How to compare HP solvers ?


I´ve been checking the different solvers for some HP calculators and I wonder if there is any organized paper that compares the features and limitations of of them. Since the one that we have in the HP 80, that might have been the very first one, HP created a whole family of those time saving tools.

I´ve seen several messages here at MoHPC discussing some types of solvcers, but I´m looking for something more comprehensive and complete. Can someone tell me where to find a paper on HP solvers ?



Try this, a good detailed descriptions of HP solvers.

To my mind, the best solver is the one featured on 17BII/19BII; also in 27S, even though it does not seem to have symbolic simplification (which is transparent in the user interface).
More than a solver, this is a true programming language, almost as powerful as BASIC (unfortunately, the lack of user-defined functions limits its power). The L() and G() functions allows intermediate variables and true programming. A pity that despite this, the 17BII/19BII/27S are often refered to as 'non-programmable devices' !!

Next would be the 42S solver, which lacks algebraic equation entry (RPN is nice, but NOT for equation entry) and forces you to 'MVAR' any variable supposed to appear in the menu (But let you access to the full power of RPN programming). A pity, really - think of the killer machine a merge of 42S and 27S would be...

Next, the 32SII/33S solver - neat, simple to use, well integrated with RPN (a unique case in HP calcs of harmony between RPN and algebraic equations), but with severe limitations: no editing capabilities of equations, no long variable names, no implicit multiplication (a nonsense when you don't have long variable names - you could have at least the benefit when you pay for the cost !), and somewhat clumsy interface (you need to circulate through all variables instead of the neat menus of 17BII/19BII/27S/42S). However, this works well for most problems.

Hope this helps.


I think that the solver on the 100LX/200LX (and 95LX?) is the most sophisticated. It interfaces with Lotus 1-2-3 as well as the other calc functions (like list-based statistics). You can use 1-2-3 as a R/W array and *really* write BASIC-equivalent programs. Take a look at the this thread and the pi program at the bottom of it:


I am preparing a presentation for the HHC2005 conference in Chicago this coming September to compare HP solvers. I expect it to be posted on the web. I am using a set of 17 equations to test various solvers, ranging from the HP34C to the HP49G+. The solvers seem to fall into a family of implementations:

1. The financial calculators
2. The HP28S, HP42s, and the graphics calculators (HP48SX did show some minor differences in results)
3 The HP32S, HP32SII, HP33s set of calculators.

I did test the TI-200 also and it showed superior results in the case of where the initial guess is near a minimum of an equation that has a root (y = exp(x) - 3 * x^2 + 8). None of the HP solvers found the root given initial guesses near the minimuum--most DID report the minimum value. The TI-200 found the root.

The HP solvers seem to have a common root (the HP34C solver) and share common criteria for when to continue to search and when to stop iterating.




Will you be posting your results anywhere on the internet as I am sure people including myself would be interested in your results? In fact I would expect the 17 equations would be enough to create some dialog.

You could possibly benefit by posting them early and see the programming techniques that are used by various people to solve them using the Solver function.

Chris Dean


I have the info on PowerPoint slides and will convert them into PDF that are easy to post. I also have a leading part of the presentation that includes a discussion (and brief comparison) between various algorithms (Bisection, Newton, Secant, Richmond (Halley), Householder, Brent, and Ridder). The presentation includes psuedo-code so folks can implement them in their favorite language. This too comes as a PowerPoint presentation that I will submit as a PDF. Both PDFs will be posted on the net. The presentation also includes a new algorithm that I designed that improves on Bisection. Moreover, I present a suggestion by DeMoivre that reduces the number of slope caculations. This has the effect of reeducing the number of function calls when approximating the derivatives using difference equations.

If you can't wait, then I encourage you to attent HHC2005 in Chicago.




Thanks for the offer but work commitments will not allow going to conferences as I am based in England. I will await the PDFs.

Good luck with the presentation.

Chris Dean


Hi Namir, all;

this is one of the (so too many) subjects I`d like to enhance my knowledge about. I`m sad I have no means to go to the HHC2005, so please, my name in the list waitting for your papers.

Good luck in your presentation (should it be 'break a leg'?)

Best regards.

Luiz (Brazil)


Thank you guys for yoru comments. Root-finding has been my hobby for the last 30 years!! I recently switched to playing with optimization methods because you can use then to solve multiple nonlienar equations AS WELL AS non-linear regression.

I also have a C# and VB.Net listing of a class that solves for a root of single-variable nonlinear equations and take into account the weaknesses of Newton methods-- low slope value near root and functions with parallel assymptotes (such as artan or tanh functions). I have the pcode for that cobined algorithm, which should appear in the PDF file.



Hello, Namir;

I`d like to drop you some lines related to numerical root-fiding for your appreciation. The issue is related to the root-fiding process itself, but probably will not add anything to your words (and presentations) at HHC2005. Would you contact me so I can send you some files?

lcvieira at quantica dot com dot br

Thank you.

Luiz (Brazil)

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