Details

sample79.0ms

Algorithm

intervals

Results

40.0ms	117×	body	1280	valid
21.0ms	93×	body	640	valid
5.0ms	32×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	14×	body	160	valid

simplify161.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* n (log n))
0.2b	(* (+ n 1.0) (log (+ n 1.0)))
4.3b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite23.0ms

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:

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

series412.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(* n (log n))
64.0ms	(* (+ n 1.0) (log (+ n 1.0)))
177.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	419	643
1	1786	587
2	5002	568

prune171.0ms

Filtered

90 candidates to 63 candidates (70.0%)

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: 0.0b

Counts

91 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
0.0b	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
0.1b	(* 0.16666666666666669 (/ 1 (pow n 2)))
1.2b	(/ 1 (pow n 2))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
56×	`times-frac`
52×	`*-un-lft-identity`
37×	`add-cube-cbrt`
33×	`add-exp-log`
28×	`associate-r`
23×	`unpow-prod-down` `add-log-exp`
12×	`div-exp`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`diff-log` `associate-/r*`
6×	`pow1` `pow-to-exp` `rec-exp` `1-exp` `pow-exp`
5×	`sum-log` `distribute-lft-out--`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `sub-neg` `flip3--` `flip--` `cbrt-unprod` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`associate--l-` `associate-+l-` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `associate--r+` `inv-pow`

Counts

4 → 157

Calls

4 calls:

17.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
6.0ms	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
11.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series413.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
336.0ms	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
24.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
16.0ms	(/ 1 (pow n 2))

simplify65.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	545	1151
1	2184	973
2	5001	890

prune266.0ms

Filtered

169 candidates to 90 candidates (53.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	1	170

Merged error: 0b

Counts

170 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.5 (/ 1 n))
1.1b	(/ 0.16666666666666669 (pow n 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

35×	`times-frac`
34×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`add-cube-cbrt`
16×	`add-exp-log`
13×	`associate-r`
12×	`unpow-prod-down`
9×	`add-cbrt-cube`
8×	`associate-/r*`
5×	`div-exp`
4×	`pow1` `prod-exp` `unpow2` `sqr-pow`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv` `add-log-exp`
1×	`pow-to-exp` `rec-exp` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `un-div-inv` `-commutative`

Counts

2 → 85

Calls

2 calls:

7.0ms	(* 0.5 (/ 1 n))
5.0ms	(/ 0.16666666666666669 (pow n 2))

series44.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(* 0.5 (/ 1 n))
25.0ms	(/ 0.16666666666666669 (pow n 2))

simplify42.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	317	379
1	1427	324
2	5002	303

prune155.0ms

Filtered

91 candidates to 57 candidates (62.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Merged error: 0b

Counts

92 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	3610×	body	1280	valid
608.0ms	2649×	body	640	valid
216.0ms	1336×	body	320	valid
95.0ms	8000×	pre	80	true
40.0ms	405×	body	160	valid

Details

sample79.0ms

simplify161.0ms

prune2.0ms

localize13.0ms

rewrite23.0ms

series412.0ms

simplify54.0ms

prune171.0ms

localize15.0ms

rewrite46.0ms

series413.0ms

simplify65.0ms

prune266.0ms

localize12.0ms

rewrite15.0ms

series44.0ms

simplify42.0ms

prune155.0ms

simplify1.0ms

end0.0ms

sample2.3s

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