Details

sample62.0ms

Algorithm

intervals

Results

29.0ms	79×	body	1280	valid
11.0ms	134×	body	80	valid
8.0ms	26×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	6×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
1.9b	(- (atan (+ N 1)) (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` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

3.0ms	(atan (+ N 1))
7.0ms	(- (atan (+ N 1)) (atan N))

series17.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
15.0ms	(- (atan (+ N 1)) (atan N))

simplify2.0s

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
5	4138
4	1124
3	385
2	153
1	77
0	41

prune80.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.9b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite282.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
3×	`associate-r`
2×	`associate-*l/` `insert-posit16` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

281.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series45.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify489.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
2	770
1	131
0	55

prune98.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.9b	(atan2 1 (+ 1 (* (+ N 1) N)))
13.0b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 44

Calls

4 calls:

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
6.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify1.2s

Counts

56 → 56

Iterations

Iter	Nodes
done	5002
5	3194
4	944
3	333
2	129
1	52
0	32

prune163.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.9b	(atan2 1 (+ 1 (* (+ N 1) N)))
13.0b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 50

Calls

4 calls:

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

series45.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify1.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	5002
5	3194
4	944
3	333
2	129
1	52
0	32

prune201.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes27.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
1	11
0	6

end0.0ms

sample1.3s

Algorithm

intervals

Results

733.0ms	2937×	body	1280	valid
182.0ms	3972×	body	80	valid
164.0ms	615×	body	640	valid
72.0ms	327×	body	320	valid
15.0ms	149×	body	160	valid