The FMA instruction set has been around for roughly the past decade with both Intel and AMD processors. Only now this week thanks to the work of Intel engineer Sunil K Pandey is there an FMA-optimized tanh function along with atanh and sinh functions.
Testing of the FMA'ed tanh on an Intel Skylake CPU is showing a max improvement around 14% while the min/mean improvement clocks in around 4% faster than the prior code. Those interested can find the FMA optimized tanh function via this Glibc commit .
The sinh optimization is 4~17% faster. The atanh optimization is around 2% faster.
Not bad for something that's been commonplace among Intel/AMD x86_64 CPUs for years though surprising it took this long for the optimization to be cracked. In any event, Intel continues to deserve kudos for all their open-source toolchain optimizations over the years and especially when it comes to tuning the GNU C Library (glibc) for new x86_64 instruction set capabilities.
These improvements will be found in the GNU C Library 2.42 release due out around August.