Details

sample68.0ms

Algorithm

intervals

Results

37.0ms	98×	body	1280	valid
8.0ms	117×	body	80	valid
6.0ms	24×	body	640	valid
3.0ms	14×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize8.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `diff-atan` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

5.0ms

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

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify2.5s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
4	2162
3	737
2	287
1	136
0	62

prune89.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 1 expressions with local error:

0.6b	(atan2 1.0 (fma N (+ 1.0 N) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 9

Calls

1 calls:

0.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify2.6s

Counts

12 → 12

Iterations

Iter	Nodes
done	5001
9	1219
8	427
7	205
6	131
5	101
4	82
3	61
2	37
1	25
0	18

prune59.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (fma N (+ 1.0 N) 1))
0.6b	(atan2 1.0 (fma N (+ 1.0 N) 1))
14.9b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.9b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `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 (+ 1.0 N) 1))
0.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
2.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
13.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
21.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

simplify2.3s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
7	1528
6	608
5	256
4	151
3	106
2	69
1	46
0	33

prune213.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (fma N (+ 1.0 N) 1))
14.9b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.9b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
14.9b	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `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 (+ 1.0 N) 1))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ 1.0 N) 1)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.9s

Counts

66 → 66

Iterations

Iter	Nodes
done	5000
7	1528
6	608
5	256
4	151
3	106
2	69
1	46
0	33

prune256.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	6

end0.0ms

sample1.4s

Algorithm

intervals

Results

593.0ms	2881×	body	1280	valid
475.0ms	4036×	body	80	valid
121.0ms	625×	body	640	valid
33.0ms	302×	body	320	valid
12.0ms	156×	body	160	valid