I found an interesting files there
$CUDALinkPath -> ../GPUTools
here
Wolfram/WolframEngine/13.0/SystemFiles/Links/GPUTools/SymbolicGPU.m
the content looks like if it was a part of complied code of Mathematica to CUDA/OpenCL translator
iGPUExpression[Power[x_, Rational[1, 2]], opts:OptionsPattern[]] := CStandardMathOperator[Sqrt, {iGPUExpression[x, opts]}]
iGPUExpression[Power[x_, Rational[-1, 2]], opts:OptionsPattern[]] := COperator[Divide, {1.0, CStandardMathOperator[Sqrt, {iGPUExpression[x, opts]}]}]
iGPUExpression[Power[x_, r:Rational[_, _]], opts:OptionsPattern[]] := CStandardMathOperator[Power, {iGPUExpression[x, opts], iGPUExpression[r, opts]}]
iGPUExpression[Power[x_, 2], opts:OptionsPattern[]] := COperator[Times, {iGPUExpression[x, opts], iGPUExpression[x, opts]}]
iGPUExpression[Power[x_, y_], opts:OptionsPattern[]] := CStandardMathOperator[Power, {iGPUExpression[x, opts], iGPUExpression[y, opts]}]
...
Reminds me SymbolicC package. Has anyone tried to use this library for something? Is there a documentation for it?
