additivity(?) of execution time.ipynb

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      "Julia Version 1.0.0\n",
      "Commit 5d4eaca0c9 (2018-08-08 20:58 UTC)\n",
      "Platform Info:\n",
      "  OS: Linux (x86_64-pc-linux-gnu)\n",
      "  CPU: Intel(R) Core(TM) i5-4460T CPU @ 1.90GHz\n",
      "  WORD_SIZE: 64\n",
      "  LIBM: libopenlibm\n",
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   "source": [
    "versioninfo()"
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  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using BenchmarkTools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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     "text": [
      "\u001b[32m\u001b[1m    Status\u001b[22m\u001b[39m `~/.julia/environments/v1.0/Project.toml`\n",
      " \u001b[90m [6e4b80f9]\u001b[39m\u001b[37m BenchmarkTools v0.4.1\u001b[39m\n",
      " \u001b[90m [7073ff75]\u001b[39m\u001b[37m IJulia v1.12.0\u001b[39m\n"
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   "source": [
    "]st"
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\mathrm{time}(x) + \\mathrm{time}(y) < \\mathrm{time}(x+y)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  78.20 KiB\n",
       "  allocs estimate:  2\n",
       "  --------------\n",
       "  minimum time:     665.527 ns (61.76% GC)\n",
       "  median time:      791.880 ns (61.89% GC)\n",
       "  mean time:        928.644 ns (69.11% GC)\n",
       "  maximum time:     175.168 μs (99.69% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     383"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark v = Vector{Float64}(undef, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  0 bytes\n",
       "  allocs estimate:  0\n",
       "  --------------\n",
       "  minimum time:     2.829 μs (0.00% GC)\n",
       "  median time:      2.952 μs (0.00% GC)\n",
       "  mean time:        3.201 μs (0.00% GC)\n",
       "  maximum time:     9.150 μs (0.00% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     9"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Vector{Float64}(undef, 10000)\n",
    "@benchmark fill!(v, 100.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  78.20 KiB\n",
       "  allocs estimate:  2\n",
       "  --------------\n",
       "  minimum time:     11.046 μs (0.00% GC)\n",
       "  median time:      14.174 μs (0.00% GC)\n",
       "  mean time:        28.475 μs (42.19% GC)\n",
       "  maximum time:     76.135 ms (99.98% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark begin\n",
    "   v = Vector{Float64}(undef, 10000)\n",
    "   fill!(v, 100.0)\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# $\\mathrm{time}(x) + \\mathrm{time}(y) > \\mathrm{time}(x+y)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  148.27 KiB\n",
       "  allocs estimate:  9489\n",
       "  --------------\n",
       "  minimum time:     246.750 μs (0.00% GC)\n",
       "  median time:      284.499 μs (0.00% GC)\n",
       "  mean time:        308.342 μs (5.51% GC)\n",
       "  maximum time:     71.376 ms (99.59% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = Vector{Float64}(undef, 10000)\n",
    "@benchmark for i in 1:10000\n",
    "    v[i] = 100.0\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BenchmarkTools.Trial: \n",
       "  memory estimate:  78.20 KiB\n",
       "  allocs estimate:  2\n",
       "  --------------\n",
       "  minimum time:     12.023 μs (0.00% GC)\n",
       "  median time:      16.631 μs (0.00% GC)\n",
       "  mean time:        32.058 μs (40.89% GC)\n",
       "  maximum time:     77.440 ms (99.93% GC)\n",
       "  --------------\n",
       "  samples:          10000\n",
       "  evals/sample:     1"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@benchmark begin\n",
    "    v = Vector{Float64}(undef, 10000)\n",
    "    for i in 1:10000\n",
    "        v[i] = 100.0\n",
    "    end\n",
    "end"
   ]
  }
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