Details

sample48.0ms

Algorithm

intervals

Results

22.0ms	85×	body	1280	valid
8.0ms	130×	body	80	valid
5.0ms	27×	body	640	valid
2.0ms	11×	body	320	valid
0.0ms	3×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize22.0ms

Local error

Found 1 expressions with local error:

1.7b	(- (atan (+ N 1)) (atan N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `diff-atan` `add-exp-log` `add-cube-cbrt` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 16

Calls

1 calls:

11.0ms

(- (atan (+ N 1)) (atan N))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(- (atan (+ N 1)) (atan N))

simplify1.7s

Counts

19 → 19

Iterations

Iter	Nodes
done	5000
5	1968
4	692
3	307
2	147
1	73
0	36

prune93.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite38.0ms

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:

36.0ms	(* (+ N 1) N)
1.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series77.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.9s

Counts

36 → 36

Iterations

Iter	Nodes
done	5008
4	2728
3	706
2	266
1	121
0	55

prune155.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))
0.4b	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 53

Calls

4 calls:

7.0ms	(cbrt (+ N 1))
8.0ms	(cbrt (+ N 1))
7.0ms	(cbrt (+ N 1))
0.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(cbrt (+ N 1))
49.0ms	(cbrt (+ N 1))
54.0ms	(cbrt (+ N 1))
5.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

simplify1.9s

Counts

65 → 65

Iterations

Iter	Nodes
done	5003
4	2058
3	747
2	346
1	167
0	80

prune324.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1))
0.3b	(cbrt (cbrt (+ N 1)))
0.3b	(cbrt (* (cbrt (+ N 1)) (cbrt (+ N 1))))
0.4b	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (* (cbrt (* (cbrt (+ N 1)) (cbrt (+ N 1)))) (cbrt (cbrt (+ N 1)))) N))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-div`
16×	`cbrt-prod`
11×	`*-un-lft-identity`
8×	`flip3-+` `flip-+`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`frac-times` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`pow1/3`
2×	`associate-l/` `associate-r/` `distribute-lft-out`

Counts

4 → 59

Calls

4 calls:

4.0ms	(cbrt (+ N 1))
4.0ms	(cbrt (cbrt (+ N 1)))
13.0ms	(cbrt (* (cbrt (+ N 1)) (cbrt (+ N 1))))
0.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (* (cbrt (* (cbrt (+ N 1)) (cbrt (+ N 1)))) (cbrt (cbrt (+ N 1)))) N))))

series161.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(cbrt (+ N 1))
59.0ms	(cbrt (cbrt (+ N 1)))
41.0ms	(cbrt (* (cbrt (+ N 1)) (cbrt (+ N 1))))
4.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (* (cbrt (* (cbrt (+ N 1)) (cbrt (+ N 1)))) (cbrt (cbrt (+ N 1)))) N))))

simplify1.5s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
3	1947
2	786
1	355
0	178

prune505.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.4b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	11
1	11
0	6

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s	2765×	body	1280	valid
296.0ms	4107×	body	80	valid
147.0ms	665×	body	640	valid
57.0ms	328×	body	320	valid
16.0ms	135×	body	160	valid