Details

sample30.0ms

Algorithm

intervals

Results

14.0ms	96×	body	1280	valid
4.0ms	113×	body	80	valid
2.0ms	19×	body	640	valid
2.0ms	23×	body	320	valid
0.0ms	5×	body	160	valid

simplify5.0ms

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

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: 18.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.2b	(- (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))

series13.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify75.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142

prune50.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	2	29

Merged error: 0.8b

Counts

29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.8b	(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)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify55.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

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

prune66.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	29	7	36

Merged error: 0.8b

Counts

36 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
0.8b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

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

series532.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(cbrt N)
178.0ms	(cbrt N)
177.0ms	(cbrt N)
6.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))

simplify85.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (81.0ms)

Iter	Nodes	Cost
0	75	232
1	164	204
2	533	198
3	2411	194
4	5001	191

prune156.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	52	7	59

Merged error: 0.7b

Counts

59 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.8b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.0b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.0b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 40

Calls

4 calls:

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

series33.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify73.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	49	332
1	79	294
2	159	294
3	330	292
4	1202	292
5	5002	292

prune84.0ms

Filtered

52 candidates to 34 candidates (65.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	51	8	59

Merged error: 0.7b

Counts

59 → 8

regimes29.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample806.0ms

Algorithm

intervals

Results

440.0ms	2871×	body	1280	valid
140.0ms	4041×	body	80	valid
79.0ms	649×	body	640	valid
30.0ms	307×	body	320	valid
10.0ms	132×	body	160	valid

Details

sample30.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series13.0ms

simplify75.0ms

prune50.0ms

localize6.0ms

rewrite7.0ms

series47.0ms

simplify55.0ms

prune66.0ms

localize10.0ms

rewrite5.0ms

series532.0ms

simplify85.0ms

prune156.0ms

localize8.0ms

rewrite4.0ms

series33.0ms

simplify73.0ms

prune84.0ms

regimes29.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample806.0ms

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