Details

sample82.0ms

Algorithm

intervals

Results

41.0ms	117×	body	1280	valid
20.0ms	82×	body	640	valid
8.0ms	45×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	12×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	15
1	18	15
2	43	15
3	89	15
4	155	15
5	239	15
6	345	15
7	538	15
8	890	15
9	1003	15
10	1105	15
11	1271	15
12	1496	15
13	1707	15
14	1983	15
15	2080	15
16	2389	15
17	2505	15
18	2960	15
done	5000	15

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

localize18.0ms

Local error

Found 3 expressions with local error:

0.3b	(* n (log n))
0.3b	(* (+ n 1.0) (log (+ n 1.0)))
4.6b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite26.0ms

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:

5.0ms	(* n (log n))
9.0ms	(* (+ n 1.0) (log (+ n 1.0)))
10.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series35.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(* n (log n))
5.0ms	(* (+ n 1.0) (log (+ n 1.0)))
13.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify460.0ms

Counts

90 → 90

Iterations

Useful iterations: done (452.0ms)

Iter	Nodes	Cost
0	182	1240
1	444	1163
2	1485	1034
done	5001	1025

prune147.0ms

Filtered

64 candidates to 90 candidates (-40.6%)

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

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (/ 0.5 n) (+ 1.0 0)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)))
0.0b	(- (- (+ (/ 0.5 n) (+ 1.0 0)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0))) 1.0)
0.5b	(/ 0.16666666666666669 (* n n))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-log-exp`
28×	`*-un-lft-identity`
25×	`diff-log`
12×	`sum-log`
10×	`distribute-lft-out--`
9×	`add-sqr-sqrt`
8×	`add-exp-log` `frac-sub` `add-cbrt-cube`
6×	`flip3--` `associate--l+` `flip--` `distribute-lft-out`
5×	`add-cube-cbrt`
4×	`sub-neg` `flip3-+` `frac-add` `flip-+`
3×	`pow1` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `associate--r+` `associate--r-` `difference-of-squares`
1×	`associate--l-` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

3 → 82

Calls

3 calls:

19.0ms	(- (+ (/ 0.5 n) (+ 1.0 0)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)))
23.0ms	(- (- (+ (/ 0.5 n) (+ 1.0 0)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0))) 1.0)
5.0ms	(/ 0.16666666666666669 (* n n))

series19.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(- (+ (/ 0.5 n) (+ 1.0 0)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)))
9.0ms	(- (- (+ (/ 0.5 n) (+ 1.0 0)) (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0))) 1.0)
3.0ms	(/ 0.16666666666666669 (* n n))

simplify686.0ms

Counts

91 → 91

Iterations

Useful iterations: 2 (220.0ms)

Iter	Nodes	Cost
0	222	2500
1	724	2109
2	2900	1954
done	5000	1954

prune128.0ms

Filtered

60 candidates to 91 candidates (-51.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	1	92

Merged error: 0b

Counts

92 → 1

localize10.0ms

Local error

Found 1 expressions with local error:

0.5b	(/ 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))

simplify386.0ms

Counts

52 → 52

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	89	534
1	157	485
2	497	412
3	1492	412
done	5000	412

prune66.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	13	14
done	13	14

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	3585×	body	1280	valid
667.0ms	2686×	body	640	valid
219.0ms	1282×	body	320	valid
87.0ms	8000×	pre	80	true
49.0ms	447×	body	160	valid

Details

sample82.0ms

simplify1.6s

prune3.0ms

localize18.0ms

rewrite26.0ms

series35.0ms

simplify460.0ms

prune147.0ms

localize13.0ms

rewrite50.0ms

series19.0ms

simplify686.0ms

prune128.0ms

localize10.0ms

rewrite7.0ms

series3.0ms

simplify386.0ms

prune66.0ms

simplify1.0ms

end0.0ms

sample2.5s

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