Writing a fork involves sitting down at your laptop and coding it out.
$ hyperfine -w 100 -m 1000 -L bin jq,jaq "echo '[1,2,3]' | {bin} '.[1]'"
Summary
echo '[1,2,3]' | jaq '.[1]' ran
1.57 ± 0.15 times faster than echo '[1,2,3]' | jq '.[1]'
I've commented before that I expect Rust to be a language that is generally faster than even C or C++ in a way that's hard to capture in small benchmarks, because the borrow checker permits code to be written safely that does less copying that other languages have to do for safety. Given the nature of what jq/jaq does, I wouldn't be surprised that that is some of the effect here. It would be interesting to instrument them up with tools that can track the amount of memory traffic each benchmark does to compare (that is, not memory used but total traffic in and out of RAM); I bet the Rust code shows a lot less.
$ hyperfine -N -w 100 -m 1000 -L bin jq,jaq "echo '[1,2,3]' | {bin} '.[1]'"
Benchmark 1: echo '[1,2,3]' | jq '.[1]'
Time (mean ± σ): 3.4 ms ± 1.7 ms [User: 0.6 ms, System: 2.6 ms]
Range (min … max): 0.7 ms … 5.8 ms 1000 runs
Benchmark 2: echo '[1,2,3]' | jaq '.[1]'
Time (mean ± σ): 3.4 ms ± 1.7 ms [User: 0.5 ms, System: 2.7 ms]
Range (min … max): 0.7 ms … 5.8 ms 1000 runs
Summary
echo '[1,2,3]' | jq '.[1]' ran
1.00 ± 0.71 times faster than echo '[1,2,3]' | jaq '.[1]'