Details

analyze13.0ms

Algorithm: search

sample88.0ms

Algorithm

intervals

Results

49.0ms	123×	body	1280	valid
20.0ms	76×	body	640	valid
7.0ms	43×	body	320	valid
3.0ms	256×	pre	80	true
2.0ms	14×	body	160	valid

simplify154.0ms

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

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 1.0) (log (+ n 1.0)))
0.3b	(* n (log n))
5.8b	(- (* (+ 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:

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

series34.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* (+ n 1.0) (log (+ n 1.0)))
18.0ms	(* n (log n))
11.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (45.0ms)

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

prune131.0ms

Filtered

63 candidates to 90 candidates (-42.9%)

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

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
67×	`times-frac`
55×	`*-un-lft-identity`
45×	`add-cube-cbrt`
42×	`add-exp-log`
41×	`associate-r`
33×	`add-log-exp`
23×	`unpow-prod-down`
16×	`add-cbrt-cube`
14×	`div-exp` `prod-exp`
13×	`diff-log`
12×	`unswap-sqr`
9×	`sum-log` `unpow2` `sqr-pow`
8×	`pow1` `associate-/r*`
7×	`rec-exp` `1-exp`
6×	`pow-to-exp` `associate-l` `pow-exp`
4×	`associate--l+` `cbrt-unprod`
3×	`cbrt-undiv` `div-inv` `associate-/l*` `distribute-lft-out--`
2×	`sub-neg` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative`
1×	`associate--l-` `flip3--` `pow-flip` `frac-2neg` `clear-num` `flip--` `inv-pow` `difference-of-squares`

Counts

4 → 181

Calls

4 calls:

7.0ms	(* 0.5 (/ 1 n))
17.0ms	(- (- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) 1.0)
12.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series14.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* 0.5 (/ 1 n))
7.0ms	(- (- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) 1.0)
3.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
2.0ms	(/ 1 (pow n 2))

simplify70.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	665	1216
1	2806	990
2	5001	886

prune302.0ms

Filtered

102 candidates to 193 candidates (-89.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	193	1	194

Merged error: 0b

Counts

194 → 1

localize13.0ms

Local error

Found 1 expressions with local error:

0.6b	(/ 0.16666666666666669 (pow n 2))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
18×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
8×	`associate-/r*`
6×	`add-exp-log`
4×	`unpow2` `sqr-pow`
3×	`div-exp` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `add-log-exp`

Counts

1 → 49

Calls

1 calls:

5.0ms

(/ 0.16666666666666669 (pow n 2))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(/ 0.16666666666666669 (pow n 2))

simplify102.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	153	258
1	616	217
2	3265	208
3	5002	208

prune62.0ms

Filtered

32 candidates to 52 candidates (-62.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	52	1	53

Merged error: 0b

Counts

53 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

analyze13.0ms

Algorithm: search

sample2.5s

Algorithm

intervals

Results

1.4s	3646×	body	1280	valid
643.0ms	2568×	body	640	valid
238.0ms	1368×	body	320	valid
87.0ms	8000×	pre	80	true
47.0ms	418×	body	160	valid

Details

analyze13.0ms

sample88.0ms

simplify154.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series34.0ms

simplify52.0ms

prune131.0ms

localize20.0ms

rewrite48.0ms

series14.0ms

simplify70.0ms

prune302.0ms

localize13.0ms

rewrite7.0ms

series3.0ms

simplify102.0ms

prune62.0ms

simplify1.0ms

end0.0ms

analyze13.0ms

sample2.5s

Profiling