Three roads to a root.

What the comparison is really showing

Iteration count is not the whole cost of a numerical method. Newton asks for a derivative evaluation at every step. Bisection asks only for function values but needs a valid bracket. The secant method avoids an explicit derivative, but the estimated slope can become poor or collapse.

The laboratory therefore treats the graph as a way to inspect behavior, not a scoreboard declaring one method universally superior. Numerical analysis is mostly the art of knowing which assumptions you can afford.