Details

sample70.0ms

Algorithm

intervals

Results

35.0ms	122×	body	1280	valid
19.0ms	88×	body	640	valid
4.0ms	36×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	10×	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	2467	8
14	3308	8
15	5002	8

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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 1.0) (log (+ n 1.0)))
0.2b	(* n (log n))
4.1b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
31×	`add-sqr-sqrt`
28×	`log-prod`
15×	`add-cube-cbrt`
14×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
9×	`pow1`
8×	`associate-r` `associate--l+`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate--r+` `distribute-lft-out--` `unswap-sqr`
5×	`add-log-exp`
4×	`difference-of-squares`
2×	`pow-prod-down` `associate-l/` `prod-exp` `log-pow` `-commutative` `cbrt-unprod`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 91

Calls

3 calls:

8.0ms	(* (+ n 1.0) (log (+ n 1.0)))
4.0ms	(* n (log n))
20.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series449.0ms

Counts

3 → 9

Calls

3 calls:

71.0ms	(* (+ n 1.0) (log (+ n 1.0)))
184.0ms	(* n (log n))
193.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify56.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	431	766
1	1786	709
2	5002	688

prune162.0ms

Filtered

100 candidates to 68 candidates (32.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	1	101

Merged error: 0.0b

Counts

101 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
0.0b	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
0.1b	(* 0.16666666666666669 (/ 1 (pow n 2)))
0.6b	(/ 1 (pow n 2))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
92×	`times-frac`
91×	`add-sqr-sqrt`
69×	`add-cube-cbrt`
56×	`associate--r+`
54×	`associate-+l+`
52×	`log-prod`
33×	`add-exp-log`
29×	`associate--l-` `associate-+l-`
28×	`associate-r`
26×	`distribute-rgt-in` `unpow-prod-down` `distribute-lft-in`
23×	`add-log-exp`
17×	`distribute-lft-out--`
16×	`associate-/r*`
14×	`associate-*r/` `distribute-lft-out`
12×	`div-exp`
11×	`associate-l` `add-cbrt-cube`
10×	`prod-exp` `unpow2` `sqr-pow`
9×	`unswap-sqr`
8×	`pow1` `diff-log`
7×	`associate-/l*`
6×	`pow-to-exp` `rec-exp` `pow-flip` `1-exp` `pow-exp` `div-inv`
5×	`sum-log`
4×	`associate--l+`
3×	`+-commutative` `sub-neg` `pow-unpow` `clear-num` `un-div-inv`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `flip--` `cbrt-unprod` `difference-of-squares`
1×	`pow-pow` `pow-prod-down` `*-commutative` `inv-pow`

Counts

4 → 243

Calls

4 calls:

61.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
43.0ms	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
17.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
6.0ms	(/ 1 (pow n 2))

series448.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
360.0ms	(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
26.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
22.0ms	(/ 1 (pow n 2))

simplify86.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	921	1763
1	3044	1521
2	5001	1400

prune475.0ms

Filtered

255 candidates to 157 candidates (38.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	255	1	256

Merged error: 0b

Counts

256 → 1

localize18.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n))))
0.4b	(/ 0.16666666666666669 (pow n 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

45×	`*-un-lft-identity`
42×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt`
26×	`associate-+r+` `log-prod`
13×	`distribute-rgt-in` `distribute-lft-in`
12×	`unpow-prod-down`
8×	`associate-/r*`
7×	`add-exp-log` `add-log-exp`
6×	`log-rec` `distribute-rgt-neg-out` `distribute-lft-out`
5×	`associate-/l*`
4×	`add-cbrt-cube` `unpow2` `sqr-pow`
3×	`div-exp` `unsub-neg` `clear-num` `sum-log` `div-inv`
2×	`pow1` `+-commutative` `associate-+l+` `associate-l`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `flip-+`

Counts

2 → 99

Calls

2 calls:

20.0ms	(+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n))))
5.0ms	(/ 0.16666666666666669 (pow n 2))

series380.0ms

Counts

2 → 6

Calls

2 calls:

350.0ms	(+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n))))
29.0ms	(/ 0.16666666666666669 (pow n 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	462	702
1	1497	625
2	5001	562

prune252.0ms

Filtered

105 candidates to 72 candidates (31.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	1	106

Merged error: 0b

Counts

106 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	13
1	26	13

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.1s	3661×	body	1280	valid
497.0ms	2630×	body	640	valid
166.0ms	1315×	body	320	valid
71.0ms	8000×	pre	80	true
30.0ms	394×	body	160	valid