[SI-LIST] step response simulators

I have a dilemma.  I hope you can help me resolve it.
 
If we were to multiply the following numbers together:
 
6.7894323  x
3.4965 x
4.208 x
2.08 
 
A spreadsheet or calculator might yield the result:
 
207.7811094
 
However, the spreadsheet or calculator does not distinguish between
 
2.08, and the value 2.0800000
 
The appropriate answer is:
 
207.78
 
Any result past two decimal points is uncertain since the least accurate number 
of our series contains only two decimal places.*
 
*Reference:
 
http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
 
An important consequent to correctly determining the number of decimal points 
of accuracy is ?errors per part?.  One digit of inaccuracy in the reported 
value of 207.7811094 is
 
0.0000001 errors / 207.7811094 parts = 4.81E-10 errors / part
 
This expression appears to have greater accuracy than the more appropriate 
determination:
 
0.01 errors / 207.78 parts = 4.81E-05 errors / part
 
Likewise with respect to division, each number of the following series is 
divided by the next:
 
6.7894323  /
3.4965 /
4.208 /
2.08 
 
A spreadsheet or calculator might yield the result:
 
0.2218507
 
However, the spreadsheet or calculator may not distinguish between
 
2.08, and 2.0800000
 
The appropriate answer is:
 
0.22
 
Any result past two decimal points is uncertain since the least accurate number 
of our series contains only two decimal places.
 
Consult reference:
 
http://www.physics.uoguelph.ca/tutorials/sig_fig/SIG_dig.htm
 
for similar rules for other mathematical calculations.
 
************
 
Ok, let?s apply the described principle to simulation and simulators.
 
Suppose that we work hard to reduce our error of a simulation down to just 50 
ps.  If the simulation runs 1000 ns, the result will be:
 
50e-12 errors / 1000 e-9 parts  = 5e-5 errors / part
 
The result for a 100 ns second simulation is:
 
50e-12 errors / 100 e-9 parts  = 5e-4 errors / part}
 
Let?s suppose that we were particularly diligent and we reduced our error in 
half to just 25 ps.  If the simulation runs 1000 ns, the result will be:
 
25e-12 errors / 1000 e-9 parts  = 2.5e-5 errors / part
 
The result for a 100 ns second simulation is:
 
25e-12 errors / 100 e-9 parts  = 2.50E-04 errors / part}
 
For emphasis let?s consider what happens if we had some way of reducing our 
error to just 10 ps:
 
If the simulation runs 1000 ns, the result will be:
 
10e-12 errors / 1000 e-9 parts  = 1e-5 errors / part
 
The result for a 100 ns second simulation is:
 
10e-12 errors / 100 e-9 parts  = 1E-04 errors / part
 
One more time:  Let?s suppose there existed someway for us to reduce our error 
of simulation to just 1 ps.
 
1e-12 errors / 1000 e-9 parts  = 1e-6 errors / part
 
The result for a 100 ns second simulation is:
 
1e-12 parts of error / 100 e-9 total parts  = 1E-05 errors / part
 
*****
 
Step Response Simulators take a given simulation deck, along with its 
associated models and projects error rates of 1e-12.  I?d be grateful if you 
can help me to understand how it is possible to use a simulation that is no 
more accurate than 1e-6 errors per part and yield valid results of 1e-12 errors 
per part using a Step Response Simulator.  Note that errors / part is not 
associated with any particular physical quantity such as length, time, bits, 
etc ..
 
- As an aside, in many circumstances simulation error is worse than 1e-3.
Much appreciation,
 
Cliff Clark
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