What is Eureka: The Solver?

When TK!Solver was removed from the Macintosh software market, the market was left with a gap. Spreadsheets, programming languages and statistics pro grams could grind through calculations when the user had already worked out a path to the solution. Stella and Stella for Business didn’t require a solution path because they applied their own path: a simple forward march to update variables. For some problems, this worked splendidly. But for many, it was inadequate, so we were left without a mass-market product to digest and solve almost any equation set. Borland saw this product opportunity and responded by developing Eureka: The Solver, a freeform numerical equation solver.

Eureka is useful for anyone who doesn’t just add up columns of numbers and prepare profit and loss statements. It does much more than just compute cell values from formulas. First you give Eureka the governing equations for the model, up to a maximum of 20 equations, and define any functions or unit conversions you’ll need, up to ten of each. You can also enter initial guesses and constraints to speed things up and to prevent a search from starting in an undesired area. Then tell Eureka to search for a solution or display an error message explaining why it can’t find one.

Standard trigonometric and logarithmic functions are available, as is treatment of imaginary and complex numbers. Time value of money, numerical integration and differentiation and normal probability distribution calculations arc supported as well. Error functions, Bessel functions and other esoteric functions used in science and engineering are not supported, and no interface is provided to expand the functions available by linking compiled subroutines. Hopefully a future upgrade will include this capability because it will greatly increase the number of problems that can be solved. In the meantime, if you can find a series expansion to approximate the desired function, the SUM function might give a reasonable approximation. Compound functions (like x = 1 if y is positive and x = -1 if y is negative) are not supported at all.

If you ask it to, Eureka can search for maximum or minimum values of a variable. Many real-world problems — like maximizing profit with respect to widget selling price, or like finding the best number of lathes versus drill presses to buy under a fixed budget — don’t have a direct algebraic solution. Either they require examining many possibilities and choosing the best or they require knowing how fast values change with respect to other values. With an equation solver, they become easy. Rather than setting up a spreadsheet and comparing many repetitive "what if" analyses (where you’ll never be sure you couldn’t do just a little bit better), use Eureka and find the best conditions directly.

While numbers are the goal of math models, often they aren’t useful by themselves. So Eureka lets you go further. You can generate a graph of any two variables against one another and zoom in and out to change the graph scale. Or you can produce lists of any variable versus another to print out or to import into a spreadsheet for further analysis. Verifying that the solution really satisfies the model is easy, as is search for multiple solutions. To protect your work as you change a model, you can produce a log of any work you do so you can refer to it later, or store a MacWrite-compatible report of the equations used and the solutions and graphs created. Borland also outlines a method you can use to create equation files from Turbo Pascal (or from a spreadsheet), but it will rarely save time over typing the problem into Eureka from the start.

If you have a 68881 coprocessor (standard on a Mac II, and available on other Macs through third-party accelerator boards), you’ll gain increased performance (in some cases up to 50 times faster) by using a special version of Eureka included on the standard product disk. Problems involving complicated models, misbehaved functions and high required degrees of accuracy will benefit the most. Even without a coprocessor and operating on a 512K Mac, however, Eureka isn’t a slouch. Its algorithms arc built to run efficiently. Choosing intelligent first guesses and setting reasonable accuracy limits arc the easiest ways to get speedy answers.

Learning to use Eureka takes a little time. Typing in equations and getting answers is easy enough, though the error messages can be obscure. On-screen help is available, but it’s too brief to be useful. The manual provides a good introduction to the product. It includes 21 examples from chemistry, finance, physics and game theory that point out important features. The program disk includes all the examples from the manual and 11 additional worked problems. If you become an advanced user and start pushing the limits, you’ll probably find the manual lacking. Understandably, the manual is meant to discuss the Eureka interface and not to provide a course in linear programming or problem solving, so consider getting a good textbook in the area of your model to read along with the manual.

Custer, Linda. (March 1988). Eureka: Problem Solver. MacUser. (pgs. 87, 90).

Download Eureka: The Solver for Mac

Architecture

Motorola 68K

Compatibility notes

Emulating this? It could probably run under: Mini vMac