Details

sample51.0ms

Algorithm

intervals

Results

22.0ms	86×	body	1280	valid
7.0ms	123×	body	80	valid
6.0ms	29×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	5×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ 1.0 N))
1.4b	(- (atan (+ 1.0 N)) (atan N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

2.0ms	(atan (+ 1.0 N))
8.0ms	(- (atan (+ 1.0 N)) (atan N))

series19.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ 1.0 N))
17.0ms	(- (atan (+ 1.0 N)) (atan N))

simplify2.1s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
5	3978
4	1072
3	364
2	154
1	79
0	43

prune126.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1.0))
0.4b	(atan2 1.0 (+ (* N (+ N 1.0)) 1))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `add-cube-cbrt`
3×	`associate-l`
2×	`associate-*r/` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

17.0ms	(* N (+ N 1.0))
0.0ms	(atan2 1.0 (+ (* N (+ N 1.0)) 1))

series84.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* N (+ N 1.0))
5.0ms	(atan2 1.0 (+ (* N (+ N 1.0)) 1))

simplify798.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
2	748
1	156
0	56

prune135.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ (* N (+ N 1.0)) 1))
0.6b	(* (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))) (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))))
14.9b	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
14.9b	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ (* N (+ N 1.0)) 1))
20.0ms	(* (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))) (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))))
2.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
2.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1.0 (+ (* N (+ N 1.0)) 1))
4.0ms	(* (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))) (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))))
20.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
24.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))

simplify7.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	4350
2	522
1	136
0	64

prune411.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize61.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
14.9b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
15.4b	(cbrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
15.4b	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 42

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
1.0ms	(cbrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
1.0ms	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

series273.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
126.0ms	(cbrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
127.0ms	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify2.4s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	1367
2	343
1	94
0	56

prune243.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes70.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	2832×	body	1280	valid
215.0ms	4037×	body	80	valid
108.0ms	630×	body	640	valid
45.0ms	336×	body	320	valid
16.0ms	165×	body	160	valid