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Perform advanced algebraic, trigonometric, logarithmic, exponential, and combinatoric evaluations with strict PEMDAS/BODMAS algebraic hierarchy, Radian/Degree trigonometry, combinatorics (nPr, nCr), and 64-bit IEEE 754 floating-point accuracy.
() > Functions sin, cos, ln > Powers x^y > Multiplication/Division * / > Addition/Subtraction + -.θ in Degree mode, convert to radians θ_{rad} = θ_{deg} × (π / 180) before executing CORDIC transcendental series approximations.x^y = e^{y ln(x)}, square roots sqrt{x} = x^{0.5}, factorials n! = prod_{k=1}^n k, permutations nPr = rac{n!}{(n-r)!}, and combinations nCr = rac{n!}{r!(n-r)!}.|x - ext{round}(x)| < 10^{-12} to correct precision artifacts, formatting large or microscopic magnitudes into scientific notation m imes 10^n (e.g. 6.022e23).Radian mode measures angles based on the geometric radius of a circle, where one complete revolution equals 2π radians (~6.28318 rad). Degree mode divides a full circle into 360 arbitrary angular increments. Radians are mathematically fundamental for calculus, harmonic oscillation, and Taylor series because d/dx[sin(x)] = cos(x) holds true only when x is in radians.
Computers use binary IEEE 754 floating-point numbers (base-2), in which fractions like 1/10 (0.1) and 1/5 (0.2) become repeating infinite binary fractions, identical to 1/3 in base-10. When summed, tiny truncation residues occur at the 53rd bit of precision. This engine applies epsilon rounding thresholds (1e-12) to ensure clean exact arithmetic display.
Invented by Edsger Dijkstra, the Shunting-Yard algorithm uses an operator stack and an output queue. High-precedence operators (like exponents and functions) are executed before lower-precedence operators (like addition and subtraction), and parentheses force nested sub-expressions to be completely evaluated before being used as operands.
Permutations (nPr = n! / (n-r)!) calculate the number of ordered arrangements where sequence matters (e.g., race rankings or security pins). Combinations (nCr = n! / (r!(n-r)!)) calculate groupings where arrangement order is irrelevant (e.g., lottery numbers or poker hands), dividing out the r! redundant symmetries.