Details

sample88.0ms

Algorithm

intervals

Results

42.0ms	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

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	15
1	18	15
2	43	15
3	89	15
4	157	15
5	217	15
6	333	15
7	550	15
8	1011	15
9	1328	15
10	1593	15
11	1867	15
12	2272	15
13	2884	15
14	3794	15
done	5001	15

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:

0.3b	(* 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)))

series35.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(* n (log n))
5.0ms	(* (+ n 1.0) (log (+ n 1.0)))
13.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify444.0ms

Counts

90 → 90

Iterations

Useful iterations: done (441.0ms)

Iter	Nodes	Cost
0	182	1240
1	444	1167
2	1401	1038
done	5000	1026

prune143.0ms

Filtered

64 candidates to 90 candidates (-40.6%)

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

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (+ 1.0 0) (/ 0.5 n)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)))
0.0b	(- (- (+ (+ 1.0 0) (/ 0.5 n)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0))) 1.0)
0.5b	(/ 0.16666666666666669 (* n n))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 82

Calls

3 calls:

19.0ms	(- (+ (+ 1.0 0) (/ 0.5 n)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)))
26.0ms	(- (- (+ (+ 1.0 0) (/ 0.5 n)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0))) 1.0)
5.0ms	(/ 0.16666666666666669 (* n n))

series16.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(- (+ (+ 1.0 0) (/ 0.5 n)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)))
6.0ms	(- (- (+ (+ 1.0 0) (/ 0.5 n)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0))) 1.0)
3.0ms	(/ 0.16666666666666669 (* n n))

simplify662.0ms

Counts

91 → 91

Iterations

Useful iterations: done (659.0ms)

Iter	Nodes	Cost
0	222	2500
1	692	2137
2	2743	1992
done	5001	1956

prune133.0ms

Filtered

62 candidates to 91 candidates (-46.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	1	92

Merged error: 0b

Counts

92 → 1

localize11.0ms

Local error

Found 1 expressions with local error:

0.5b	(/ 0.16666666666666669 (* n n))

rewrite6.0ms

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))

simplify1.4s

Counts

24 → 24

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	43	185
1	96	184
2	299	156
3	821	152
4	1838	152
5	3706	152
done	5000	152

prune28.0ms

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

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	16	14
2	18	14
done	18	14

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	3585×	body	1280	valid
687.0ms	2686×	body	640	valid
227.0ms	1282×	body	320	valid
91.0ms	8000×	pre	80	true
50.0ms	447×	body	160	valid

Details

sample88.0ms

simplify2.0s

prune3.0ms

localize10.0ms

rewrite26.0ms

series35.0ms

simplify444.0ms

prune143.0ms

localize14.0ms

rewrite53.0ms

series16.0ms

simplify662.0ms

prune133.0ms

localize11.0ms

rewrite6.0ms

series3.0ms

simplify1.4s

prune28.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling