Details

analyze5.0ms

Algorithm

Search

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

sample29.0ms

Algorithm

intervals

Results

15.0ms	97×	body	1280	valid
5.0ms	128×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	5×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	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: 13.7b

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 → 21

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

series4.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

simplify67.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5349	236

prune39.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

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

Merged error: 0.6b

Counts

28 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1.0))
0.6b	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-r` `add-cbrt-cube`
3×	`associate-l`
2×	`associate-*r/` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

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

series7.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify59.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune57.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	34	4	38

Merged error: 0.6b

Counts

38 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
0.6b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
16.8b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.8b	(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)))))

series17.0ms

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

simplify56.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4899	570
1	4899	570

prune104.0ms

Filtered

34 candidates to 52 candidates (-52.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	50	6	56

Merged error: 0.6b

Counts

56 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
16.8b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.8b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.8b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 46

Calls

4 calls:

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

series21.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4899	637
1	4899	637

prune140.0ms

Filtered

37 candidates to 58 candidates (-56.8%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	58	0	58
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	58	6	64

Merged error: 0.6b

Counts

64 → 6

regimes92.0ms

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

sample864.0ms

Algorithm

intervals

Results

475.0ms	2866×	body	1280	valid
151.0ms	4015×	body	80	valid
85.0ms	615×	body	640	valid
37.0ms	356×	body	320	valid
11.0ms	148×	body	160	valid

Details

analyze5.0ms

sample29.0ms

simplify5.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series4.0ms

simplify67.0ms

prune39.0ms

localize6.0ms

rewrite7.0ms

series7.0ms

simplify59.0ms

prune57.0ms

localize9.0ms

rewrite4.0ms

series17.0ms

simplify56.0ms

prune104.0ms

localize12.0ms

rewrite7.0ms

series21.0ms

simplify59.0ms

prune140.0ms

regimes92.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample864.0ms

Profiling