Details

sample70.0ms

Algorithm

intervals

Results

37.0ms	124×	body	1280	valid
16.0ms	87×	body	640	valid
4.0ms	34×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	11×	body	160	valid

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	15
1	18	15
2	43	15
3	113	15
4	167	15
5	230	15
6	310	15
7	452	15
8	584	15
9	616	15
10	632	15
11	649	15
12	692	15
13	756	15
14	818	15
15	882	15
16	974	15
17	1045	15
18	1302	15
19	3610	15
done	5000	15

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 63.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (+ n 1.0) (log (+ n 1.0)))
0.2b	(* n (log n))
5.9b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite64.0ms

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:

26.0ms	(* (+ n 1.0) (log (+ n 1.0)))
8.0ms	(* n (log n))
26.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series409.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* (+ n 1.0) (log (+ n 1.0)))
176.0ms	(* n (log n))
170.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify2.3s

Counts

90 → 90

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	171	1210
1	418	1150
2	1276	1036
3	4578	1015
done	5000	1015

prune171.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
0.0b	(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
1.1b	(/ 0.16666666666666669 (* n n))

rewrite2.4s

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

363.0ms	(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
2.1s	(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
8.0ms	(/ 0.16666666666666669 (* n n))

series108.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
41.0ms	(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
26.0ms	(/ 0.16666666666666669 (* n n))

simplify1.9s

Counts

66 → 66

Iterations

Useful iterations: 3 (781.0ms)

Iter	Nodes	Cost
0	137	1196
1	334	1132
2	1007	1038
3	4880	1011
done	5000	1011

prune145.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 2 expressions with local error:

1.1b	(/ 0.16666666666666669 (* n n))
4.4b	(- (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) 1.0)

rewrite493.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

8.0ms	(/ 0.16666666666666669 (* n n))
483.0ms	(- (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) 1.0)

series98.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(/ 0.16666666666666669 (* n n))
67.0ms	(- (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) 1.0)

simplify971.0ms

Counts

49 → 49

Iterations

Useful iterations: done (970.0ms)

Iter	Nodes	Cost
0	91	615
1	192	604
2	498	536
3	1914	494
done	5000	463

prune113.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	16	19
done	16	19

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.0s	3594×	body	1280	valid
500.0ms	2654×	body	640	valid
166.0ms	1335×	body	320	valid
65.0ms	8000×	pre	80	true
32.0ms	417×	body	160	valid