Details

analyze14.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	23.7%	76.3%	0
0%	23.7%	76.3%	1
11.9%	11.9%	76.3%	2
17.8%	5.9%	76.3%	3
20.8%	3%	76.3%	4
22.2%	1.5%	76.3%	5
23%	0.7%	76.3%	6
23.3%	0.4%	76.3%	7
23.3%	0.4%	76.3%	8
23.4%	0.3%	76.3%	9
23.5%	0.2%	76.3%	10
23.5%	0.2%	76.3%	11
23.5%	0.2%	76.3%	12
23.6%	0.2%	76.3%	13
23.6%	0.1%	76.3%	14

sample82.0ms (2.6%)

Algorithm

1×

intervals

Results

39.0ms	105×	body	1280	valid
24.0ms	95×	body	640	valid
7.0ms	41×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	15×	body	160	valid

simplify133.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	5997	15

prune9.0ms (0.3%)

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 (0.3%)

Local error

Found 3 expressions with local error:

0.3b	(* (+ n 1.0) (log (+ n 1.0)))
0.3b	(* n (log n))
5.1b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite24.0ms (0.8%)

Algorithm

1×	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 → 80

Calls

3 calls:

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

series32.0ms (1%)

Counts

3 → 9

Calls

3 calls:

15.0ms	(* n (log n))
13.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))
5.0ms	(* (+ n 1.0) (log (+ n 1.0)))

simplify44.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5308	1042

prune164.0ms (5.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	89	1	90

Merged error: 0b

Counts

90 → 1

localize11.0ms (0.4%)

Local error

Found 1 expressions with local error:

0.7b	(/ 0.16666666666666669 (* n n))

rewrite5.0ms (0.2%)

Algorithm

1×	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:

4.0ms

(/ 0.16666666666666669 (* n n))

series3.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

3.0ms

(/ 0.16666666666666669 (* n n))

simplify42.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5024	152

prune39.0ms (1.2%)

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 (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	18
1	41	18

end0.0ms (0%)

sample2.5s (80.6%)

Algorithm

1×

intervals

Results

1.4s	3643×	body	1280	valid
663.0ms	2610×	body	640	valid
231.0ms	1310×	body	320	valid
92.0ms	8000×	pre	80	true
49.0ms	437×	body	160	valid

Details

analyze14.0ms (0.5%)

sample82.0ms (2.6%)

simplify133.0ms (4.2%)

prune9.0ms (0.3%)

localize10.0ms (0.3%)

rewrite24.0ms (0.8%)

series32.0ms (1%)

simplify44.0ms (1.4%)

prune164.0ms (5.2%)

localize11.0ms (0.4%)

rewrite5.0ms (0.2%)

series3.0ms (0.1%)

simplify42.0ms (1.3%)

prune39.0ms (1.2%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.5s (80.6%)

Profiling