Recent hard X-ray observations found that electrons are accelerated in magnetic white dwarfs (WDs). Detection of GeV gamma rays from novae by Fermi-LAT infers that protons are accelerated to hundreds of GeV there. These facts motivated us to search for the cosmic rays (CRs) from historic outbursts of WDs accumulated in the local bubble around us. We propose CR model spectra at the heliopause including the local CRs from historic WD outbursts. The total CR spectra are assumed to consist of these and the Galactic components deduced from Fermi-LAT -ray observations. The two components are fitted to reproduce the Voyager-1 spectra and the high-energy CR data on/near Earth when summed, species by species. We find that a common local spectral shape and simple power-law Galactic spectral reproduce all nuclear CR spectra at the heliopause. The hardening of the nuclear CRs is found to be caused by the roll-down of the soft local WD CRs at around ~300 GeV. The WD CRs induce a hump in -ray emissivity in the GeV range. Such a hump is found in the inner Galaxy indicating that the fluxes of CRs from WD outbursts CRs ~2.5 times higher there than inside the local bubble.