Details

analyze13.0ms

Algorithm: search

sample85.0ms

Algorithm

intervals

Results

46.0ms	114×	body	1280	valid
21.0ms	88×	body	640	valid
7.0ms	41×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	13×	body	160	valid

simplify152.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	8
1	43	8
2	123	8
3	212	8
4	374	8
5	496	8
6	715	8
7	967	8
8	1121	8
9	1221	8
10	1481	8
11	1659	8
12	2039	8
13	2376	8
14	3209	8
15	5001	8

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: 63.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (+ n 1.0) (log (+ n 1.0)))
0.2b	(* n (log n))
5.1b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

28×	`log-prod`
25×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
14×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`associate-r` `associate--l+`
7×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`associate--r+`
5×	`distribute-lft-out` `add-log-exp`
2×	`pow-prod-down` `associate-l/` `prod-exp` `log-pow` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 81

Calls

3 calls:

8.0ms	(* (+ n 1.0) (log (+ n 1.0)))
4.0ms	(* n (log n))
9.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series34.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* (+ n 1.0) (log (+ n 1.0)))
18.0ms	(* n (log n))
12.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify53.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	439	660
1	1891	592
2	5001	573

prune128.0ms

Filtered

63 candidates to 90 candidates (-42.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	1	91

Merged error: 0.0b

Counts

91 → 1

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (/ 1 n))
0.1b	(* 0.16666666666666669 (/ 1 (pow n 2)))
0.7b	(/ 1 (pow n 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

65×	`times-frac`
61×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
43×	`add-cube-cbrt`
37×	`add-exp-log`
28×	`associate-r`
23×	`unpow-prod-down`
14×	`div-exp`
13×	`log-prod`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
7×	`pow1` `rec-exp` `1-exp`
6×	`pow-to-exp` `pow-exp`
4×	`rem-log-exp`
3×	`associate-l` `log-pow` `div-inv` `associate-/l*` `add-log-exp`
2×	`cbrt-undiv` `pow-flip` `cbrt-unprod` `inv-pow`
1×	`log-div` `frac-2neg` `associate-r/` `log-rec` `pow-prod-down` `clear-num` `un-div-inv` `-commutative`

Counts

3 → 149

Calls

3 calls:

3.0ms	(log (/ 1 n))
14.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series15.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(log (/ 1 n))
3.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
2.0ms	(/ 1 (pow n 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	414	695
1	1729	552
2	5001	456

prune202.0ms

Filtered

76 candidates to 158 candidates (-107.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	157	1	158
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	1	159

Merged error: 0b

Counts

159 → 1

localize19.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.16666666666666669 (/ 1 (pow n 2)))
0.7b	(/ 1 (pow n 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
53×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`add-cube-cbrt`
31×	`add-exp-log`
28×	`associate-r`
23×	`unpow-prod-down`
12×	`div-exp`
10×	`prod-exp`
9×	`add-cbrt-cube` `unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp`
4×	`pow1`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

2 → 120

Calls

2 calls:

11.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series5.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
2.0ms	(/ 1 (pow n 2))

simplify41.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	328	562
1	1460	439
2	5002	355

prune134.0ms

Filtered

59 candidates to 126 candidates (-113.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	126	1	127

Merged error: 0b

Counts

127 → 1

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	15
1	36	15
2	37	15
3	37	15

end0.0ms

analyze13.0ms

Algorithm: search

sample2.4s

Algorithm

intervals

Results

1.3s	3600×	body	1280	valid
658.0ms	2695×	body	640	valid
214.0ms	1277×	body	320	valid
85.0ms	8000×	pre	80	true
45.0ms	428×	body	160	valid

Details

analyze13.0ms

sample85.0ms

simplify152.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series34.0ms

simplify53.0ms

prune128.0ms

localize18.0ms

rewrite27.0ms

series15.0ms

simplify45.0ms

prune202.0ms

localize19.0ms

rewrite21.0ms

series5.0ms

simplify41.0ms

prune134.0ms

simplify2.0ms

end0.0ms

analyze13.0ms

sample2.4s

Profiling