See also [:SymbolicBenchmarks: this other page].
The Symbolic Benchmark Challenge Suite
SETUP: Let f = (x+y+z+1)^{15}. COMPUTATION: Compute all coefficients of all monomials of f\cdot (f+1), i.e., expand that expression.
SETUP: Define a function f(z) = \sqrt{1/3}\cdot z^2 + i/3. COMPUTATION: Compute the first 5 digits of the numerator of the real part of f(f(f(...(f(i/2))...) iterated 10 times.