fact: Definition mul_error prec n (f g : rpa) (X0 X : I.type) := let pf := approx f in let pg := approx g in let sx := (I.sub prec X X0) in let B := I.mul prec (Bnd.ComputeBound prec (Pol.mul_tail prec n pf pg) sx) (I.power_int prec sx (Z_of_nat n.+1)) in let Bf := Bnd.ComputeBound prec pf sx in let Bg := Bnd.ComputeBound prec pg sx in I.add prec B (I.add prec (I.mul prec (error f) Bg) (I.add prec (I.mul prec (error g) Bf) (I.mul prec (error f) (error g)))).
imports: Coq(ZArith Psatz Reals) Flocq(Raux) Coquelicot(Coquelicot) mathcomp.ssreflect(ssreflect ssrfun ssrbool eqtype ssrnat seq fintype bigop) Stdlib MathComp Coquelicot Xreal Interval Basic Xreal_derive Interval_compl Datatypes Taylor_poly Basic_rec Bound