I looked at the video a bit more closely, and it seems he requires the symmetry around 0 (he doesn't explicitly do range reduction to positive values), so you w

I looked at the video a bit more closely, and it seems he requires the symmetry around 0 (he doesn't explicitly do range reduction to positive values), so you want only odd-numbered coefficients. If so, you can do a formula of the type x * (c + x*x*(b + x*x*a)) (aka: ax⁵ + bx³ + cx; this is essentially the same as his formula with c=1 and prescaling x by a constant), which Sollya readily gives for single precision: > fpminimax(sin(x*2*Pi/65536.0),[|x,x^3,x^5|],[|SG...|],[0;16384]); Warning: For at least 2 of the constants displayed in decimal, rounding has happened. x * (9.58634263952262699604034423828125e-5 + x^2 * (-1.46252571143166976153082714517950080335140228271484e-13 + x^2 * 6.1585575698811928868593794069233315902067715796875e-23)) This has a maximum error of 0.000108 over that range. This is pretty close to optimal, but you can squeeze it ever so slightly lower (just below 0.0001) if you're willing to spend a lot of CPU time. :-)