Algorithms and approximations
Roots and Newton: laboratory
Compare nine experiments: Babylonian averaging, bisection, secant, Halley and Newton on different equations. Follow the steps and distinguish a numerical estimate from exact rational bounds.
Rule and computation status
One update per second. Bisection also shows the initial midpoint; secant shows both initial estimates. Select any table row.
Function and current-step construction
Area-N rectangle and reference square
Both sides use equal scale. The dashed square uses a numerical reference for drawing only, not for proving bounds.
Independent check with exact fractions
Open exact endpoint fractions
L =
U =
Decimal endpoints may look identical due to machine rounding. Verification uses fractions and BigInt integers, not displayed decimals. Beyond the fourth/fifth step this distinction matters.
Value table
Nine guided cases, not a universal solver. No free expressions are executed. Graphs are sampled. Machine references do not certify error; exact brackets are available only for the two indicated experiments.