Cosine Calculation without cmath library

cosine_calc2 <- function(a,b,wts) {
  a = a*wts
  b = b*wts
  crossprod(a,b)/sqrt(crossprod(a)*crossprod(b))
}

all.equal(cosine_calc1(a,b,w),cosine_calc2(a,b,w))
# [1] TRUE

# Check some timings
library(rbenchmark)
# cosine_calc2 is slower on my machine in this case
benchmark(
  cosine_calc1(a,b,w),
  cosine_calc2(a,b,w), replications=1e5, columns=1:4 )
#                    test replications user.self sys.self
# 1 cosine_calc1(a, b, w)       100000      1.06     0.02
# 2 cosine_calc2(a, b, w)       100000      1.21     0.00

# but cosine_calc2 is faster for larger vectors
set.seed(21)
a <- rnorm(1000)
b <- rnorm(1000)
w <- runif(1000)
benchmark(
  cosine_calc1(a,b,w),
  cosine_calc2(a,b,w), replications=1e5, columns=1:4 )
#                    test replications user.self sys.self
# 1 cosine_calc1(a, b, w)       100000      3.83        0
# 2 cosine_calc2(a, b, w)       100000      2.12        0

> Rprof(); for(i in 1:100000) cosine_calc2(a,b,w); Rprof(NULL); summaryRprof()
$by.self
             self.time self.pct total.time total.pct
*                 0.80    45.98       0.80     45.98
crossprod         0.56    32.18       0.56     32.18
cosine_calc2      0.32    18.39       1.74    100.00
sqrt              0.06     3.45       0.06      3.45

$by.total
             total.time total.pct self.time self.pct
cosine_calc2       1.74    100.00      0.32    18.39
*                  0.80     45.98      0.80    45.98
crossprod          0.56     32.18      0.56    32.18
sqrt               0.06      3.45      0.06     3.45

$sample.interval
[1] 0.02

$sampling.time
[1] 1.74

cosine_calc3 <- function(a,b) {
  crossprod(a,b)/sqrt(crossprod(a)*crossprod(b))
}
A = a*w
B = b*w
# Run again on the 1000-element vectors
benchmark(
  cosine_calc1(a,b,w),
  cosine_calc2(a,b,w),
  cosine_calc3(A,B), replications=1e5, columns=1:4 )
#                    test replications user.self sys.self
# 1 cosine_calc1(a, b, w)       100000      3.85     0.00
# 2 cosine_calc2(a, b, w)       100000      2.13     0.02
# 3    cosine_calc3(A, B)       100000      1.31     0.00