Jane Tanner reported her sighting immediately the police arrived on the scene of Madeleine's disappearance ... still in my opinion when timeous recovery might still have been effected.
The Smith sighting was not reported to the police for a fortnight after the event.
Take from that what you will.
AFAIK, Jane Tanner's sighting was not reported 'immediately' to the police. The GNR were talking to Kate and Gerry, neither of whom knew about the sighting at that time.
Jane became aware of Madeleine's disappearance when Kate et al were at the front of block 5. A prudent course of action would have been to inform the menfolk, so that they could search in the direction Jane saw the man walking.
I can't remember when Jane got around to informing the menfolk, but I would guesstimate it was an hour or more after she saw Tannerman, and an hour is one heck of a headstart. Personally, I would still have had a stab at searching in that direction, but that is just me.
At around 10.15 pm, Gerry seemed to be under the mistaken impression that Matthew had got the police called. Perhaps he felt it more prudent to wait with Kate for the police to arrive.
Have you any idea of when the GNR turned up at 5A? My best estimate at the moment is around 11.20 pm. Since policemen were engaged on working out the basics, I don't see how the Tannerman information could have been imparted to them before 11.30 pm. That would give Tannerman a headstart of 2 hours and 15 minutes.
I can walk from Luz to Lagos in less than this.
Precisely how 2 GNR officers could search this radius is beyond me.
IIRC, more GNR officers were called to Luz, and the incident was escalated to the PJ.
I can see nothing to criticise those first officers, but that of course is IMO.
