Details

sample31.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

15.0ms	101×	body	1280	valid
5.0ms	129×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

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: 12.6b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.0b	(- (atan (+ N 1.0)) (atan N))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

series4.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

simplify71.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2447	142
5	5001	142

prune44.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	3	29

Merged error: 0.1b

Counts

29 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.2b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
3×	`associate-r`
2×	`associate-*l/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

9.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series6.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify53.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127

prune50.0ms

Filtered

22 candidates to 34 candidates (-54.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	1	1
Picked	0	1	1
Done	1	0	1
Total	33	4	37

Merged error: 0.1b

Counts

37 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series88.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (cbrt N) (cbrt N))
20.0ms	(cbrt N)
23.0ms	(cbrt N)
21.0ms	(cbrt N)

simplify72.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (66.0ms)

Iter	Nodes	Cost
0	148	349
1	471	322
2	2276	265
3	5002	252

prune93.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	85	4	89

Merged error: 0.1b

Counts

89 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
0.2b	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
0.6b	(cbrt N)
31.7b	(cbrt (* N N))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-exp-log`
7×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-cbrt-cube`
4×	`associate-*l/` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

4 → 50

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
8.0ms	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
1.0ms	(cbrt N)
2.0ms	(cbrt (* N N))

series53.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
7.0ms	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
23.0ms	(cbrt N)
21.0ms	(cbrt (* N N))

simplify32.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	276	408
1	939	362
2	5001	321

prune80.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	62	4	66

Merged error: 0.1b

Counts

66 → 4

regimes33.0ms

Accuracy

0% (0.0b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample900.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

469.0ms	2933×	body	1280	valid
146.0ms	3997×	body	80	valid
81.0ms	612×	body	640	valid
32.0ms	323×	body	320	valid
10.0ms	135×	body	160	valid

Details

sample31.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite4.0ms

series4.0ms

simplify71.0ms

prune44.0ms

localize10.0ms

rewrite11.0ms

series6.0ms

simplify53.0ms

prune50.0ms

localize9.0ms

rewrite11.0ms

series88.0ms

simplify72.0ms

prune93.0ms

localize10.0ms

rewrite13.0ms

series53.0ms

simplify32.0ms

prune80.0ms

regimes33.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample900.0ms

Profiling