Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	90×	body	1280	valid
6.0ms	22×	body	640	valid
4.0ms	129×	body	80	valid
1.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	7
1	10	7

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: 15.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.9b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

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))
4.0ms	(- (atan (+ N 1.0)) (atan N))

series5.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
4.0ms	(- (atan (+ N 1.0)) (atan N))

simplify61.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4929	239
1	4929	239

prune37.0ms

Filtered

19 candidates to 28 candidates (-47.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	1	29

Merged error: 0.2b

Counts

29 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

7.0ms	(* N (+ N 1.0))
1.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

series7.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(* N (+ N 1.0))
2.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

simplify50.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4879	272
1	4879	272

prune67.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	32	4	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	5	37

Merged error: 0.2b

Counts

37 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N))))
15.5b	(cbrt (* N (+ 1.0 N)))
15.5b	(cbrt (* N (+ 1.0 N)))
15.5b	(cbrt (* N (+ 1.0 N)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

7.0ms	(* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N))))
5.0ms	(cbrt (* N (+ 1.0 N)))
5.0ms	(cbrt (* N (+ 1.0 N)))
5.0ms	(cbrt (* N (+ 1.0 N)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (cbrt (* N (+ 1.0 N))) (cbrt (* N (+ 1.0 N))))
12.0ms	(cbrt (* N (+ 1.0 N)))
10.0ms	(cbrt (* N (+ 1.0 N)))
10.0ms	(cbrt (* N (+ 1.0 N)))

simplify31.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4964	1057
1	4964	1057

prune234.0ms

Filtered

71 candidates to 84 candidates (-18.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	83	6	89

Merged error: 0.1b

Counts

89 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

15.5b	(cbrt (* N (+ 1.0 N)))
15.5b	(cbrt (* N (+ N 1.0)))
15.5b	(cbrt (* N (+ N 1.0)))
15.5b	(cbrt (* N (+ N 1.0)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-div` `associate-*r/`
4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `flip3-+` `pow1/3` `add-cbrt-cube` `flip-+` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(cbrt (* N (+ 1.0 N)))
10.0ms	(cbrt (* N (+ N 1.0)))
10.0ms	(cbrt (* N (+ N 1.0)))
10.0ms	(cbrt (* N (+ N 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4937	656
1	4937	656

prune236.0ms

Filtered

53 candidates to 56 candidates (-5.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	56	6	62

Merged error: 0.1b

Counts

62 → 6

regimes46.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms

sample757.0ms

Algorithm

intervals

Results

372.0ms	2812×	body	1280	valid
114.0ms	4111×	body	80	valid
70.0ms	611×	body	640	valid
24.0ms	290×	body	320	valid
10.0ms	176×	body	160	valid

Details

sample31.0ms

simplify2.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series5.0ms

simplify61.0ms

prune37.0ms

localize9.0ms

rewrite8.0ms

series7.0ms

simplify50.0ms

prune67.0ms

localize10.0ms

rewrite24.0ms

series45.0ms

simplify31.0ms

prune234.0ms

localize18.0ms

rewrite22.0ms

series40.0ms

simplify47.0ms

prune236.0ms

regimes46.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample757.0ms

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