Details

sample82.0ms

Algorithm

intervals

Results

43.0ms	121×	body	1280	valid
20.0ms	84×	body	640	valid
7.0ms	43×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	8×	body	160	valid

simplify165.0ms

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	1481	8
11	1659	8
12	2039	8
13	2376	8
14	3209	8
15	5001	8

prune11.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

localize12.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (+ n 1.0) (log (+ n 1.0)))
0.3b	(* n (log n))
3.9b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite24.0ms

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:

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

series32.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* (+ n 1.0) (log (+ n 1.0)))
16.0ms	(* n (log n))
12.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	439	660
1	1891	592
2	5001	573

prune129.0ms

Filtered

90 candidates to 63 candidates (30.0%)

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: 0b

Counts

91 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
0.0b	(log (/ 1 n))
0.1b	(* 0.16666666666666669 (/ 1 (pow n 2)))
0.6b	(/ 1 (pow n 2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

65×	`times-frac`
64×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
38×	`add-exp-log`
28×	`associate-r`
25×	`add-log-exp`
23×	`unpow-prod-down`
14×	`div-exp`
13×	`log-prod`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`sum-log` `unpow2` `unswap-sqr` `sqr-pow`
8×	`pow1` `associate-/r*`
7×	`rec-exp` `1-exp`
6×	`pow-to-exp` `diff-log` `pow-exp`
4×	`flip3-+` `rem-log-exp` `frac-sub` `flip-+`
3×	`associate-l` `log-pow` `div-inv` `associate-/l*`
2×	`cbrt-undiv` `pow-flip` `cbrt-unprod` `inv-pow`
1×	`sub-neg` `log-div` `flip3--` `frac-2neg` `associate-r/` `log-rec` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 174

Calls

4 calls:

14.0ms	(- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
3.0ms	(log (/ 1 n))
12.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series24.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
11.0ms	(log (/ 1 n))
3.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
2.0ms	(/ 1 (pow n 2))

simplify92.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	764	1458
1	3417	1246
2	5002	1138

prune319.0ms

Filtered

186 candidates to 97 candidates (47.8%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	186	1	187

Merged error: 0b

Counts

187 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	15
1	29	15

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	3577×	body	1280	valid
654.0ms	2690×	body	640	valid
218.0ms	1322×	body	320	valid
79.0ms	8000×	pre	80	true
43.0ms	411×	body	160	valid

Details

sample82.0ms

simplify165.0ms

prune11.0ms

localize12.0ms

rewrite24.0ms

series32.0ms

simplify52.0ms

prune129.0ms

localize18.0ms

rewrite42.0ms

series24.0ms

simplify92.0ms

prune319.0ms

simplify1.0ms

end0.0ms

sample2.4s

Profiling