Details

sample61.0ms

Algorithm

intervals

Results

30.0ms	93×	body	1280	valid
9.0ms	133×	body	80	valid
6.0ms	20×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	3×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.9b	(- (atan (+ N 1.0)) (atan N))

rewrite18.0ms

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:

2.0ms	(atan (+ N 1.0))
14.0ms	(- (atan (+ N 1.0)) (atan N))

series24.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
20.0ms	(- (atan (+ N 1.0)) (atan N))

simplify8.5s

Counts

44 → 44

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	66	624
1	139	506
2	506	416
3	4476	355
done	5000	355

prune79.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 1 expressions with local error:

0.8b	(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:

0.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify1.0s

Counts

12 → 12

Iterations

Useful iterations: 2 (8.0ms)

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

prune29.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize10.0ms

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))
13.6b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.6b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite4.0ms

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
3.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
14.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
19.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.2s

Counts

60 → 60

Iterations

Useful iterations: 2 (12.0ms)

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

prune134.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (fma N (+ N 1.0) 1))
13.6b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.6b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.6b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite5.0ms

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
17.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify1.2s

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

prune171.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

regimes21.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

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

sample1.4s

Algorithm

intervals

Results

568.0ms	2832×	body	1280	valid
495.0ms	4093×	body	80	valid
121.0ms	619×	body	640	valid
35.0ms	311×	body	320	valid
11.0ms	145×	body	160	valid