Find mathematical expressions given a number.
Sometimes you have a decimal number and wonder if there is a closed-form expression for it.
By iterating over all possible expressions and seeing which one evaluates to the same decimal expansion.
It combines:
- Primitives: 1, 2, 3, 5, e, and pi
- Operations: negation, addition, multiplication, division
- Functions: exponentiation, root, logarithm, and cosine
View on the web: https://ex.leovandriel.com
Run locally:
./bin/serve.sh
open http://localhost:8000
Build for web, install Emscripten and run ./bin/build.sh.
Run in CLI:
./bin/find.sh [number]
- https://mrob.com/pub/ries/index.html
- https://isc.carma.newcastle.edu.au
- https://oeis.org
- https://xkcd.com/1047
- https://katex.org
The search tree is pruned by skipping operations that have an identical counterpart given the sub-tree, see use of iter->all. Optimization candidates can be found by looking for duplicate expressions, see collision.c. Excessive pruning can lead to missing values, which can be detected by comparing the optimized and un-optimized iterators, see missing.c. To get an overview of expression count, see stats.c.
The finder can generate over 1M expressions per second on a 2.4GhHz Core i5 machine. With every node added, the number of expressions grows with a factor 7. Expressions of up to 10 nodes are generated within seconds, see bench.c. Beyond that the time in seconds is about 1e-8 * 7^nodes.
MIT