Print information with every function evaluation used to find a root:

Count evaluations:

Use Reap and Sow to collect evaluation data:

Show the superlinear convergence of the method:

Monitor the time integration of a wave equation:

Monitor the solution progress when solving the sine–Gordon PDE:

Evaluations for a numerical minimization:

Evaluations for computing a numerical integral with NIntegrate:

Show a plot of the evaluation position versus evaluation number:

Evaluations for solving a differential equation with NDSolve with a extrapolation method:

A plot shows that with this method, not all evaluations are on the solution curve:

Count evaluations for doing a surface plot:

When the function is evaluated, it takes fewer evaluations since symbolic derivatives are used:

Evaluate any expression:

With a different starting value, the computation is stopped:

Distinguish between function and derivative evaluations in doing a numerical minimization:

Show function, gradient, and Hessian evaluations in blue, yellow and red, respectively:

Show where evaluations were done for part of a plot using a tooltip that indicates order:

Show number of evaluations required to find a root as a function of starting value:

Compare evaluations required for different local minimization methods:

Compare evaluations and timing required for different ODE integration methods in NDSolve:

Steps and evaluations as a function of PrecisionGoal and AccuracyGoal in NDSolve:

Use a fixed order explicit Runge–Kutta method:

Use an adaptive order extrapolation method:

Compare the two methods. Beyond a goal of about 12, adaptive order is clearly superior:

Evaluations in parameter space for a nonlinear fit:

The evaluation points on a contour plot of the sum of squares:

Use a better starting value:

Compare the two fits with the data: