This is a Mathematica function which takes an expression and spits out an optimized C code to evaluate this expression.
The basic idea that Mathematica expression like
x*x / (1 + x*x)is turned into C code
double tmp = x*x;
return out = tmp / (1 + tmp);Therefore the value x*x is computed only once and reused to compute the final value.
A more complicated example: the fourth derivative of Sin[Cos[x]] is:
Cos[x] Cos[Cos[x]] + 6 Cos[x] Cos[Cos[x]] Sin[x]^2 - 3 Cos[x]^2 Sin[Cos[x]] + 4 Sin[x]^2 Sin[Cos[x]] + Sin[x]^4 Sin[Cos[x]]Calling OptimizeExpressionToC[{D[Sin[Cos[x]], {x,4}]}] produces:
double tmp2 = Cos(x);
double tmp3 = Cos(tmp2);
double tmp6 = Sin(x);
double tmp7 = Power(tmp6,2);
double tmp11 = Sin(tmp2);
return -3*tmp11*Power(tmp2,2) + tmp2*tmp3 + tmp11*Power(tmp6,4) + 4*tmp11*tmp7 + 6*tmp2*tmp3*tmp7;The exact output is a little bit different, run the command yourself to see the exact result and have a look at example/example.nb how can be the result used.
You can find an example of implementing stereographic projection and its derivative at example/example.nb and example/example.cpp.
The notebook example.nb generates the mathematical expressions for stereographic projection turns them into a C++ code which is then inserted into example.cpp and final main.cpp is generated. This can then be compiled with g++ main.cpp.