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Matching increasing experimental precision of ttH production at LHC and HL-LHC would soon require NNLO-level predictions on the theory side, but calculating massive five-point two-loop virtual amplitudes needed for that is at the frontier of what is possible with the current methods of solving IBP relations and evaluation of Feynman integrals. In this talk I would like to go into the detail of how the computational challenges are resolved in a recent calculation of the Nf part of qq->ttH amplitude, and what is planned after that.
Based on: 2402.03301, 2211.03572, and 2305.19768.