No, it's more expensive for me to use the bike. But, I suspect that my situation is unique.

Non-bike commute: 200m walk, 22 min subway ride, 200m walk (each direction). cost per month (€21 or €0.70/day)
Bike commute: 25km round-trip is roughly 60-65 min (rolling time) depending on cycle traffic.

Health insurance benefits: no difference as full-coverage health insurance (with the exception of a once-a-year €10 payment the first time you use it) is mandatory (roughly 8% of gross pay)

Bike costs: Bike, lock, starting gear was €790. Helmet was €100. Clothes have been about €30. Lights/tubes/bag: €50.

Extra food costs: 500kcal extra/day due to riding (we should assume that I eat most of the kcal as my weight is steady at roughly 72kg). Depends on what I eat: usually a mazipan croissant (€1.20) and extra cafe latte (€1.60) and usually a beer in the evening (€1.20) ... for €4/day. When I don't ride, I usually don't take the croissant/coffee at work or the beer while preparing dinner.

Loss of reading time: I do miss the reading time on the subway. I would always read the NYT, SZ and DN on the mobile phone on the subway (€0.05/day with prepaid card at €0.09/MB).

I really enjoy riding, but I don't save money doing it.

In addition, I may even make the environment worse when one considers the excellent public transport I don't use and the extra food that I eat (production/water/transport costs).

I should also state that I do own a car that I use once/month for a 750km round-trip drive. €2500 up front, €600/year insurance/taxes/inspection, €1.60/l fuel, €500/year repairs