Details

sample63.0ms

Algorithm

intervals

Results

30.0ms	106×	body	1280	valid
17.0ms	96×	body	640	valid
5.0ms	38×	body	320	valid
2.0ms	256×	pre	80	true
1.0ms	16×	body	160	valid

simplify155.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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	1497	8
11	1752	8
12	2132	8
13	2469	8
14	3314	8
15	5001	8

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 63.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (+ n 1.0) (log (+ n 1.0)))
0.3b	(* n (log n))
6.6b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite33.0ms

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:

17.0ms	(* (+ n 1.0) (log (+ n 1.0)))
4.0ms	(* n (log n))
10.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series425.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(* (+ n 1.0) (log (+ n 1.0)))
176.0ms	(* n (log n))
182.0ms	(- (* (+ 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	419	643
1	1786	587
2	5001	568

prune187.0ms

Filtered

90 candidates to 63 candidates (70.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite337.0ms

Algorithm

rewrite-expression-head

Rules

65×	`times-frac`
64×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
44×	`add-cube-cbrt`
38×	`add-exp-log`
28×	`associate-r`
23×	`unpow-prod-down`
18×	`add-log-exp`
14×	`div-exp`
13×	`log-prod`
11×	`add-cbrt-cube`
10×	`prod-exp`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`pow1` `associate-/r*`
7×	`rec-exp` `1-exp`
6×	`pow-to-exp` `diff-log` `pow-exp`
4×	`rem-log-exp` `sum-log` `distribute-lft-out--`
3×	`associate-l` `log-pow` `div-inv` `associate-/l*`
2×	`cbrt-undiv` `pow-flip` `cbrt-unprod` `distribute-lft-out` `inv-pow`
1×	`associate--l-` `associate-+l-` `sub-neg` `log-div` `flip3--` `frac-2neg` `associate-r/` `log-rec` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `flip--` `difference-of-squares`

Counts

4 → 170

Calls

4 calls:

2.0ms	(log (/ 1 n))
311.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
14.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
4.0ms	(/ 1 (pow n 2))

series201.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(log (/ 1 n))
41.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
24.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
16.0ms	(/ 1 (pow n 2))

simplify55.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	557	1061
1	2160	885
2	5001	783

prune333.0ms

Filtered

182 candidates to 93 candidates (51.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 1 expressions with local error:

0.9b	(/ 0.16666666666666669 (pow n 2))

rewrite5.0ms

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:

4.0ms

(/ 0.16666666666666669 (pow n 2))

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

(/ 0.16666666666666669 (pow n 2))

simplify101.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	153	244
1	571	217
2	3249	208
3	5003	208

prune111.0ms

Filtered

52 candidates to 32 candidates (61.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.0s	3656×	body	1280	valid
450.0ms	2534×	body	640	valid
164.0ms	1393×	body	320	valid
75.0ms	8000×	pre	80	true
31.0ms	417×	body	160	valid