Invalid simplification from Expression.simplify_rational()

[orlitzky]

Well, I thought this one was safe. Not so!

sage: u,x = var('u,x')
sage: F = -1/12*(2*(sqrt(24*sqrt(2) - 30)*(155*sqrt(2) - 228) + 2368*sqrt(2) - 3086)*u^3 + (8*(5*(3*sqrt(2) - 4)*sqrt(24*sqrt(2) - 30) - 128*sqrt(2) + 106)*u^3 + 32*(5*(3*sqrt(2) - 4)*sqrt(24*sqrt(2) - 30) - 128*sqrt(2) + 106)*u^2 + (sqrt(24*sqrt(2) - 30)*(385*sqrt(2) - 492) - 6976*sqrt(2) + 6902)*u)*x^3 + 2*(sqrt(24*sqrt(2) - 30)*(525*sqrt(2) - 764) + 6592*sqrt(2) - 8834)*u^2 + 3*(8*(5*(3*sqrt(2) - 4)*sqrt(24*sqrt(2) - 30) - 128*sqrt(2) + 106)*u^3 + 32*(5*(3*sqrt(2) - 4)*sqrt(24*sqrt(2) - 30) - 128*sqrt(2) + 106)*u^2 + (sqrt(24*sqrt(2) - 30)*(575*sqrt(2) - 788) - 1216*sqrt(2) - 118)*u)*x^2 + (5*sqrt(24*sqrt(2) - 30)*(191*sqrt(2) - 276) + 10304*sqrt(2) - 14158)*u + 3*(8*(5*(3*sqrt(2) - 4)*sqrt(24*sqrt(2) - 30) - 128*sqrt(2) + 106)*u^3 + 2*(sqrt(24*sqrt(2) - 30)*(335*sqrt(2) - 468) + 832*sqrt(2) - 1814)*u^2 + (sqrt(24*sqrt(2) - 30)*(765*sqrt(2) - 1084) + 4544*sqrt(2) - 7138)*u)*x)/(sqrt(24*sqrt(2) - 30)*(95*sqrt(2) - 148) + 2880*sqrt(2) - 3510)
sage: b = -1/6*(128*x^3 + 384*x^2 + 6*sqrt(24*sqrt(2) - 30)*((3*sqrt(2) - 4)*x + 3*sqrt(2) - 4) + (x + 1)*sqrt(9216*sqrt(2) + 1216*x^4 + 22144*x^3 + 16*(576*sqrt(2) - 1253)*x + 13056*x^2 + 24*sqrt(24*sqrt(2) - 30)*(4*(3*sqrt(2) - 4)*x^4 - 8*(3*sqrt(2) - 4)*x^3 + 16*(3*sqrt(2) - 4)*x^2 + 25*(3*sqrt(2) - 4)*x - 9*sqrt(2) + 12) - 12176) + 204*x - 52)/(16*x^3 + 48*x^2 + (3*sqrt(2) - 4)*sqrt(24*sqrt(2) - 30) + 48*x - 14)
sage: p  = plot(F(u=b), x, -1, 0)
sage: p += plot(F(u=b).simplify_rational(), x, -1, 0, color='red')
sage: p

Component: symbolics

Issue created by migration from https://trac.sagemath.org/ticket/12794

[orlitzky]

A .sage file exhibiting the problem

[kcrisman]

comment:1

Attachment: simplify_rational_gone_wild.sage.gz

If you could narrow it down, that would be helpful. I'm adding this to the description, as well as the graphic.

[kcrisman]

Shows the problem

[kcrisman]

comment:2

Attachment: tmp_0.png

But I should point out that there are lots of cool examples of "simplification" actually making things simpler. Could this just be a loss of significance error? Otherwise, try

sage: plot(((x^3+4)^2-x^6)/x^3,(x,0,10^6))

(courtesy of the calculus text we currently teach from here).

So I'm more concerned about the left end of your graph than the right.

[kcrisman]

Attachment: better.png

shows the solution!

[kcrisman]

comment:3

The attached picture actually is for #12795, but as it was the same, it's still worth posting here too. I think they are probably both invalid, or more precisely are warnings about how rewriting expressions in different ways allows for a lot of numerical error to creep in. Good stuff. (Not good enough for me to want to teach a numerical analysis course, but good enough for me to want to take a numerical analysis course...)