On your fast system, Smath spits out this 4 pages document in ~ 10 sec.
It reconciliates spline derivatives & integration
l_p_c_splines are those found in Mathcad, Matlab ... [universal].
All modules are scalar and thus support "dichotomy solve"

Jean

Maths EDU Reconciliation [l_p_c_splines].sm (76 KiB) downloaded 103 time(s).

Erratum, var:=5.9879