Details

sample79.0ms

Algorithm

intervals

Results

42.0ms	123×	body	1280	valid
19.0ms	83×	body	640	valid
6.0ms	39×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	11×	body	160	valid

simplify166.0ms

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	5002	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:

0.3b	(* n (log n))
0.3b	(* (+ n 1.0) (log (+ n 1.0)))
4.6b	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite28.0ms

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)))
13.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series444.0ms

Counts

3 → 9

Calls

3 calls:

182.0ms	(* n (log n))
71.0ms	(* (+ n 1.0) (log (+ n 1.0)))
191.0ms	(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	419	643
1	1786	587
2	5002	568

prune174.0ms

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

localize15.0ms

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)))
0.7b	(/ 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)
12.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms	(/ 1 (pow n 2))

series84.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
25.0ms	(* 0.16666666666666669 (/ 1 (pow n 2)))
22.0ms	(/ 1 (pow n 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	481	916
1	1944	760
2	5002	671

prune220.0ms

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:

0.7b	(/ 0.16666666666666669 (pow n 2))

rewrite7.0ms

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))

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

(/ 0.16666666666666669 (pow n 2))

simplify108.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	153	244
1	571	217
2	3236	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

sample2.3s

Algorithm

intervals

Results

1.2s	3623×	body	1280	valid
609.0ms	2638×	body	640	valid
202.0ms	1285×	body	320	valid
90.0ms	8000×	pre	80	true
48.0ms	454×	body	160	valid

Details

sample79.0ms

simplify166.0ms

prune2.0ms

localize10.0ms

rewrite28.0ms

series444.0ms

simplify54.0ms

prune174.0ms

localize15.0ms

rewrite38.0ms

series84.0ms

simplify61.0ms

prune220.0ms

localize12.0ms

rewrite7.0ms

series26.0ms

simplify108.0ms

prune86.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling