It doesn't seem like FPGA reprogramming time will be an issue. Presumably, they will work on one problem at a time. They will have a custom instruction to calculate Pi and let the machine run for a few months and then switch to crunching data from seismic oil well probes.
Modern FPGAs can be reprogrammed in a few milliseconds, which seems like a long time in the computer world. In essence megabytes of SRAM need to be written to in order to configure an FPGA.
Also, FPGAs have the ability to do partial reconfiguration, but the support is spotty. In the ideal world, parts of an FPGA would be reconfigured while the other parts were still in operation.
The issue I was thinking of is if you needed multiple "custom instructions" within a loop. Another related issue, if multiple tiles are considered, is the interconnect between the processor core and the tiles. Interconnect is expensive, so there's a trade off to be made. Profiling data showing a curve of unique accelerator functions for the targeted problem domains and their temporal relationship (e.g. there may be ten accelerator functions but they are executed several milliseconds apart or functions A and B tend to appear in an inner loop together) would help make the trade off.
Modern FPGAs can be reprogrammed in a few milliseconds, which seems like a long time in the computer world. In essence megabytes of SRAM need to be written to in order to configure an FPGA.
Also, FPGAs have the ability to do partial reconfiguration, but the support is spotty. In the ideal world, parts of an FPGA would be reconfigured while the other parts were still in operation.