Precision of SOLVER ?

[Thomas Okken]

The function contains a RND. That's the cause of your display mode sensitivity right there.

[Walter]

I deleted the step RND. Consequence: Solving time multiplies - the procedure converges _V_E_R_Y_ slowly although I supplied power via USB. Looking at the results in particular:

1. With SCI 2, the interval for R was 2E-4 after over 15' and wasn't shrinking for minutes. After more than 45', the interval was 1E-4. After some 55', the interval became <1E-12! Surprise! Nevertheless I went to sleep. The result was achieved 3 ± 3 h later: |f(root)| ≈ 9.9E-34, final interval = 5E-34.
2. With ALL, the interval for R was 2E-4 after over 15' and wasn't shrinking for minutes.

Ok, I can't find results depending on display format anymore (for time reasons). Q.e.d. Great!
My good old WP 34S, however, solves this problem orders of magnitude faster. For solving on the DM42, implementing an exit test like
IF |y - x| < ACC_solve THEN STOP is highly recommended at least.

Please note I'm more than satisfied by the progress in the last decade. [/irony]

[Thomas Okken]

The integrator can be slow to converge, and using the solver on such an integral is going to be even slower, obviously.

I am aware of numerical integration algorithms that tend to converge faster than the one used in Free42, but I remain unconvinced that the speed improvement is worth the increased risk of getting bad results. Sticking with the HP-like Romberg integration has the advantage that the behavior of the Free42 solver is similar to that of the HP-42S solver, and that is something I generally try to maintain.

As for the speed issue, of course waiting 3 hours for a result is not something you want, but then again, the DM42 isn't exactly the fastest platform. It's a lot faster than the HP-42S, but it's also a lot slower than any smartphone or computer you're likely to encounter nowadays.

But for the most part, when people complain to me about poor INTEG performance, it's always ACC being 0 or unset. Setting it to something less aggressive, like 1E-12, almost always results in usable speed, even on the DM42.

[Walter]

As for the speed issue, of course waiting 3 hours for a result is not something you want, but then again, the DM42 isn't exactly the fastest platform. It's a lot faster than the HP-42S, but it's also a lot slower than any smartphone or computer you're likely to encounter nowadays.

But for the most part, when people complain to me about poor INTEG performance, it's always ACC being 0 or unset. Setting it to something less aggressive, like 1E-12, almost always results in usable speed, even on the DM42.

Hmmh, I set ACC to 1E-5 and assumed this being less aggressive than 1E-12 - correct?

And regarding speed, I just wonder why the DM42 is so much worse than the WP 34S launched in 2011.

[Thomas Okken]

Well, feel free to ask SM to change INTEG to use tanh-sinh quadrature, or whichever algorithm it is you prefer.
I know I'm not going to.