Details

sample33.0ms

Algorithm

intervals

Results

16.0ms	96×	body	1280	valid
4.0ms	113×	body	80	valid
3.0ms	19×	body	640	valid
3.0ms	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))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

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

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
10.0ms	(- (atan (+ N 1.0)) (atan N))

simplify49.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	129	365
1	345	264
2	1480	254
3	5001	198

prune64.0ms

Filtered

44 candidates to 27 candidates (61.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	2	45

Merged error: 0.8b

Counts

45 → 2

localize6.0ms

Local error

Found 1 expressions with local error:

0.8b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

1.0ms

(atan2 1.0 (fma N (+ N 1.0) 1))

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

(atan2 1.0 (fma N (+ N 1.0) 1))

simplify96.0ms

Algorithm

egg-herbie

Counts

12 → 12

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	57
1	32	50
2	55	50
3	70	50
4	89	50
5	143	50
6	567	50
7	1779	50
8	5001	50

prune28.0ms

Filtered

12 candidates to 9 candidates (75.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	9	3	12
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	10	4	14

Merged error: 0.8b

Counts

14 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 48

Calls

4 calls:

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

series27.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify178.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 6 (46.0ms)

Iter	Nodes	Cost
0	37	296
1	62	276
2	100	276
3	148	276
4	341	276
5	975	276
6	3911	274
7	5001	274

prune116.0ms

Filtered

60 candidates to 42 candidates (70.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	58	6	64

Merged error: 0.8b

Counts

64 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (fma N (+ N 1.0) 1))
15.0b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.4b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.4b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 50

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
112.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
109.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify57.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	52	352
1	109	319
2	235	315
3	808	315
4	5002	315

prune154.0ms

Filtered

62 candidates to 46 candidates (74.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	60	8	68

Merged error: 0.8b

Counts

68 → 8

regimes33.0ms

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	9	3
1	9	3

end0.0ms

sample863.0ms

Algorithm

intervals

Results

468.0ms	2871×	body	1280	valid
149.0ms	4041×	body	80	valid
86.0ms	649×	body	640	valid
32.0ms	307×	body	320	valid
10.0ms	132×	body	160	valid

Details

sample33.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite6.0ms

series12.0ms

simplify49.0ms

prune64.0ms

localize6.0ms

rewrite1.0ms

series2.0ms

simplify96.0ms

prune28.0ms

localize8.0ms

rewrite5.0ms

series27.0ms

simplify178.0ms

prune116.0ms

localize13.0ms

rewrite5.0ms

series235.0ms

simplify57.0ms

prune154.0ms

regimes33.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample863.0ms

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