Details

sample152.0ms

Algorithm

intervals

Results

95.0ms	134×	body	1280	valid
26.0ms	67×	body	640	valid
11.0ms	42×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	13×	body	160	valid

simplify8.3s

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 63.0b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite87.0ms

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:

50.0ms	(* (+ n 1.0) (log (+ n 1.0)))
8.0ms	(* n (log n))
24.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series561.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(* (+ n 1.0) (log (+ n 1.0)))
247.0ms	(* n (log n))
221.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify3.1s

Counts

90 → 90

Iterations

Useful iterations: 3 (1.5s)

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

prune257.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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)
0.5b	(/ 0.16666666666666669 (* n n))

rewrite3.2s

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:

451.0ms	(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
2.8s	(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
13.0ms	(/ 0.16666666666666669 (* n n))

series136.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
62.0ms	(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
28.0ms	(/ 0.16666666666666669 (* n n))

simplify2.8s

Counts

66 → 66

Iterations

Useful iterations: 3 (1.0s)

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

prune180.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite461.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 66

Calls

3 calls:

318.0ms	(- (+ (/ 0.5 n) 1.0) (+ (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)) 1.0))
131.0ms	(+ (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)) 1.0)
8.0ms	(/ 0.16666666666666669 (* n n))

series622.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(- (+ (/ 0.5 n) 1.0) (+ (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)) 1.0))
520.0ms	(+ (- (/ 0.16666666666666669 (* n n)) (* (log n) 1.0)) 1.0)
45.0ms	(/ 0.16666666666666669 (* n n))

simplify905.0ms

Counts

75 → 75

Iterations

Useful iterations: done (901.0ms)

Iter	Nodes	Cost
0	158	1638
1	440	1559
2	1502	1455
done	5000	1319

prune213.0ms

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	13	18
1	16	18
done	16	18

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.4s	3669×	body	1280	valid
1.0s	2599×	body	640	valid
288.0ms	1300×	body	320	valid
232.0ms	8000×	pre	80	true
161.0ms	432×	body	160	valid