Details

analyze14.0ms (0.4%)

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

sample85.0ms (2.8%)

Algorithm

1×

intervals

Results

41.0ms	111×	body	1280	valid
20.0ms	80×	body	640	valid
13.0ms	48×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	17×	body	160	valid

simplify111.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5997	15

prune7.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 62.0b

Counts

2 → 1

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.3b	(* n (log n))
0.3b	(* (+ n 1.0) (log (+ n 1.0)))
5.3b	(- (* (+ n 1.0) (log (+ n 1.0))) (+ 1.0 (* n (log n))))

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`log-prod`
17×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`pow1`
8×	`associate-r` `associate--l+` `add-log-exp`
7×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`associate-*l/`
5×	`flip3-+` `flip-+` `distribute-lft-out`
4×	`frac-sub`
2×	`diff-log` `pow-prod-down` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `sum-log` `flip--` `associate--r+`

Counts

3 → 80

Calls

3 calls:

11.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (+ 1.0 (* n (log n))))
8.0ms	(* (+ n 1.0) (log (+ n 1.0)))
4.0ms	(* n (log n))

series35.0ms (1.1%)

Counts

3 → 9

Calls

3 calls:

18.0ms	(* n (log n))
13.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (+ 1.0 (* n (log n))))
5.0ms	(* (+ n 1.0) (log (+ n 1.0)))

simplify46.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4962	1267
1	4962	1267

prune178.0ms (5.8%)

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

localize9.0ms (0.3%)

Local error

Found 1 expressions with local error:

0.4b	(/ 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))

simplify39.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5024	152

prune38.0ms (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

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms (0%)

sample2.5s (80.3%)

Algorithm

1×

intervals

Results

1.3s	3621×	body	1280	valid
666.0ms	2661×	body	640	valid
222.0ms	1276×	body	320	valid
84.0ms	8000×	pre	80	true
49.0ms	442×	body	160	valid

Details

analyze14.0ms (0.4%)

sample85.0ms (2.8%)

simplify111.0ms (3.6%)

prune7.0ms (0.2%)

localize10.0ms (0.3%)

rewrite27.0ms (0.9%)

series35.0ms (1.1%)

simplify46.0ms (1.5%)

prune178.0ms (5.8%)

localize9.0ms (0.3%)

rewrite5.0ms (0.2%)

series3.0ms (0.1%)

simplify39.0ms (1.2%)

prune38.0ms (1.2%)

simplify1.0ms (0%)

end0.0ms (0%)

sample2.5s (80.3%)

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