Details

sample34.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

17.0ms	79×	body	1280	valid
5.0ms	142×	body	80	valid
3.0ms	21×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	2×	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

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: 13.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.8b	(- (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))

simplify74.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (10.0ms)

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

prune38.0ms

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: 0.6b

Counts

29 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.6b	(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:

5.0ms	(* (+ 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)))

simplify54.0ms

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

prune56.0ms

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: 0.6b

Counts

35 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify65.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (14.0ms)

Iter	Nodes	Cost
0	95	268
1	172	237
2	446	207
3	1754	200
4	5001	200

prune77.0ms

Filtered

41 candidates to 52 candidates (-26.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	52	6	58

Merged error: 0.6b

Counts

58 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
15.0b	(cbrt (* (+ N 1.0) N))
15.0b	(cbrt (* (+ N 1.0) N))
15.0b	(cbrt (* (+ N 1.0) N))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series31.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
9.0ms	(cbrt (* (+ N 1.0) N))
9.0ms	(cbrt (* (+ N 1.0) N))
11.0ms	(cbrt (* (+ N 1.0) N))

simplify56.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	207	623
1	572	575
2	1929	533
3	5001	525

prune151.0ms

Filtered

47 candidates to 52 candidates (-10.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	51	7	58

Merged error: 0.6b

Counts

58 → 7

regimes42.0ms

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

sample861.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

432.0ms	2770×	body	1280	valid
150.0ms	4096×	body	80	valid
84.0ms	649×	body	640	valid
31.0ms	321×	body	320	valid
12.0ms	164×	body	160	valid

Details

sample34.0ms

simplify5.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series3.0ms

simplify74.0ms

prune38.0ms

localize6.0ms

rewrite7.0ms

series6.0ms

simplify54.0ms

prune56.0ms

localize9.0ms

rewrite5.0ms

series67.0ms

simplify65.0ms

prune77.0ms

localize10.0ms

rewrite14.0ms

series31.0ms

simplify56.0ms

prune151.0ms

regimes42.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample861.0ms

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