Details

sample64.0ms

Algorithm

intervals

Results

30.0ms	106×	body	1280	valid
16.0ms	89×	body	640	valid
6.0ms	46×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	15×	body	160	valid

simplify162.0ms

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

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

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (+ n 1.0) (log (+ n 1.0)))
0.2b	(* n (log n))
5.4b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite24.0ms

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

series438.0ms

Counts

3 → 9

Calls

3 calls:

70.0ms	(* (+ n 1.0) (log (+ n 1.0)))
182.0ms	(* n (log n))
186.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify58.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	419	643
1	1786	587
2	5001	568

prune182.0ms

Filtered

90 candidates to 63 candidates (70.0%)

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

localize16.0ms

Local error

Found 3 expressions with local error:

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)))
0.3b	(/ 1 (pow n 2))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt` `times-frac`
49×	`*-un-lft-identity`
36×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-r`
23×	`unpow-prod-down`
17×	`add-log-exp`
12×	`div-exp`
10×	`prod-exp` `add-cbrt-cube`
9×	`unpow2` `unswap-sqr` `sqr-pow`
8×	`associate-/r*`
6×	`pow-to-exp` `rec-exp` `diff-log` `1-exp` `pow-exp`
5×	`pow1`
4×	`sum-log` `distribute-lft-out--`
3×	`associate-l` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod` `div-inv` `distribute-lft-out`
1×	`associate--l-` `associate-+l-` `sub-neg` `flip3--` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `associate--l+` `clear-num` `un-div-inv` `-commutative` `flip--` `inv-pow` `difference-of-squares`

Counts

3 → 141

Calls

3 calls:

15.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
11.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
6.0ms	(/ 1 (pow n 2))

series86.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
26.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
22.0ms	(/ 1 (pow n 2))

simplify65.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	481	928
1	1943	772
2	5001	683

prune229.0ms

Filtered

150 candidates to 75 candidates (50.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	1	151

Merged error: 0b

Counts

151 → 1

localize12.0ms

Local error

Found 1 expressions with local error:

0.3b	(/ 0.16666666666666669 (pow n 2))

rewrite6.0ms

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))

series30.0ms

Counts

1 → 3

Calls

1 calls:

30.0ms

(/ 0.16666666666666669 (pow n 2))

simplify103.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	153	258
1	616	217
2	3278	208
3	5002	208

prune86.0ms

Filtered

52 candidates to 32 candidates (61.5%)

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	19	8
1	19	8

end0.0ms

sample1.9s

Algorithm

intervals

Results

1000.0ms	3542×	body	1280	valid
499.0ms	2725×	body	640	valid
165.0ms	1331×	body	320	valid
68.0ms	8000×	pre	80	true
30.0ms	402×	body	160	valid