Details

sample69.0ms

Algorithm

intervals

Results

31.0ms	108×	body	1280	valid
16.0ms	86×	body	640	valid
6.0ms	49×	body	320	valid
5.0ms	256×	pre	80	true
1.0ms	13×	body	160	valid

simplify156.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* n (log n))
0.2b	(* (+ n 1.0) (log (+ n 1.0)))
6.1b	(- (* (+ 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:

4.0ms	(* n (log n))
8.0ms	(* (+ n 1.0) (log (+ n 1.0)))
9.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series435.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(* n (log n))
65.0ms	(* (+ n 1.0) (log (+ n 1.0)))
189.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify55.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (47.0ms)

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

prune175.0ms

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

localize19.0ms

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)))
0.8b	(/ 1 (pow n 2))

rewrite41.0ms

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:

3.0ms	(log (/ 1 n))
15.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
12.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series209.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(log (/ 1 n))
38.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
31.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
17.0ms	(/ 1 (pow n 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	557	1089
1	2263	881
2	5001	783

prune283.0ms

Filtered

182 candidates to 93 candidates (51.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	182	1	183

Merged error: 0b

Counts

183 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* 0.5 (/ 1 n)) (/ 0.16666666666666669 (pow n 2)))
0.8b	(/ 0.16666666666666669 (pow n 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
8×	`associate-/r*`
7×	`add-exp-log`
4×	`add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`
3×	`div-exp` `associate-/l*`
2×	`pow1` `frac-sub`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `associate-*r/` `pow-exp` `clear-num` `un-div-inv` `flip--` `div-inv`

Counts

2 → 63

Calls

2 calls:

13.0ms	(- (* 0.5 (/ 1 n)) (/ 0.16666666666666669 (pow n 2)))
5.0ms	(/ 0.16666666666666669 (pow n 2))

series98.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (* 0.5 (/ 1 n)) (/ 0.16666666666666669 (pow n 2)))
25.0ms	(/ 0.16666666666666669 (pow n 2))

simplify36.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	243	378
1	952	339
2	5002	319

prune122.0ms

Filtered

69 candidates to 45 candidates (65.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	1	70

Merged error: 0b

Counts

70 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	8
1	19	8

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s	3641×	body	1280	valid
498.0ms	2616×	body	640	valid
170.0ms	1338×	body	320	valid
69.0ms	8000×	pre	80	true
32.0ms	405×	body	160	valid