Compute optimizations for low precision machine learning operations

A data processing system comprising:

• a memory stack including multiple memory dies;
• and
• a general-purpose graphics processing unit (GPGPU) coupled with the memory stack via one or more memory controllers, the GPGPU including a plurality of multiprocessors having a single instruction, multiple thread (SIMT) architecture, the GPGPU including a dynamic precision floating-point unit including a functional unit to perform variable precision floating-point operations, the dynamic precision floating-point unit including a hardware control unit having a precision tracker to track an available number of bits of precision for computed data relative to a target precision and a numerical transform unit to perform an intermediate numerical transform on computed data when the computed data reaches a threshold precision, wherein the numerical transform unit is to perform a multiplication operation using a logarithm to transform an intermediate value to prevent an underflow during a sequence of operations and perform a division operation using a logarithm to reverse the transform.