Details

analyze1.0ms

Algorithm: search

sample29.0ms

Algorithm

intervals

Results

15.0ms	104×	body	1280	valid
4.0ms	120×	body	80	valid
2.0ms	20×	body	640	valid
1.0ms	9×	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

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: 17.1b

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

series3.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

simplify72.0ms

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

prune40.0ms

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

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite7.0ms

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:

6.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series7.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(* (+ 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

prune58.0ms

Filtered

22 candidates to 34 candidates (-54.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	6	35

Merged error: 0.2b

Counts

35 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (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:

6.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series92.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (cbrt N) (cbrt N))
22.0ms	(cbrt N)
21.0ms	(cbrt N)
22.0ms	(cbrt N)

simplify71.0ms

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

prune107.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	84	7	91

Merged error: 0.2b

Counts

91 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
0.2b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
0.6b	(cbrt N)
27.8b	(cbrt (* N N))

rewrite14.0ms

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:

8.0ms	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
1.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
1.0ms	(cbrt N)
3.0ms	(cbrt (* N N))

series54.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
3.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
22.0ms	(cbrt N)
21.0ms	(cbrt (* N N))

simplify34.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (27.0ms)

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

prune83.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	61	8	69

Merged error: 0.2b

Counts

69 → 8

regimes47.0ms

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	12	4
1	12	4

end0.0ms

analyze1.0ms

Algorithm: search

sample789.0ms

Algorithm

intervals

Results

429.0ms	2868×	body	1280	valid
140.0ms	4044×	body	80	valid
78.0ms	620×	body	640	valid
30.0ms	319×	body	320	valid
14.0ms	149×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify4.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series3.0ms

simplify72.0ms

prune40.0ms

localize6.0ms

rewrite7.0ms

series7.0ms

simplify53.0ms

prune58.0ms

localize11.0ms

rewrite11.0ms

series92.0ms

simplify71.0ms

prune107.0ms

localize11.0ms

rewrite14.0ms

series54.0ms

simplify34.0ms

prune83.0ms

regimes47.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample789.0ms

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