There are many hashes that use more thorough mixing functions than can be achieved with one or a few arithmetic operations (like in universal hashes), thus for them the collision probability reaches the limit imposed by the length of the hash value. Modern CPUs have various instructions that can be exploited in mixing functions that have about the same speed as simpler arithmetic operations, but which achieve a better mixing.
An example is the Alred construction (Joan Daemen & Vincent Rijmen, in 2005-02), which was inspired by the old CBC-MAC algorithm, but it is much more efficient (in this construction, the hash mixing function is derived from the internal mixing function used in some block cipher function, for example the AES block cipher function, so it can be implemented with the AES round function instructions of x86-64 and Aarch64, which are very fast in modern processors; this hash function uses the AES instructions but it is several times faster than the AES encryption/decryption algorithms, which are already very fast).
Another example is any hash function that has the structure used in the Jutla authentication method (Charanjit Singh Jutla @ IBM, 2000-04-14; in this method, the input text is partitioned in blocks with the length equal to the hash length, an LFSR, i.e. linear-feedback shift register, generates a sequence that is added to each block, to make the hash depend on the order of the input blocks, then a parallel mixing function transforms each input text block into a scrambled text, in a different space of values, then in the transformed space a simple additive function, even the simplest, which is bitwise addition modulo 2, can be used to reduce the transformed message to a single intermediate hash value, and finally the inverse of the mixing function is applied to the intermediate hash value to produce the final hash value by going back to the original space of values; this makes the computation of the hash parallelizable, thus very fast; there are universal hashes based on scalar products which have the same structure like this, but the difference is that they use a simple multiplication instead of a complex mixing function).