\documentclass[border=10pt,varwidth]{standalone}
\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{times}
\usepackage{geometry}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathrsfs}
\usepackage{amsfonts}
\usepackage{amsthm}
\usepackage{lipsum}
\usepackage{amscd}
\usepackage{graphicx}
\usepackage{fancyhdr}
\usepackage{textcomp}
\usepackage{pgfplots}
\usepackage{txfonts}
\usepackage[all]{xy}
\usepackage{paralist}
\usepackage[colorlinks=true]{hyperref}
\usepackage{array}
\usepackage{tikz}
\usepackage{slashed}
\usepackage{pdfpages}
\usepackage{cite}
\usepackage{url}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{tikz}
\usepackage{pgfplotstable}
\usetikzlibrary{arrows,matrix,positioning}
\usetikzlibrary{overlay-beamer-styles}
\usetikzlibrary{matrix.skeleton}
\usetikzlibrary{automata,positioning}
\usetikzlibrary{decorations.text}
\usepackage{listings}
\usepackage{multirow}
\usepackage{color}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
xmode=log, ymode=log,
xmin=60, xmax=5000,
ymin=1e-4, ymax=2e3,
grid=both,
major grid style={black!50},
xlabel = data Input ($n$),
ylabel = {time ($s$)},
legend pos=north west,
very thick,
scale only axis=true,
width=12cm, height=8cm,
       log basis x={10}
]
\addlegendentry{Winograd}
\addplot[    color=purple,
] coordinates {
% (2,   0.000001)
% (4,   0.000001)
% (8,   0.000002)
% (16,  0.000011)
% (32,  0.000100)
(64,  0.000654)
(128, 0.005229)
(256, 0.057440)
(512, 0.517850)
(1024,4.539413)
(2048,130.627663)
(4096,1179.261048)
};
\addlegendentry{Strassen}
\addplot [    color=black,
]coordinates {
  %  (2,0.000001 )
  %  (4,0.000003 )
  %  (8,0.000010 )
  % (16,0.000066 )
  % (32,0.000470 )
  (64,0.003368 )
 (128,0.024232 )
 (256,0.172000 )
 (512,1.209262 )
(1024,8.457472 )
(2048,59.267256)
(4096,414.648901)
};

\addlegendentry{MM div and conq}
\addplot[    color=green,
] coordinates {
  %  (2,0.000003   )
  %  (4,0.000002   )
  %  (8,0.000010   )
  % (16,0.000068   )
  % (32,0.000594   )
  (64,0.004264   )
 (128,0.036289   )
 (256,0.324645   )
 (512,2.612010   )
(1024,19.928951  )
(2048,159.333884 )
(4096,1147.106865)
};

\addlegendentry{MM}
\addplot [    color=red,
]coordinates {
  %  (2,0.000001   )
  %  (4,0.000001   )
  %  (8,0.000001   )
  % (16,0.000010   )
  % (32,0.000081   )
  (64,0.000654   )
 (128,0.005556   )
 (256,0.054253   )
 (512,0.487317   )
(1024,4.162845   )
(2048,125.909034 )
(4096,1111.312696)
};
\addlegendentry{BLAS}
\addplot[    color=blue,
] coordinates {
  %  (2,0.000001 )
  %  (4,0.000001 )
  %  (8,0.000001 )
  % (16,0.000003 )
  % (32,0.000022 )
  (64,0.000179 )
 (128,0.001278  )
 (256,0.010165  )
 (512,0.074739  )
(1024,0.704748  )
(2048,6.845095  )
(4096,55.845038)
};
\end{axis}
\end{tikzpicture}

\end{document}