Details

sample29.0ms

Algorithm

intervals

Results

14.0ms	95×	body	1280	valid
5.0ms	130×	body	80	valid
2.0ms	20×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	4×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 16.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

series13.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify75.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	74	154
1	143	145
2	289	143
3	681	142
4	2491	142
5	5001	142

prune42.0ms

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: 0.7b

Counts

29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite8.0ms

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)))

series50.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(* (+ 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	120	152
1	432	127
2	2314	127
3	5002	127

prune51.0ms

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: 0.7b

Counts

36 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
14.6b	(cbrt (* (+ N 1.0) N))
14.6b	(cbrt (* (+ N 1.0) N))
14.6b	(cbrt (* (+ N 1.0) N))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
19×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`associate-l`
9×	`associate-r`
6×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

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

series319.0ms

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)))))
102.0ms	(cbrt (* (+ N 1.0) N))
107.0ms	(cbrt (* (+ N 1.0) N))
103.0ms	(cbrt (* (+ N 1.0) N))

simplify87.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (78.0ms)

Iter	Nodes	Cost
0	238	809
1	709	761
2	3000	719
3	5001	702

prune212.0ms

Filtered

88 candidates to 71 candidates (80.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	88	0	88
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	88	6	94

Merged error: 0.7b

Counts

94 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series35.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify73.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	49	332
1	79	294
2	159	294
3	330	292
4	1195	292
5	5002	292

prune77.0ms

Filtered

52 candidates to 34 candidates (65.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	51	7	58

Merged error: 0.7b

Counts

58 → 7

regimes23.0ms

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

sample759.0ms

Algorithm

intervals

Results

399.0ms	2748×	body	1280	valid
135.0ms	4155×	body	80	valid
74.0ms	609×	body	640	valid
30.0ms	325×	body	320	valid
11.0ms	163×	body	160	valid