On twitter @sebbbi mentions a cheap approximation of sin(π x) on [-1,1]
sin(π x)/4 ≈ x - x |x|
Normally if we want a two term approximation of an odd function we're stuck with the form:
a(x) = c₁ x + c₃ x³
but if we move away from pure polynomials then another two term form is possible:
b(x) = k₁ x + k₂ x |x|
and this generalizes to however many term odd/even function approximations (filling in otherwise skipped powers with one as abs which spit into two subexpressions w & w/o abs)
