Details

sample31.0ms

Algorithm

intervals

Results

15.0ms	91×	body	1280	valid
5.0ms	126×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 15.3b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.1b	(- (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))

series13.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify50.0ms

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

prune63.0ms

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: 1.0b

Counts

45 → 2

localize5.0ms

Local error

Found 1 expressions with local error:

1.0b	(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

prune31.0ms

Filtered

12 candidates to 9 candidates (75.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	8	4	12
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	9	5	14

Merged error: 1.0b

Counts

14 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(log1p (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))))
0.0b	(expm1 (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 31

Calls

3 calls:

1.0ms	(log1p (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))))
1.0ms	(expm1 (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

series148.0ms

Counts

3 → 9

Calls

3 calls:

110.0ms	(log1p (expm1 (atan2 1.0 (fma N (+ N 1.0) 1))))
37.0ms	(expm1 (atan2 1.0 (fma N (+ N 1.0) 1)))
2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

simplify34.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	46	193
1	92	170
2	196	169
3	750	169
4	5002	169

prune63.0ms

Filtered

40 candidates to 24 candidates (60.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	41	4	45

Merged error: 1.0b

Counts

45 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

1.0b	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0b	(atan2 1.0 (fma N (+ N 1.0) 1))
15.1b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.1b	(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)))

series25.0ms

Counts

4 → 12

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

simplify176.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 6 (42.0ms)

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

prune102.0ms

Filtered

60 candidates to 42 candidates (70.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	57	3	60
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	57	7	64

Merged error: 1.0b

Counts

64 → 7

regimes24.0ms

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	11	5
1	11	5

end0.0ms

sample821.0ms

Algorithm

intervals

Results

444.0ms	2835×	body	1280	valid
143.0ms	4054×	body	80	valid
79.0ms	632×	body	640	valid
30.0ms	312×	body	320	valid
12.0ms	167×	body	160	valid