CLANS stands for “Closed Loop Analysis of Noise Shapers”.
Inside the Sigma-Delta modulator–which converts multi-bit PCM to a 1-bit DSD signal–there is a component called a “noise shaper”. This is comprised mainly of a filter which pushes quantization noise inherent to 1-bit systems out of the audible range. Every system which produces a DSD stream (whether it be in software or in the mastering environment) must do some form of noise shaping.
“Traditionally” designed noise shapers are essentially built to spec using roughly the same filter design concepts as are used for analog/IIR filters (speaker crossovers, etc). The “Order 5” and “Order 7” filters fall in this category.
CLANS uses an iterative optimization technique called dynamic programming to improve on the technical specs of a traditionally designed filter. At filter design time, the computer chugs for a while by making tiny iterative changes to the filter designs and tracking improvement or compromise in certain technical characteristics. The filter that pops out at the end is the most optimized one that it could come up with.
The CLANS filters don’t use any more or less CPU at runtime than the other options because the filter topology (7th order loop filter) is the same either way.
How much of a sonic difference you perceive will depend a lot on how your DAC is architected. Small differences in noise shaper design are most noticeable on discrete DSD DACs like the HOLO Spring, T+A DAC-8 DSD, DSC-1 since these DACs perform no further processing of the signal in the digital domain. DACs with their own signal processing–like the Dave–may obscure some of the differences depending on exactly what is going on inside.