Details

sample31.0ms

Algorithm

intervals

Results

14.0ms	91×	body	1280	valid
5.0ms	126×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	3×	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: 15.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.1b	(- (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))

simplify74.0ms

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	2491	142
5	5001	142

prune49.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	2	29

Merged error: 1.0b

Counts

29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
1.0b	(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)))

series48.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

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

prune54.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	30	6	36

Merged error: 1.0b

Counts

36 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

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

series542.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt N)
175.0ms	(cbrt N)
174.0ms	(cbrt N)
6.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))

simplify87.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (83.0ms)

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

prune128.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	51	7	58

Merged error: 1.0b

Counts

58 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
1.0b	(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))))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt N)
181.0ms	(cbrt N)
176.0ms	(cbrt N)
7.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (* (cbrt (* (cbrt N) (cbrt N))) (cbrt (cbrt N))))))

simplify120.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (116.0ms)

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

prune142.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	52	7	59

Merged error: 1.0b

Counts

59 → 7

regimes25.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample903.0ms

Algorithm

intervals

Results

480.0ms	2835×	body	1280	valid
157.0ms	4054×	body	80	valid
91.0ms	632×	body	640	valid
35.0ms	312×	body	320	valid
13.0ms	167×	body	160	valid