Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample29.0ms

Algorithm

intervals

Results

16.0ms	109×	body	1280	valid
4.0ms	116×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	5×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

prune3.0ms

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: 14.8b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.9b	(- (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 → 21

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))

simplify21.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5041	236

prune38.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.5b

Counts

28 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

1 → 7

Calls

1 calls:

1.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify124.0ms

Algorithm

egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4712	109
1	4712	109

prune24.0ms

Filtered

8 candidates to 10 candidates (-25.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	7	4	11

Merged error: 0.4b

Counts

11 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
18.6b	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
18.6b	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
18.6b	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite6.0ms

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

series98.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
33.0ms	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
31.0ms	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
32.0ms	(cbrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4909	621
1	4909	621

prune135.0ms

Filtered

37 candidates to 52 candidates (-40.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	51	5	56

Merged error: 0.4b

Counts

56 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
1.3b	(exp (log (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
18.9b	(log (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `exp-prod`
3×	`exp-sum` `add-cbrt-cube` `add-log-exp`
2×	`log-pow`
1×	`rem-log-exp` `rem-exp-log`

Counts

3 → 34

Calls

3 calls:

1.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
2.0ms	(exp (log (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
1.0ms	(log (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

series25.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
2.0ms	(exp (log (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
21.0ms	(log (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4812	476
1	4812	476

prune59.0ms

Filtered

26 candidates to 43 candidates (-65.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	43	5	48

Merged error: 0.4b

Counts

48 → 5

regimes36.0ms

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	11	9
1	11	9

end0.0ms

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample808.0ms

Algorithm

intervals

Results

442.0ms	2821×	body	1280	valid
144.0ms	4090×	body	80	valid
81.0ms	636×	body	640	valid
29.0ms	295×	body	320	valid
11.0ms	158×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series3.0ms

simplify21.0ms

prune38.0ms

localize6.0ms

rewrite1.0ms

series2.0ms

simplify124.0ms

prune24.0ms

localize10.0ms

rewrite6.0ms

series98.0ms

simplify45.0ms

prune135.0ms

localize10.0ms

rewrite4.0ms

series25.0ms

simplify57.0ms

prune59.0ms

regimes36.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample808.0ms

Profiling