In the first comparison, r sqrt(5)^2has better mean timing compared to r sqrt(5^2). Why is this happening?
In the second comparison the above is reversed. I have tried it with more number of iterations (times). Finding it difficult to understand what is going on.
microbenchmark::microbenchmark(sqrt(5)^2,sqrt(5^2), times = 1e3)
#> Unit: nanoseconds
#> expr min lq mean median uq max neval cld
#> sqrt(5)^2 144 151 210.705 162 169 6304 1000 a
#> sqrt(5^2) 148 157 269.604 169 226 25936 1000 b
microbenchmark::microbenchmark(sqrt(5)^2,sqrt(5^2), log(exp(5)), times = 1e3)
#> Unit: nanoseconds
#> expr min lq mean median uq max neval cld
#> sqrt(5)^2 145 168 193.956 180 184 3059 1000 a
#> sqrt(5^2) 149 159 189.753 170 176 3778 1000 a
#> log(exp(5)) 132 147 183.599 154 166 8062 1000 a
Created on 2023-07-19 by the reprex package (v2.0.1)
Doesn't make much sense to compare with one input - 5. Try longer vector. We can see medians are consistent.
x <- 1:10000
microbenchmark::microbenchmark(sqrt(x)^2, sqrt(x^2), times = 10000)
# Unit: microseconds
# expr min lq mean median uq max neval cld
# sqrt(x)^2 29.0 51.6 95.77408 54.9 58.3 79210.8 10000 a
# sqrt(x^2) 35.4 47.0 61.64323 48.8 52.0 8017.2 10000 b
microbenchmark::microbenchmark(sqrt(x)^2, sqrt(x^2), log(exp(x)), times = 10000)
# Unit: microseconds
# expr min lq mean median uq max neval cld
# sqrt(x)^2 28.2 52.25 100.85237 56.1 60.4 80131.9 10000 a
# sqrt(x^2) 35.4 47.70 57.88721 49.7 53.5 4441.1 10000 a
# log(exp(x)) 162.1 196.90 262.39865 202.4 220.5 83254.2 10000 b