Details

sample29.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

14.0ms	91×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	9×	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: 15.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.3b	(- (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))

series4.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify76.0ms

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: 0.7b

Counts

29 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.7b	(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)))

series6.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify55.0ms

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

prune63.0ms

Filtered

22 candidates to 34 candidates (-54.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	26	8	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	9	35

Merged error: 0.7b

Counts

35 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
0.7b	(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))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify66.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (15.0ms)

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

prune85.0ms

Filtered

41 candidates to 52 candidates (-26.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	3	4	7
Picked	1	0	1
Done	1	0	1
Total	54	7	61

Merged error: 0.7b

Counts

61 → 7

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow N 2) (+ (* 1.0 N) 1))
0.7b	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
4×	`*-un-lft-identity`
3×	`sum-log`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `distribute-lft-out`

Counts

2 → 21

Calls

2 calls:

7.0ms	(+ (pow N 2) (+ (* 1.0 N) 1))
1.0ms	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

series5.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(+ (pow N 2) (+ (* 1.0 N) 1))
2.0ms	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

simplify76.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	114	181
1	447	154
2	2686	153
3	5001	150

prune39.0ms

Filtered

20 candidates to 27 candidates (-35.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	27	7	34

Merged error: 0.7b

Counts

34 → 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	14	5
1	14	5

end0.0ms

sample792.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 0%

Results

440.0ms	2878×	body	1280	valid
141.0ms	4023×	body	80	valid
76.0ms	614×	body	640	valid
32.0ms	325×	body	320	valid
11.0ms	160×	body	160	valid

Details

sample29.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series4.0ms

simplify76.0ms

prune38.0ms

localize6.0ms

rewrite7.0ms

series6.0ms

simplify55.0ms

prune63.0ms

localize12.0ms

rewrite5.0ms

series66.0ms

simplify66.0ms

prune85.0ms

localize7.0ms

rewrite8.0ms

series5.0ms

simplify76.0ms

prune39.0ms

regimes42.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample792.0ms

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