results from CANDELS [@Rod2014], the Supernova Legacy Survey [SNLS @Per2012], the Cluster Lensing And Supernova survey with Hubble [CLASH @Gra2014], the Subaru Deep Field [SDF @Gra2011] and the Sloan Digital Sky Survey [SDSS @Dil2010]. Black symbols include results from @Gra2013 [@Bar2012; @Mel2012; @Li2011; @Rod2010; @Bot2008; @Dah2008; @Dil2008; @Hor2008; @Bla2004; @Ton2003; @Pai2002; @Har2000; @Cap1999]. []{data-label="sn_rate"}](SNrate){width="48.00000%"}

We compute the volumetric type Ia supernova rate as the convolution of the delay time distribution $\rm{DTD}(t)$ with the star formation history $\psi(t)$, i.e. $$n_{\rm SNIa}(t)=\int_{0}^{t}\psi(t-\tau)\rm{DTD}(\tau)\textrm{d}\tau.$$ For the star formation history, we employ a model from @Mad2014, based on a compilation of the cosmic star formation rates determined from UV and IR observations: $$\psi(z)=0.015\frac{(1+z)^{2.7}}{1+[(1+z)/2.9]^{5.6}}\;M_{\odot}\;\rm{yr}^{-1}\;h_{\rm 70}\;\rm{Mpc}^{-3}.$$ Following @Rod2014, we assume that the delay time distribution is accurately described by the following piecewise function: $$\rm{DTD}(t)= \left\{ \begin{array}{ll}
0 & \rm{if}\;\;\;t<0.04\;\rm{Gyr} \\
\eta_{1} & \rm{if}\;\;\;0.5\;\rm{Gyr}<t<0.04\;\rm{Gyr} \\
\eta_{0}t^{-1} & \rm{if}\;\;\;t>0.5\;\rm{Gyr}
\end{array}\right.
\label{dtd}$$ where $\eta_{0}$ and $\eta_{1}$ are free parameters. This model is well motivated by observations [@Rod2014; @And2018] as well as theoretical arguments derived from the evolution of binary systems [@Mao2012]. It accounts both for the population of prompt supernovae with delay time $t<0.5\;\rm{Gyr}$ [with $40\;\rm{Myr}$ as the shortest possible time before explosion, @Bel2005] and delayed supernovae with $\rm{DTD}\propto t^{-1}$ 