Details

sample26.0ms

Algorithm

intervals

Results

11.0ms	85×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	20×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	7×	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: 18.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.8b	(- (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))

series11.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
10.0ms	(- (atan (+ N 1.0)) (atan N))

simplify74.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142

prune48.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.6b

Counts

29 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.6b	(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:

45.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

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

prune66.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	27	7	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	8	35

Merged error: 0.5b

Counts

35 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
13.1b	(cbrt (* (+ N 1.0) N))
13.1b	(cbrt (* (+ N 1.0) N))
13.1b	(cbrt (* (+ N 1.0) N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 40

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
4.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))

series308.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
97.0ms	(cbrt (* (+ N 1.0) N))
98.0ms	(cbrt (* (+ N 1.0) N))
106.0ms	(cbrt (* (+ N 1.0) N))

simplify65.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	208	572
1	609	524
2	2244	482
3	5002	474

prune184.0ms

Filtered

52 candidates to 47 candidates (90.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	52	8	60

Merged error: 0.5b

Counts

60 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.6b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite10.0ms

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-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 49

Calls

4 calls:

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

series273.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(cbrt (+ N 1.0))
88.0ms	(cbrt (+ N 1.0))
89.0ms	(cbrt (+ N 1.0))
7.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify53.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	198	498
1	513	454
2	1617	445
3	5002	430

prune176.0ms

Filtered

61 candidates to 53 candidates (86.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	62	7	69

Merged error: 0.5b

Counts

69 → 7

regimes27.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b 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

sample768.0ms

Algorithm

intervals

Results

401.0ms	2794×	body	1280	valid
134.0ms	4113×	body	80	valid
79.0ms	615×	body	640	valid
33.0ms	319×	body	320	valid
11.0ms	159×	body	160	valid