print omega,$2}' file

$ awk 'BEGIN{print "#time", "omega"} /^Max value of omega =/{omega=$NF; next} /^Time =/{print $NF, omega}' file
#time omega
0.000001 3.0355
0.000013 4.3644
0.000025 3.7319
1.32125 7.0695

but this will probably be faster:

$ grep -E '^(Max value of omega|Time) =' file |
    awk 'BEGIN{print "#time", "omega"} NR%2{omega=$NF; next} {print $NF, omega}'
#time omega
0.000001 3.0355
0.000013 4.3644
0.000025 3.7319
1.32125 7.0695