The verify(P, Q, function_shells) calling sequence verifies the approximate equality between two function plots.

The parameters, P and Q, are assumed to be either PLOT data structures, sets or lists of CURVES data structures, or a CURVES data structure.

The verify(P, Q, function_shells) returns true for CURVES data structures P and Q if the points of each curve fall within an epsilon shell of a linear piecewise interpolation of the points of the other curve.

The points in the CURVES data structure must be in order and the x-coordinates must be monotonically increasing.

If P or Q are PLOT data structures or sets or lists of CURVES data structures, it checks that for each CURVES data structure in either P or Q, there exists a CURVES data structure in the other set which matches it.

This procedure does not compare any other features of the PLOT or CURVES data structures.

$a≔\mathrm{plot}\left(\sin \left(x\right)\,x=0..1\right)\:$

$b≔\mathrm{plot}\left(\sin \left(x\right)\,x=0..1\,\mathrm{numpoints}=10\,\mathrm{adaptive}=\mathrm{false}\right)\:$

$c≔\mathrm{plot}\left(\sin \left(x\right)\,x=0..1\,\mathrm{numpoints}=37\,\mathrm{adaptive}=\mathrm{false}\right)\:$

$d≔\mathrm{plot}\left(\sin \left(x\right)+\frac{x}{10}\,x=0..1\right)\:$

$\mathrm{verify}\left(a\,b\,\mathrm{function\_shells}\left(0.01\right)\right)$

$\mathrm{true}$

$\mathrm{verify}\left(a\,c\,\mathrm{function\_shells}\left(0.01\right)\right)$

$\mathrm{true}$

$\mathrm{verify}\left(a\,d\,\mathrm{function\_shells}\left(0.01\right)\right)$

$\left[\mathrm{false}\,\left[0.102500000000000\,0.102320612500000\right]\,\left[0.102500000000000\,0.112570612500000\right]\right]$

$\mathrm{verify}\left(a\,d\,\mathrm{function\_shells}\left(0.1\right)\right)$

$\mathrm{true}$