Details

sample87.0ms

Algorithm

intervals

Results

45.0ms	111×	body	1280	valid
21.0ms	84×	body	640	valid
9.0ms	53×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	8×	body	160	valid

simplify154.0ms

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	1481	8
11	1659	8
12	2039	8
13	2376	8
14	3209	8
15	5001	8

prune3.0ms

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:

0.3b	(* n (log n))
0.3b	(* (+ n 1.0) (log (+ n 1.0)))
3.7b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite23.0ms

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

series34.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(* n (log n))
5.0ms	(* (+ n 1.0) (log (+ n 1.0)))
11.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify53.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	439	660
1	1891	592
2	5001	573

prune129.0ms

Filtered

63 candidates to 90 candidates (-42.9%)

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

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt`
67×	`times-frac`
55×	`*-un-lft-identity`
45×	`add-cube-cbrt`
42×	`add-exp-log`
41×	`associate-r`
33×	`add-log-exp`
23×	`unpow-prod-down`
16×	`add-cbrt-cube`
14×	`div-exp` `prod-exp`
13×	`diff-log`
12×	`unswap-sqr`
9×	`sum-log` `unpow2` `sqr-pow`
8×	`pow1` `associate-/r*`
7×	`rec-exp` `1-exp`
6×	`pow-to-exp` `associate-l` `pow-exp`
4×	`associate--l+` `cbrt-unprod`
3×	`cbrt-undiv` `div-inv` `associate-/l*` `distribute-lft-out--`
2×	`sub-neg` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative`
1×	`associate--l-` `flip3--` `pow-flip` `frac-2neg` `clear-num` `flip--` `inv-pow` `difference-of-squares`

Counts

4 → 181

Calls

4 calls:

16.0ms	(- (- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) 1.0)
7.0ms	(* 0.5 (/ 1 n))
13.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series14.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) 1.0)
2.0ms	(* 0.5 (/ 1 n))
3.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
2.0ms	(/ 1 (pow n 2))

simplify69.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	665	1216
1	2806	990
2	5001	886

prune299.0ms

Filtered

102 candidates to 193 candidates (-89.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	193	1	194

Merged error: 0b

Counts

194 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ 0.5 n) (/ 0.16666666666666669 (pow n 2)))
0.9b	(/ 0.16666666666666669 (pow n 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
39×	`times-frac`
25×	`*-un-lft-identity`
19×	`add-cube-cbrt`
14×	`unpow-prod-down`
10×	`difference-of-squares`
8×	`associate-/r*`
7×	`add-exp-log`
6×	`unpow2` `sqr-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`div-exp` `associate-/l*`
2×	`pow1` `distribute-lft-out--`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `clear-num` `frac-sub` `flip--` `div-inv`

Counts

2 → 74

Calls

2 calls:

21.0ms	(- (/ 0.5 n) (/ 0.16666666666666669 (pow n 2)))
7.0ms	(/ 0.16666666666666669 (pow n 2))

series9.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(- (/ 0.5 n) (/ 0.16666666666666669 (pow n 2)))
3.0ms	(/ 0.16666666666666669 (pow n 2))

simplify33.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	280	492
1	903	446
2	5001	435

prune97.0ms

Filtered

51 candidates to 80 candidates (-56.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	1	81

Merged error: 0b

Counts

81 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	3637×	body	1280	valid
657.0ms	2643×	body	640	valid
219.0ms	1258×	body	320	valid
87.0ms	8000×	pre	80	true
53.0ms	462×	body	160	valid

Details

sample87.0ms

simplify154.0ms

prune3.0ms

localize10.0ms

rewrite23.0ms

series34.0ms

simplify53.0ms

prune129.0ms

localize18.0ms

rewrite48.0ms

series14.0ms

simplify69.0ms

prune299.0ms

localize10.0ms

rewrite30.0ms

series9.0ms

simplify33.0ms

prune97.0ms

simplify1.0ms

end0.0ms

sample2.5s

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