I have a situation where I am trying to plot errors, which are small but are nowhere near subnormal numbers in Float64.

Unfortunately, plot() is producing an incorrect graph, using Gadfly 1.3.1 in Julia 1.5.3.

Here is a simple demonstration of problem:

using Gadfly;
xvals = range( 0.0, 1.0, length=20 );
yvals = [ 0.0 , 1.5770373161480791e-18 , 2.983115103490406e-18 , 4.197248008233336e-18 , 5.3945317696645016e-18 , 6.844316881913259e-18 , 8.708236700751923e-18 , 1.0863668278404468e-17 , 1.2894457644236792e-17 , 1.4317750840733128e-17 , 1.4965586158467704e-17 , 1.5276181431484313e-17 , 1.6182869477102057e-17 , 1.8443012277801592e-17 , 2.1692238089739158e-17 , 2.4126051771260834e-17 , 2.4010574742241276e-17 , 2.306119442978225e-17 , 2.6917955234178657e-17 , 2.575849671298423e-17 ];
# this plots a line of zeros along the x axis
plot( x = xvals, y = yvals )
# this (still) plots a line of zeros
plot( x = xvals, y = yvals * 8 )
# this plots something that looks right, but its choice of yscale labels is strange
# and of course the scale is not correct :(
plot( x = xvals, y = yvals * 9 )
# this plots the correct shape
# but of course the scale is not correct :(
plot( x = xvals, y = yvals * 10 )

While I have worked around the problem for this data set, it raises the issue that the graphs are not necessarily reliable, which is obviously troubling for future use.

A good graph never comes out of the box automatically out of any box.
It’s not the tool I have to rely on, whenever I have to interprete a graph, but it is the creator of the graph, which is you, in this case.

Having said this and out of the way, I would recommend to change the order of magnitude of the y axis by 10^17, e.g. with:

plot( x = xvals, y = yvals * 10^17 , Guide.ylabel("y x 10^17"))

This is much easier to comprehend by the box (Gadfly) and by the viewer.

Regarding this

# this plots a line of zeros along the x axis
plot( x = xvals, y = yvals )

there obviously takes place some rounding or something similar for the purpose of pretty printing the numbers on the y axis. If you want more reliability from Gadfly in the future, you should open an issue about this at Issues · GiovineItalia/Gadfly.jl · GitHub . A short search didn’t come up with an existing issue.