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I'll leave the question open, but here are some other attempts. Credit goes to RMartinhoFernandes for solution3, which requires his Pointfree module for the /\ combinator.

sumProgressions3 :: Integer -> Integer
sumProgressions3 limit = solve [1 .. limit]
multipleOf n = (== 0) . (`mod` n)
multipleOf3Or5 = uncurry (||) . ((multipleOf 3) /\ (multipleOf 5))
solve = sum . filter multipleOf3Or5

And solution4 is a completely in-lined version of the simplified formula in my question:

sumProgressions4 :: Integer -> Integer -> Integer -> Integer
sumProgressions4 d1 d2 lim = let d3 = d1 * d2
 in d1 * (lim `div` d1) * (1 + (lim `div` d1)) `div` 2 
 + d2 * (lim `div` d2) * (1 + (lim `div` d2)) `div` 2 
 - d3 * (lim `div` d3) * (1 + (lim `div` d3)) `div` 2

I've repeated the benchmarks on my machine with the same parameters as above.

I'll leave the question open, but here are some other attempts. Credit goes to RMartinhoFernandes for solution3, which requires his Pointfree module for the /\ combinator.

sumProgressions3 :: Integer -> Integer
sumProgressions3 limit = solve [1 .. limit]
multipleOf n = (== 0) . (`mod` n)
multipleOf3Or5 = uncurry (||) . ((multipleOf 3) /\ (multipleOf 5))
solve = sum . filter multipleOf3Or5

And solution4 is a completely in-lined version of the simplified formula in my question:

sumProgressions4 :: Integer -> Integer -> Integer -> Integer
sumProgressions4 d1 d2 lim = let d3 = d1 * d2
 in d1 * (lim `div` d1) * (1 + (lim `div` d1)) `div` 2 
 + d2 * (lim `div` d2) * (1 + (lim `div` d2)) `div` 2 
 - d3 * (lim `div` d3) * (1 + (lim `div` d3)) `div` 2

I've repeated the benchmarks on my machine with the same parameters as above.

I'll leave the question open, but here are some other attempts. Credit goes to RMartinhoFernandes for solution3, which requires his Pointfree module for the /\ combinator.

sumProgressions3 :: Integer -> Integer
sumProgressions3 limit = solve [1 .. limit]
multipleOf n = (== 0) . (`mod` n)
multipleOf3Or5 = uncurry (||) . ((multipleOf 3) /\ (multipleOf 5))
solve = sum . filter multipleOf3Or5

And solution4 is a completely in-lined version of the simplified formula in my question:

sumProgressions4 :: Integer -> Integer -> Integer -> Integer
sumProgressions4 d1 d2 lim = let d3 = d1 * d2
 in d1 * (lim `div` d1) * (1 + (lim `div` d1)) `div` 2 
 + d2 * (lim `div` d2) * (1 + (lim `div` d2)) `div` 2 
 - d3 * (lim `div` d3) * (1 + (lim `div` d3)) `div` 2

I'll leave the question open, but here are some other attempts. Credit goes to RMartinhoFernandes for solution3, which requires his Pointfree module for the /\ combinator.

sumProgressions3 :: Integer -> Integer
sumProgressions3 limit = solve [1 .. limit]
multipleOf n = (== 0) . (`mod` n)
multipleOf3Or5 = uncurry (||) . ((multipleOf 3) /\ (multipleOf 5))
solve = sum . filter multipleOf3Or5

And solution4 is a completely in-lined version of the simplified formula in my question:

sumProgressions4 :: Integer -> Integer -> Integer -> Integer
sumProgressions4 d1 d2 lim = let d3 = d1 * d2
 in d1 * (lim `div` d1) * (1 + (lim `div` d1)) `div` 2 
 + d2 * (lim `div` d2) * (1 + (lim `div` d2)) `div` 2 
 - d3 * (lim `div` d3) * (1 + (lim `div` d3)) `div` 2

I've repeated the benchmarks on my machine with the same parameters as above.

Repeated benchmarks on my machine with the same parameters as above:

benchmarking solution1
mean: 496.9938 ns, lb 467.8051 ns, ub 532.6672 ns, ci 0.950
std dev: 166.0609 ns, lb 142.3465 ns, ub 185.5721 ns, ci 0.950
found 25 outliers among 100 samples (25.0%)
 24 (24.0%) high severe
variance introduced by outliers: 97.866%
variance is severely inflated by outliers
benchmarking solution2
mean: 476.2878 ns, lb 455.9949 ns, ub 501.5564 ns, ci 0.950
std dev: 116.3743 ns, lb 95.50535 ns, ub 138.1666 ns, ci 0.950
found 11 outliers among 100 samples (11.0%)
 11 (11.0%) high mild
variance introduced by outliers: 95.759%
variance is severely inflated by outliers
benchmarking solution3
mean: 496.9193 ns, lb 485.7492 ns, ub 510.2516 ns, ci 0.950
std dev: 61.94774 ns, lb 47.27249 ns, ub 81.16098 ns, ci 0.950
found 12 outliers among 100 samples (12.0%)
 6 (6.0%) low severe
 2 (2.0%) high mild
 4 (4.0%) high severe
variance introduced by outliers: 86.239%
variance is severely inflated by outliers
benchmarking solution4
mean: 487.7629 ns, lb 457.9013 ns, ub 522.6022 ns, ci 0.950
std dev: 164.0337 ns, lb 143.6491 ns, ub 179.1870 ns, ci 0.950
variance introduced by outliers: 97.867%
variance is severely inflated by outliers