By comparing Φ(x) and f(x) we notice Φ(x) contains 3 numerical approximations. Therefore, we know in advance Φ(x) will take < 3^2 times f(x) + few more arithmetic operations ... roughly: Φ(x) will take < 100 sec. Leave the integrator accuracy 100.
... [suite], you can replace the two constant terms by their decimal evaluation. It will drop the timing nearly by ½. It will not significantly change the the integration due to the integrator not so accurate !