AutoNumerics-Zero: Evolution discovers 10-operation exp function 1Mx better
AI evolves a 10-step program that beats centuries of math by 6 orders of magnitude.
A team from Google, led by Esteban Real and Quoc V. Le, introduced AutoNumerics-Zero, a method that uses evolutionary symbolic regression to automatically discover highly efficient approximations of transcendental functions like exp, sin, and log. These functions cannot be natively computed by digital hardware and are traditionally approximated using methods like Taylor series, which were designed for arbitrary accuracy. However, for most modern applications using finite-precision types (e.g., float32), extra accuracy is wasted. The researchers realized that by abandoning the goal of arbitrary precision, evolution could find far more efficient programs.
Starting from empty code, the system combined only basic operations (+,-,×,÷) to build novel mathematical expressions. The standout result: a program using just 10 operations that approximates the exponential function to 14 significant figures — more than 1 million times more accurate than any known approximation of that size. The paper, accepted at ICML 2026, also includes proofs and additional results. This work opens the door to automatically generating high-performance math libraries for scientific computing, potentially replacing hand-crafted approximations with AI-discovered ones.
- 10-operation program computes exp(x) to 14 significant figures, surpassing prior methods by >6 orders of magnitude
- Uses evolutionary symbolic regression with no prior math knowledge beyond basic arithmetic operations
- Accepted to ICML 2026; applicable to finite-precision types like float32 commonly used in ML and HPC
Why It Matters
AI discovers faster, more accurate math functions, potentially replacing centuries-old hand-crafted approximations in scientific computing.