Inverse RPN calculator for numerical experimentsConstant Recognition
A browser version of a constant-recognition experiment: enter a numerical result and search whether a short sequence of scientific calculator operations can reproduce it.
z = 0.51404189589007076139762973957688K max = 8candidate = 5*pi^2/96status = numerical leadProblem
The usual calculator problem is reversed.
Normally one enters a formula and obtains a number. Here the input is a number, and the program enumerates formulas that could have produced it. This is useful when a computation returns a decimal value and the next question is whether it has a compact analytic form.
- 1A virtual scientific RPN calculator defines the alphabet of operations.
- 2Integer codes enumerate button sequences in a fixed order.
- 3Each code is evaluated numerically and compared with the target value z.
- 4The search proceeds by increasing code length K, so short formulas appear first.
Examples
Numerical values should be treated as hypotheses, not answers.
A match is a candidate identity. It becomes mathematics only after independent verification: higher precision, symbolic manipulation, or a derivation from the original problem.
| Input value | Candidate expression | Use in practice |
|---|---|---|
| 0.51404189589007076139762973957688 | 5*pi^2/96 | recognition of a numerical result from a high-precision calculation |
| -0.0833333333333 | -1/12 | simple rational value hidden by decimal notation |
| 11/13 | tanh(log(sqrt(12))) | example of a non-obvious identity useful in teaching |
Cost of search
Increasing K is expensive.
The original single-threaded browser version notes that each step in code length increases the search time by roughly a factor of 36. The parallel and WebGPU versions are attempts to make larger searches more practical, not a reason to ignore the combinatorial growth.
What the web version is for
- Checking numerical results from calculations or simulations.
- Preparing examples for teaching elementary functions.
- Comparing exact-looking formulas before doing a proof.
- Exploring the behavior of brute-force symbolic search.