\form#0:\begin{eqnarray*}GE = Parallel\; Efficiency\; \; x\; \; Computation\; Efficiency\end{eqnarray*}
\form#1:\begin{eqnarray*}PE = Load\; Balance\; \; x\; \; Communication\; Efficiency\end{eqnarray*}
\form#2:\begin{eqnarray*}Load\; Balance\; Efficiency = \frac{avg(computation\; time)}{max(computation\; time)}\end{eqnarray*}
\form#3:\begin{eqnarray*}CommE = maximum\; across\; processes\frac{computation\; time}{total\; runtime}\end{eqnarray*}
\form#4:\begin{eqnarray*}CommE = Serialisation\; Efficiency\; \; x\; \; Transfer\; Efficiency\end{eqnarray*}
\form#5:\begin{eqnarray*}SerE = maximum\; across\; processes(\frac{computation\; time }{total\; runtime\; on\; ideal\; network})\end{eqnarray*}
\form#6:\begin{eqnarray*}TE = \frac{ maximum\; across\; processes(total\; runtime\; on\; ideal\; network )}{ maximum\; across\; processes(total\; measured\; runtime)}\end{eqnarray*}
\form#7:\begin{eqnarray*}PE = Process\; Efficiency\; +\; Thread\; Efficiency - 1\end{eqnarray*}
\form#8:\begin{eqnarray*}PE = \frac{avg(computation time)}{max(runtime)} = Process\; Efficiency\; +\; Thread\; Efficiency - 1\end{eqnarray*}
\form#9:\begin{eqnarray*}Process\; Efficiency=\frac{(avg(time\; in\; OpenMP) + avg(serial\; computation))}{max(runtime)} = Computation\; Load\; Balance\; \; +\; \; MPI\; Communication\; Efficiency\; -\; 1\end{eqnarray*}
\form#10:\begin{eqnarray*}Computation\; Load\; Balance = (max(runtime) - max(time\; in\; OpenMP + serial\; computation\; time) + avg(time\; in\; OpenMP) + avg(time\; in\; serial\; computation)) / max(runtime) \end{eqnarray*}
\form#11:\begin{eqnarray*}Comm E= \frac{(max(time\; in\; OpenMP + serial\; computation\; time)) }{max(runtime)} \end{eqnarray*}
\form#12:\begin{eqnarray*}SerE = maximum\; across\; processes(\frac{computation\; time}{total\; runtime\; on\; ideal\; network}) \end{eqnarray*}
\form#13:\begin{eqnarray*}TE = \frac{ maximum\; across\; processes(total\; runtime\; on\; ideal\; network)}{maximum\; across\; processes(total\; measured\; runtime )}\end{eqnarray*}
\form#14:\begin{eqnarray*} Thread Efficiency= \frac{max(runtime) - avg(time\; in\; OpenMP) + avg(time\; in\; useful\; computation\; within\; OpenMP) - avg(idling\; time\; of\; OpenMP\; threads)} {max(runtime)} = Amdahl's\; Efficiency\; \; +\; \; OpenMP\; Region\; Efficiency\; -\; 1\end{eqnarray*}
\form#15:\begin{eqnarray*}avg(idling\; time\; of\; OpenMP\; threads) = \sum_{process=0}^{num\; of\; processes} serial\; computation\frac{(number\; of\; threads\; per\; process\; - 1)}{number\; of\; all\; available\; threads}\end{eqnarray*}
\form#16:\begin{eqnarray*}Amdahl's\; Efficiency= \frac{(max(runtime) - avg(idling\; time\; of\; OpenMP\; threads))}{max(runtime)}\end{eqnarray*}
\form#17:\begin{eqnarray*}OpenMP\; Region\; Efficiency=\frac{max(runtime) - avg(time\; in\; OpenMP) + avg(time\; in\; useful\; computation\; within\; OpenMP)}{max(runtime)}\end{eqnarray*}
\form#18:\begin{eqnarray*} PE = Process\; Efficiency\; \; x\; \; Thread\; Efficiency\end{eqnarray*}
\form#19:\begin{eqnarray*}PE = \frac{avg(comp)}{max(runtime)} = Process\; Efficiency\; \; x\; \; Thread\; Efficiency\end{eqnarray*}
\form#20:\begin{eqnarray*}PE = \frac{ avg(time in OpenMP) + avg(serial computation) }{max(runtime)} = Computation\; Load\; Balance\; \; x\; \; MPI\; Communication\; Efficiency.\end{eqnarray*}
\form#21:\begin{eqnarray*}Computation\; Load\; Balance = \frac{( avg(time\; in\; OpenMP) + avg(serial\; computation))}{ max(time\; in\; OpenMP + serial\; computation\; time)}\end{eqnarray*}
\form#22:\begin{eqnarray*}CommE = \frac{max(time in OpenMP + serial computation time) }{ max(runtime)}\end{eqnarray*}
\form#23:\begin{eqnarray*}CommE = Serialisation\; Efficiency\;\; x\;\; Transfer\; Efficiency\end{eqnarray*}
\form#24:\begin{eqnarray*}Thread Efficiency = \frac{avg( computation time)}{(avg( time in OpenMP ) + avg( serial computation ) )} = Amdahl's\; Efficiency\; \; x\; \; OpenMP\; Region\; Efficiency\end{eqnarray*}
\form#25:\begin{eqnarray*} Thread\; Efficiency = \frac{avg( computation time) }{( avg( time in OpenMP ) + avg( serial computation ) ) } = Amdahl's\; Efficiency\; \; x\; \; OpenMP\; Region\; Efficiency\end{eqnarray*}
\form#26:\begin{eqnarray*}OpenMP Region Efficiency = \frac{(avg(time in useful computation within OpenMP ) + avg( serial computation ))}{(avg( time in OpenMP ) + avg( serial computation ))}\end{eqnarray*}
\form#27:\begin{eqnarray*}HPE = \frac{avg(computation time)}{max(runtime)} = Hybrid\; Load\; Balance\; Efficiency\; \; x\; \; Hybrid\; Communication\; Efficiency\end{eqnarray*}
\form#28:\begin{eqnarray*}Hybrid\; Load\; Balance\; Efficiency = \frac{computation\; time}{maximum\; computation\; time}\end{eqnarray*}
\form#29:\begin{eqnarray*}Hybrid\; Communication\; Efficiency = \frac{max(computation\; time)}{max(runtime)}\end{eqnarray*}
\form#30:\begin{eqnarray*}MPE = \frac{avg(time\; outside\; of\; MPI)}{max(runtime)} = MPI\; Load\; Balance\; Efficiency\; \; x\; \; MPI\; Communication\; Efficiency\end{eqnarray*}
\form#31:\begin{eqnarray*}MPI\; Load\; Balance\; Efficiency = \frac{avg(time\; outside\; of\; MPI)}{max(time\; outside\; of\; MPI)}\end{eqnarray*}
\form#32:\begin{eqnarray*}MPI\; Communication\; Efficiency = \frac{max(time\; outside\; of\; MPI)}{max(runtime)}\end{eqnarray*}
\form#33:\begin{eqnarray*}OMPE = \frac{avg(computation\; time) }{avg(time\; outside\; of\; MPI) } = \frac{Hybrid\; Parallel\; Efficiency }{MPI\; Parallel\; Efficiency} \end{eqnarray*}
\form#34:\begin{eqnarray*} OpenMP\; Load\; Balance\; Efficiency = \frac{Hybrid\; Load\; Balance\; Efficiency }{ MPI\; Load\; Balance\; Efficiency}\end{eqnarray*}
\form#35:\begin{eqnarray*}OpenMP\; Communication\; Efficiency = \frac{max(computation\; time)}{max(time\; outside\; of\; MPI)} = \frac{Hybrid\; Communication\; Efficiency }{ MPI\; Communication\; Efficiency} \end{eqnarray*}
\form#36:\begin{eqnarray*}IO = 1 - POSIX\; IO + MPI\; IO \end{eqnarray*}
\form#37:\begin{eqnarray*}POSIX\; IO = \frac{time\; in\; POSIX\; IO\; calls}{total\; runtime} \end{eqnarray*}
\form#38:\begin{eqnarray*}MPI\; IO = \frac{time\; in\; MPI\; IO\; calls}{total\; runtime} \end{eqnarray*}
\form#39:\begin{eqnarray*}\frac{PAPI\_RES\_STL }{ PAPI\_TOT\_CYC}\end{eqnarray*}
\form#40:\begin{eqnarray*} \frac{(stalled\_cycles\_backend + stalled\_cycles\_frontend) }{cycles}\end{eqnarray*}
\form#41:\begin{eqnarray*} \frac{stalled\_cycles\_backend }{ cycles}\end{eqnarray*}
\form#42:\begin{eqnarray*} \frac{stalled\_cycles\_frontend }{ cycles}\end{eqnarray*}
\form#43:$ \sum_{i=1}^n tol*v_i^m$
\form#44:$ \sum_{i \in N} v_i \, \le \, thrh \times \sum_{i \in M} v_i $
