Different answers from Solve app and solve.SOLVE - latter is "wrong"

[DavZell]

I was browsing the calculator subreddit and someone posted an equation that their Casio couldn't solve despite it being simple. I decided to check the Prime.

Please note that I'm going through a calculator binge right now, as my trusty 48SX screen just died after 35+ years. I got a 48gII and 50g (eBay), and a Prime G2 (new). So my testing this was purely to play around different ways. Boy, were not in 48sx-land any more. The 50g got this correct, too, by the way.

The equation is: 300×10^-3 = ((6.625×10^-34 × 3×10^8) × X) ÷ 6625×10^-10

The correct answer is 10^18.

Solve.SOLVE(eqn,x) yeilds 9.99999999998E17
The Solve app yeilds 1E18

The HP 50g NUM.SLV yeilds 1000000000000000000 (1E18)

It seems odd that the first solution is off considering the only division is in numbers resulting in a power of 10.

Any thoughts?

[klesl]

I used Casio fx-991DE X and fx-991DE CW to solve mentioned equation and the result is 1×10^18

[DavZell]

(04-06-2024 05:30 PM)klesl Wrote:  I used Casio fx-991DE X and fx-991DE CW to solve mentioned equation and the result is 1×10^18

Agreed. I am wondering g why the two different answers on the Prime. Is there a reason the solve.SOLVE() returns different results? Does it work differently intentionally? A bug? Something else?

Thanks for your earlier response.

[Johnh]

Are we really saying that a result which is accurate to 10 SF is 'wrong'?

[DavZell]

(04-06-2024 10:39 PM)Johnh Wrote:  Are we really saying that a result which is accurate to 10 SF is 'wrong'?

Rather than saying wrong, then, say different. Why does that solve.SOLVE routine result in a different result than other methods on several other calculators from multiple brands? It seems odd (and interesting to me) that this would occur with an equation that has all components equally divisible and/or powers of 10. We aren't dealing with trig functions, roots, logs, pi, or e, for example.

[jte]

Two possibilities that jump to my mind for why an inexact result may be produced for a linear equation of this sort are that

1. a binary floating-point may be in use (that a base of 2, not 10, is being used with the floating-point scaling portion --- A * 2^B can be stored and processed exactly, rather than A * 10^B [for integers A and B within the ranges allowed by the floating-point arithmetic being used]), and
2. an iterative approach is being used to find solutions.
   

When I try this with the current public version, I do see that the Solve app gives different answers depending on the value of X before the Solve app's Solve menu button is pressed. (Solutions found by iterative methods can easily depend on the starting position.)

[DavZell]

(04-18-2024 01:24 AM)jte Wrote:  Two possibilities that jump to my mind for why an inexact result may be produced for a linear equation of this sort are that

1. a binary floating-point may be in use (that a base of 2, not 10, is being used with the floating-point scaling portion --- A * 2^B can be stored and processed exactly, rather than A * 10^B [for integers A and B within the ranges allowed by the floating-point arithmetic being used]), and
2. an iterative approach is being used to find solutions.
   

When I try this with the current public version, I do see that the Solve app gives different answers depending on the value of X before the Solve app's Solve menu button is pressed. (Solutions found by iterative methods can easily depend on the starting position.)

Good thoughts. Thanks