Details

sample86.0ms

Algorithm

intervals

Results

41.0ms	117×	body	1280	valid
20.0ms	82×	body	640	valid
8.0ms	45×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	12×	body	160	valid

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	15
1	18	15
2	43	15
3	87	15
4	150	15
5	196	15
6	282	15
7	444	15
8	685	15
9	709	15
10	734	15
11	792	15
12	872	15
13	975	15
14	1109	15
15	1173	15
16	1409	15
17	1472	15
18	1825	15
19	3684	15
done	5000	15

prune8.0ms

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:

0.3b	(* n (log n))
0.3b	(* (+ n 1.0) (log (+ n 1.0)))
4.6b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite26.0ms

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:

5.0ms	(* n (log n))
9.0ms	(* (+ n 1.0) (log (+ n 1.0)))
10.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series34.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(* n (log n))
5.0ms	(* (+ n 1.0) (log (+ n 1.0)))
12.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify720.0ms

Counts

90 → 90

Iterations

Useful iterations: done (717.0ms)

Iter	Nodes	Cost
0	182	1240
1	432	1163
2	1296	1034
done	5000	1020

prune139.0ms

Filtered

66 candidates to 90 candidates (-36.4%)

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

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-log-exp`
8×	`add-exp-log` `diff-log` `sum-log` `add-cbrt-cube`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`add-cube-cbrt`
3×	`pow1` `associate-+l+` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `associate-+l-` `sub-neg` `div-exp` `associate--l+`
1×	`+-commutative` `associate--l-` `flip3--` `frac-2neg` `flip3-+` `prod-exp` `clear-num` `associate-/r*` `flip--` `cbrt-unprod` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 57

Calls

3 calls:

15.0ms	(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
20.0ms	(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
5.0ms	(/ 0.16666666666666669 (* n n))

series16.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
6.0ms	(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
3.0ms	(/ 0.16666666666666669 (* n n))

simplify2.1s

Counts

66 → 66

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	140	1216
1	353	1148
2	1113	1046
3	4926	1011
done	5000	1011

prune83.0ms

Filtered

46 candidates to 66 candidates (-43.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	1	67

Merged error: 0b

Counts

67 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

0.5b	(/ 0.16666666666666669 (* n n))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`pow1` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `add-log-exp`

Counts

1 → 21

Calls

1 calls:

5.0ms

(/ 0.16666666666666669 (* n n))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(/ 0.16666666666666669 (* n n))

simplify3.6s

Counts

24 → 24

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	43	185
1	94	182
2	275	152
3	1009	152
4	3817	152
done	5000	152

prune26.0ms

Filtered

16 candidates to 24 candidates (-50.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Merged error: 0b

Counts

25 → 1

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	12	14
done	12	14

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	3585×	body	1280	valid
654.0ms	2686×	body	640	valid
224.0ms	1282×	body	320	valid
87.0ms	8000×	pre	80	true
51.0ms	447×	body	160	valid

Details

sample86.0ms

simplify5.2s

prune8.0ms

localize10.0ms

rewrite26.0ms

series34.0ms

simplify720.0ms

prune139.0ms

localize12.0ms

rewrite42.0ms

series16.0ms

simplify2.1s

prune83.0ms

localize9.0ms

rewrite5.0ms

series3.0ms

simplify3.6s

prune26.0ms

simplify1.0ms

end0.0ms

sample2.5s

Profiling