Inverse Symbolic Calculator illustration

Inverse Symbolic Calculator

Turns a decimal back into the exact expression that produced it. Integer-relation searches (continued fractions, PSLQ) test rational multiples, sums, ratios and powers of π, e, √2, ln 2, φ, γ, ζ(3) and dozens of named constants, and every candidate is scored against the digits you supplied so chance fits are rejected. The sequence mode recognises named integer sequences, polynomials and linear recurrences and predicts the next terms.

Whole numbers separated by commas or spaces; at least 4 terms.

Demo with sample data

Examples

Notes

  • Complexity counts the decimal digits a candidate’s integer coefficients could explain by luck; a match is only shown when your input carries at least 3 more digits than that, and called convincing at 6 or more.
  • Search basis: π, e, √2, √3, √5, ln 2, ln 3, ln 10, φ, γ, ζ(3), Catalan’s G, plus algebraic numbers up to degree 4, elementary functions of small rationals, and about 40 named constants (Feigenbaum, Khinchin, Glaisher, Dottie, …).
  • Sequences are matched against about 80 named sequences (with any offset), polynomials in n, and linear recurrences with constant coefficients.

Explore the idea

This interactive demo needs JavaScript.