Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	91×	body	1280	valid
5.0ms	135×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify4.0ms

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 (100.0%)

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: 15.0b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.9b	(- (atan (+ N 1.0)) (atan N))

rewrite4.0ms

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))

series3.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

simplify72.0ms

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	2447	142
5	5001	142

prune36.0ms

Filtered

28 candidates to 19 candidates (32.1%)

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: 0.4b

Counts

29 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.4b	(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:

5.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series7.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify53.0ms

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 (35.3%)

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	0	0	0
Total	29	6	35

Merged error: 0.4b

Counts

35 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series93.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt N) (cbrt N))
21.0ms	(cbrt N)
24.0ms	(cbrt N)
22.0ms	(cbrt N)

simplify71.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	148	349
1	471	322
2	2276	265
3	5002	252

prune98.0ms

Filtered

85 candidates to 56 candidates (34.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	83	8	91

Merged error: 0.4b

Counts

91 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt N)
2.0ms	(cbrt (cbrt N))
2.0ms	(cbrt (cbrt N))
2.0ms	(cbrt (cbrt N))

series115.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt N)
30.0ms	(cbrt (cbrt N))
30.0ms	(cbrt (cbrt N))
32.0ms	(cbrt (cbrt N))

simplify77.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (13.0ms)

Iter	Nodes	Cost
0	99	309
1	175	287
2	404	247
3	1393	237
4	5002	237

prune80.0ms

Filtered

65 candidates to 52 candidates (20.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	65	8	73

Merged error: 0.4b

Counts

73 → 8

regimes44.0ms

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

sample819.0ms

Algorithm

intervals

Results

426.0ms	2853×	body	1280	valid
133.0ms	4031×	body	80	valid
77.0ms	642×	body	640	valid
33.0ms	336×	body	320	valid
10.0ms	138×	body	160	valid

Details

sample32.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite4.0ms

series3.0ms

simplify72.0ms

prune36.0ms

localize5.0ms

rewrite7.0ms

series7.0ms

simplify53.0ms

prune53.0ms

localize9.0ms

rewrite11.0ms

series93.0ms

simplify71.0ms

prune98.0ms

localize14.0ms

rewrite7.0ms

series115.0ms

simplify77.0ms

prune80.0ms

regimes44.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample819.0ms

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