$ jq -n -r -f nth_root_machine_precision.jq
5^(1/   n):             builtin       precision=1e-10           precision=0
5^(1/    1):  4.999999999999999 vs                  5 vs 5
5^(1/   -5): 0.7247796636776955 vs 0.7247796636776956 vs 0.7247796636776955
5^(1/   -3): 0.5848035476425733 vs 0.5848035476425731 vs 0.5848035476425731
5^(1/   -1):                0.2 vs                0.2 vs 0.2
5^(1/    1):  4.999999999999999 vs                  5 vs 5
5^(1/    3):  1.709975946676697 vs  1.709975946676697 vs 1.709975946676697
5^(1/    5): 1.3797296614612147 vs 1.3797296614612147 vs 1.379729661461215
5^(1/ 1000): 1.0016107337527294 vs 1.0016107337527294 vs 1.0016107337527294
5^(1/10000): 1.0001609567433902 vs 1.0001609567433902 vs 1.0001609567433902