High-precision value
Computed expression values are displayed here, separately from RIES candidates.
Continued fraction, base expansions, and digit statistics
Results
| candidate | value / root | error |
|---|
Search depth and display
Stage time limits are active search budgets after any lazy database package has loaded. Enter 0 to remove that module's internal time deadline. Depth-specific database modules show separate budgets for each depth tier.
RIES equation roots
Builds unary/binary expressions from digits and constants, then solves equations around the target.
Constants
Unary operations
Binary operations
Algebraic polynomial relation
Uses integer relation reconstruction for direct decimal inputs; precision controls remain internal.
Log-combination relation
Searches sparse linear relations among selected logarithmic or raw constants.
Target transforms
Default basis
Optional candidates
Low-precision linear combo
Looks for one-, two-, and three-term rational combinations of the low-precision constant basis.
Möbius constant relations
Checks fractional-linear relations in selected constants, including direct, log|x|, and exp(x) variants.
Constant database
Compares x and selected transforms with the 300-entry constant database by rational, algebraic, Möbius, and log-linear passes.
Depth transforms
Relation passes
Hard constant database
Loads the pruned harddb once at depth 4; depths 5/6 reuse the same rows with richer comparison constants.
Database depths
Relation passes
Hypergeometric pFq database
Lazy-loads cumulative depth 4/5/6 pFq chunks and compares H with multiplier families.
Database depths
Multiplier families
Integral/sum database
Lazy-loads integral and series identities: depth 4 uses the simplest low-height rows, while depths 5/6 use the full table with richer multiplier families.
Database depths
Multiplier families
L-function database
Compares decimal inputs against L(f,s) rational, quadratic, and logarithmic catalogued forms.
Integer search
For exact integer input: factorization, structured/precomputed database, and deterministic shortform search.