Trace of FullSimplify

Question

I have a symbolic function and I used FullSimplify command to simplify the equation given below. I am calculating it by hand but I couldn't reach the same solution. I used Trace command to observe the intermediate steps but trace only gives the expression before FullSimplify. Are there any possible methods that I can observe the steps of simplification?

    Trace[FullSimplify[2 b (-(1/(1 - fd)) + 1/fd) + 
   (2 a (1 - (b (1 - 1/fd + 1/(fd t)))/(a + b)) t)/
   (1 - (1 - fd) t - (b fd (1 - 1/fd + 1/(fd t)) t)/(a + b)) == 0]]

a little bit related http://mathematica.stackexchange.com/q/148/5478 — Kuba, Jun 22 '13 at 15:18
In general, the simplification methods internally used by Mathematica do not necessarily correspond to how one might simplify by hand; remember that a method that is simple for computers to do is not necessarily simple for humans, and vice-versa. — J. M.'s missing motivation, Jun 22 '13 at 15:26
@J. M. that is true. What I computed by hand doesn't have any similarities with the Mathematica solution. But I wonder if it is possible for Mathematica to show the steps? Or any alternative calculation method? — HarveyMudd, Jun 22 '13 at 15:32
"if it is possible for Mathematica to show the steps" - not in this case, I believe. — J. M.'s missing motivation, Jun 22 '13 at 15:33
I tried calculating again and I think I am getting closer to the same solution. Now, at a point: [(b-2fdb)((tfd-t)+1) -[(a+b)tfd(fd-1) - b(fd-1)]] \ (-fdt(fd-1)^2-fd(fd-1)) — HarveyMudd, Jun 22 '13 at 15:53
The reason I asked, is that I broke it down into smaller chunks to try the simplify and got a different answer. (I was treating the entire thing as a fraction, which is not how it is stated.) — Fred Daniel Kline, Jun 22 '13 at 15:56
@FredKline no there is two fractions one which starts with 2b and the other starting with 2a. — HarveyMudd, Jun 22 '13 at 15:58
I put a ( before the 2b and a ) before the / on the second line, which made only one fraction. — Fred Daniel Kline, Jun 22 '13 at 16:01

score 16 · Accepted Answer · answered Jun 22 '13 at 16:47

16

To see the full details of what FullSimplify is doing you can use the option TraceInternal -> True in Trace. It probably won't help much though, as it will generate pages and pages of inscrutable output.

One thing I have done in the past is to add Sow as a TransformationFunction. This shows the intermediate expressions that Simplify encounters as it works. It's far from being a step-by-step walkthrough, but you can sometimes get a few clues.

FullSimplify[expr, TransformationFunctions -> {Sow, Automatic}] // Reap

answered Jun 22 '13 at 16:47

Simon Woods

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Thanks this was really helpful. I actually solved it by hand. – HarveyMudd Jun 22 '13 at 21:05
1

Nice answer! Great tools for learning more. It seems that some caching is going on by the way, if you don't get the output you expect, give it a good ol' ClearSystemCache[]. – Jacob Akkerboom Jun 23 '13 at 10:31

Trace of FullSimplify

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