A variation on biexponential scaling similar to logicle scaling. The biexonential scale is a combination of linear and log scaling on a single axis using an arcsine function as its backbone. Biexponential scales are more generally referred to as hybrid scales and include other variations like lin/log or log with negative.
More information on Hyperlog scaling can be found here:
Bagwell, CB. (2005). Hyperlog-a flexible log-like transform for negative, zero, and positive valued data. Cytometry. 64: 34-42.