ADDITIONAL INFORMATION (I think this might be more likely the issue):
I believe that -equalize in the default setting (all channels together) is not working correctly (since IM 6.8.4.0) and may be using linear channels.
This is a comparison of -equalize with my redist in the same mode (shape= uniform)
convert zelda3.jpg -equalize zelda3_equal.jpg
redist -s uniform -m rgb -g
rec601 zelda3.jpg zelda3_uni_rec601.jpg
redist -s uniform -m rgb -g
rec709 zelda3.jpg zelda3_uni_rec709.jpg
The two look the same when channels are processed separately.
convert zelda3.jpg -channel rgb -equalize zelda3_channels_equal.jpg
convert zelda3.jpg -intensity rec601luma -separate +channel zelda3_channels_%d.png
redist -s uniform -m rgb zelda3_channels_0.png zelda3_channel_uniform_0.png
redist -s uniform -m rgb zelda3_channels_1.png zelda3_channel_uniform_1.png
redist -s uniform -m rgb zelda3_channels_2.png zelda3_channel_uniform_2.png
convert zelda3_channel_uniform_*.png -combine -colorspace sRGB zelda3_channels_uniform.jpg
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