Numerical calculation
z = 0.51404189589007076139762973957688
candidate = 5*pi^2/96
A high-precision numerical result can suggest a compact analytic form.
Worked examples
Examples for numerical work and teaching
The point of an example is not that the program is impressive. The point is to see how much mathematical structure is already implied by a numerical value and a chosen expression alphabet.
Floating-point output
z = 0.22222222222
candidate = 2/9
Finite decimal output can hide a simple rational number.
Elementary functions
z = 0.846153846153846
candidate = tanh(log(sqrt(12))) = 11/13
A recognizer can turn a non-obvious function identity into an exercise.
Known constants
z = 1.202056903159594
candidate = zeta(3)
Named constants are useful tests, but availability depends on the calculator alphabet.
Gaussian integral
z = 0.886226925452758
candidate = sqrt(pi)/2
A numerical integral can be checked against a familiar closed form.
Integer identity
z = 2026
candidate = 1 + (9*5)^2
Date-like and integer searches are demonstrations, not evidence of a scientific law.
How to use these examples
Start with a small K. If the expected expression does not appear, check whether the calculator alphabet contains the required constants and functions, then increase K only as needed.