Details

sample60.0ms

Algorithm

intervals

Results

26.0ms	89×	body	1280	valid
9.0ms	131×	body	80	valid
6.0ms	25×	body	640	valid
2.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

13.0ms

(- (atan (+ N 1.0)) (atan N))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(- (atan (+ N 1.0)) (atan N))

simplify10.4s

Counts

32 → 32

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	62	552
1	136	442
2	503	352
3	4368	291
done	5000	291

prune108.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.0b

localize21.0ms

Local error

Found 1 expressions with local error:

1.0b	(atan2 (+ 1.0 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 0) (fma N (+ N 1.0) 1))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(atan2 (+ 1.0 0) (fma N (+ N 1.0) 1))

simplify1.5s

Counts

12 → 12

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	18	156
1	24	132
2	36	116
3	60	116
4	84	116
5	118	116
6	187	116
7	362	116
8	1140	116
done	5000	116

prune45.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.9b

localize12.0ms

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))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite7.0ms

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:

0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
2.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
4.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
29.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
28.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.8s

Counts

60 → 60

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	29	686
1	41	638
2	82	592
3	147	592
4	215	592
5	491	592
6	2018	592
done	5000	592

prune229.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(atan2 1.0 (fma N (+ N 1.0) 1))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.4b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

0.0ms	(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)))
6.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
15.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
14.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.5s

Counts

66 → 66

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	29	765
1	41	693
2	82	656
3	147	656
4	215	656
5	491	656
6	2018	656
done	5000	656

prune216.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

regimes37.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	8	10
1	11	8
2	12	8
done	12	8

end0.0ms

sample1.2s

Algorithm

intervals

Results

616.0ms	2907×	body	1280	valid
200.0ms	3989×	body	80	valid
109.0ms	627×	body	640	valid
72.0ms	290×	body	320	valid
15.0ms	187×	body	160	valid