Add wall clock time

Author: xptree

examples/omeinsum_julia/README.md

@@ -4,17 +4,18 @@ This example introduces how to use OMEinsum, a julia-based einsum package, to co
 
 We provide two solutions:
 
-* use subprocess to call a stand-alone julia script (recommended)
+* use subprocess to call a stand-alone julia script (**recommended**)
 * use juliacall to integrate julia script into python (seems to be more elegant, but not recommended)
 
 We highly recommend to use the first solution based on subprocess, not only due to its compatibility to julia multi-threading, but also because the experimental KaHyPar-based initialization is developed based on it.
 
 ## Experiments
 
 We test contractors from OMEinsum on Google random circuits ([available online](https://datadryad.org/stash/dataset/doi:10.5061/dryad.k6t1rj8)) and compare with the cotengra contractor. 
-For circuits only differ in PRNG seed number (which means with the same tensor network structure, but different tenser entries), we choose the one with the largest seed. For example, we benchmark `circuit_n12_m14_s9_e6_pEFGH.qsim`, but skip
+For circuits only differ in PRNG seed number (which means with the same tensor network structure, but different tensor entries), we choose the one with the largest seed. For example, we benchmark `circuit_n12_m14_s9_e6_pEFGH.qsim`, but skip
 circuits like `circuit_n12_m14_s0_e6_pEFGH.qsim`. 
 We list experimental results in [benchmark_results.csv](benchmark_results.csv).
+All experiments are done with a 32GB CPU machine with 16 cores.
 
 
 Specifically, we test the following three methods:
@@ -67,7 +68,9 @@ c.expectation_ps(z=[0], reuse=False)
 Both OMEimsum and cotengra are able to optimize a weighted average of `log10[FLOPs]`, `log2[SIZE]` and `log2[WRITE]`.
 However, OMEimsum and cotengra have different weight coefficient, which makes fair comparison difficult. 
 Thus we force each method to purely optimized `FLOPs`, but we do collect all contraction information in the table, including 
-`log10[FLOPs]`, `log2[SIZE]`, `log2[WRITE]`, `PathFindingTime`.
+`log10[FLOPs]`, `log2[SIZE]`, `log2[WRITE]`, `PathFindingTime`, `WallClockTime`.
+
+For circuits with `PathFindingTime` but empty `WallClockTime`, it means we meet OOM when computing with a 32GB CPU machine.
 
 For three circuits, namely `circuit_patch_n46_m14_s19_e21_pEFGH`, `circuit_patch_n44_m14_s19_e21_pEFGH` and `circuit_n42_m14_s9_e0_pEFGH`, we meet [errors in OMEinsum](https://github.com/TensorBFS/OMEinsumContractionOrders.jl/issues/35#issuecomment-1405236778), and there results are set to empty in [benchmark_results.csv](benchmark_results.csv).