/// <summary>
/// Checks whether the given <see cref="MathProgram" /> computes a value that is consistently equivalent to that
/// computed
/// by another program according to some margin. The method works by substituting the variables in both programs'
/// expressions by random values for a certain number of trials. In each trial, the difference between the values
/// computed by both programs is calculated. If the difference is less than a given margin for all the trials, then the
/// programs are considered to be value-equivalent.
/// </summary>
/// <param name="program">The first program that we want to test.</param>
/// <param name="other">The second program that we want to test.</param>
/// <param name="margin">
/// The margin used to compare against the difference of values computed by both expressions in each
/// trial.
/// </param>
/// <param name="numTrials">The number of trials used to discern whether the given programs are equivalent.</param>
/// <returns><c>True</c> if the given programs are considered to be value-equivalent, <c>False</c> otherwise.</returns>
public static bool IsValueEquivalent(
this ITreeProgram <double> program, ITreeProgram <double> other, double margin = DEFAULT_MARGIN,
uint numTrials = DEFAULT_NUM_TRIALS)
{
// checks null
if (program == null || other == null)
{
return(false);
}
// checks equivalence
if (program.Equals(other))
{
return(true);
}
// checks expression or constant equivalence after simplification
program = program.Simplify();
other = other.Simplify();
if (program.Equals(other) ||
program.IsConstant() && other.IsConstant() && Math.Abs(program.Compute() - other.Compute()) < margin)
{
return(true);
}
// gets RMSE by replacing the values of the variables in some number of trials
return(program.GetValueRmsd(other, numTrials) <= margin);
}