Details

analyze1.0ms

Algorithm

Search

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

sample29.0ms

Algorithm

intervals

Results

13.0ms	84×	body	1280	valid
5.0ms	140×	body	80	valid
3.0ms	21×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms

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: 15.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.2b	(- (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))

simplify67.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5349	236

prune47.0ms

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: 0.4b

Counts

28 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

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

series6.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify62.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune84.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	29	9	38

Merged error: 0.4b

Counts

38 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N)))) (cbrt (* N (+ 1.0 N))))))
12.7b	(cbrt (* N (+ 1.0 N)))
12.7b	(cbrt (* N (+ 1.0 N)))
12.7b	(cbrt (* N (+ 1.0 N)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
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)))
5.0ms	(cbrt (* N (+ 1.0 N)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N)))) (cbrt (* N (+ 1.0 N))))))
9.0ms	(cbrt (* N (+ 1.0 N)))
11.0ms	(cbrt (* N (+ 1.0 N)))
10.0ms	(cbrt (* N (+ 1.0 N)))

simplify41.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4927	595
1	4927	595

prune143.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	52	9	61

Merged error: 0.4b

Counts

61 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ 1.0 N))
0.3b	(cbrt (+ 1.0 N))
0.4b	(atan2 1.0 (+ 1 (* (* N (* (cbrt (+ 1.0 N)) (cbrt (+ 1.0 N)))) (cbrt (+ N 1.0)))))

rewrite11.0ms

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

series21.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (+ N 1.0))
6.0ms	(cbrt (+ 1.0 N))
6.0ms	(cbrt (+ 1.0 N))
3.0ms	(atan2 1.0 (+ 1 (* (* N (* (cbrt (+ 1.0 N)) (cbrt (+ 1.0 N)))) (cbrt (+ N 1.0)))))

simplify50.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4912	574
1	4912	574

prune141.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	61	9	70

Merged error: 0.4b

Counts

70 → 9

regimes104.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms

sample840.0ms

Algorithm

intervals

Results

449.0ms	2805×	body	1280	valid
147.0ms	4044×	body	80	valid
89.0ms	684×	body	640	valid
32.0ms	313×	body	320	valid
11.0ms	154×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify4.0ms

prune5.0ms

localize6.0ms

rewrite5.0ms

series3.0ms

simplify67.0ms

prune47.0ms

localize6.0ms

rewrite7.0ms

series6.0ms

simplify62.0ms

prune84.0ms

localize10.0ms

rewrite15.0ms

series33.0ms

simplify41.0ms

prune143.0ms

localize14.0ms

rewrite11.0ms

series21.0ms

simplify50.0ms

prune141.0ms

regimes104.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample840.0ms

Profiling