Details

sample31.0ms

Algorithm

intervals

Results

16.0ms	100×	body	1280	valid
4.0ms	121×	body	80	valid
3.0ms	24×	body	640	valid
0.0ms	5×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 16.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify75.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2447	142
5	5001	142

prune41.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	2	29

Merged error: 1.1b

Counts

29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
1.1b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

6.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series42.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify58.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127

prune53.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	30	6	36

Merged error: 1.0b

Counts

36 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
1.1b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt N)
2.0ms	(cbrt N)
2.0ms	(cbrt N)
1.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))

series503.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(cbrt N)
163.0ms	(cbrt N)
165.0ms	(cbrt N)
9.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))

simplify85.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (81.0ms)

Iter	Nodes	Cost
0	75	232
1	164	204
2	533	198
3	2411	194
4	5001	191

prune115.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	53	5	58

Merged error: 1.0b

Counts

58 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
1.1b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (* (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N))))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

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

series531.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(cbrt N)
181.0ms	(cbrt N)
170.0ms	(cbrt N)
6.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (* (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N))))))

simplify119.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (114.0ms)

Iter	Nodes	Cost
0	80	292
1	184	252
2	664	246
3	3409	246
4	5001	243

prune140.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	52	5	57

Merged error: 1.0b

Counts

57 → 5

regimes19.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample804.0ms

Algorithm

intervals

Results

441.0ms	2924×	body	1280	valid
143.0ms	4032×	body	80	valid
72.0ms	590×	body	640	valid
27.0ms	279×	body	320	valid
12.0ms	175×	body	160	valid

Details

sample31.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series12.0ms

simplify75.0ms

prune41.0ms

localize6.0ms

rewrite7.0ms

series42.0ms

simplify58.0ms

prune53.0ms

localize12.0ms

rewrite8.0ms

series503.0ms

simplify85.0ms

prune115.0ms

localize14.0ms

rewrite5.0ms

series531.0ms

simplify119.0ms

prune140.0ms

regimes19.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample804.0ms

Profiling