Details

sample72.0ms

Algorithm

intervals

Results

40.0ms	123×	body	1280	valid
14.0ms	75×	body	640	valid
6.0ms	43×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	15×	body	160	valid

simplify160.0ms

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	1497	8
11	1752	8
12	2132	8
13	2467	8
14	3308	8
15	5002	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 63.0b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (+ n 1.0) (log (+ n 1.0)))
0.2b	(* n (log n))
6.3b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-l/` `-commutative`
1×	`sub-neg` `flip3--` `flip3-+` `flip--` `flip-+`

Counts

3 → 8

Calls

3 calls:

4.0ms	(* (+ n 1.0) (log (+ n 1.0)))
2.0ms	(* n (log n))
7.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series453.0ms

Counts

3 → 9

Calls

3 calls:

67.0ms	(* (+ n 1.0) (log (+ n 1.0)))
193.0ms	(* n (log n))
193.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify95.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	224	163
1	755	156
2	3810	145
3	5002	145

prune50.0ms

Filtered

17 candidates to 13 candidates (76.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	17	1	18

Merged error: 0.0b

Counts

18 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (+ (* 0.5 (/ 1 n)) 1.0) (- (* (log n) 1.0) (/ (/ 0.16666666666666669 n) n))) 1.0)
0.1b	(/ (/ 0.16666666666666669 n) n)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`associate--l+`
3×	`associate-/l/`
2×	`+-commutative` `sub-neg` `associate-+l+` `associate-+r+` `frac-2neg` `clear-num` `div-inv`
1×	`associate--l-` `associate-+r-` `flip3--` `flip--` `associate-/l*`

Counts

2 → 18

Calls

2 calls:

11.0ms	(- (+ (+ (* 0.5 (/ 1 n)) 1.0) (- (* (log n) 1.0) (/ (/ 0.16666666666666669 n) n))) 1.0)
3.0ms	(/ (/ 0.16666666666666669 n) n)

series70.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (+ (+ (* 0.5 (/ 1 n)) 1.0) (- (* (log n) 1.0) (/ (/ 0.16666666666666669 n) n))) 1.0)
31.0ms	(/ (/ 0.16666666666666669 n) n)

simplify65.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	159	164
1	454	157
2	2450	139
3	5002	136

prune48.0ms

Filtered

24 candidates to 15 candidates (62.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	1	25

Merged error: 0b

Counts

25 → 1

localize10.0ms

Local error

Found 1 expressions with local error:

0.1b	(/ (/ 0.16666666666666669 n) n)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-/l/`
2×	`frac-2neg` `clear-num` `div-inv`
1×	`associate-/l*`

Counts

1 → 7

Calls

1 calls:

3.0ms

(/ (/ 0.16666666666666669 n) n)

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

(/ (/ 0.16666666666666669 n) n)

simplify77.0ms

Algorithm

egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	29	19
1	50	18
2	201	18
3	1305	18
4	5001	18

prune14.0ms

Filtered

10 candidates to 5 candidates (50.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	1	11

Merged error: 0b

Counts

11 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	3611×	body	1280	valid
514.0ms	2639×	body	640	valid
176.0ms	1314×	body	320	valid
73.0ms	8000×	pre	80	true
36.0ms	436×	body	160	valid