Details

sample63.0ms

Algorithm

intervals

Results

35.0ms	98×	body	1280	valid
10.0ms	125×	body	80	valid
6.0ms	19×	body	640	valid
2.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
1.1b	(- (atan (+ N 1)) (atan N))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

2.0ms	(atan (+ N 1))
11.0ms	(- (atan (+ N 1)) (atan N))

series22.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
20.0ms	(- (atan (+ N 1)) (atan N))

simplify1.3s

Counts

46 → 46

Iterations

Iter	Nodes
done	2004
4	2004
3	773
2	288
1	140
0	67

prune148.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize19.0ms

Local error

Found 1 expressions with local error:

0.7b	(atan2 1 (fma N (+ 1 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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify1.7s

Counts

13 → 13

Iterations

Iter	Nodes
done	2004
10	2004
9	1660
8	834
7	554
6	378
5	223
4	133
3	62
2	37
1	25
0	18

prune53.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1 (fma N (+ 1 N) 1))
0.7b	(atan2 1 (fma N (+ 1 N) 1))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 52

Calls

4 calls:

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

series29.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (fma N (+ 1 N) 1))
2.0ms	(atan2 1 (fma N (+ 1 N) 1))
12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
13.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

simplify1.0s

Counts

64 → 64

Iterations

Iter	Nodes
done	2000
7	2000
6	830
5	383
4	207
3	110
2	70
1	47
0	34

prune263.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1 (fma N (+ 1 N) 1))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
14.2b	(sqrt (atan2 1 (fma N (+ 1 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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 58

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (fma N (+ 1 N) 1))
16.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))
12.0ms	(sqrt (atan2 1 (fma N (+ 1 N) 1)))

simplify995.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	2000
7	2000
6	830
5	383
4	207
3	110
2	70
1	47
0	34

prune289.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes36.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	8
1	8
0	5

end0.0ms

sample1.7s

Algorithm

intervals

Results

830.0ms	2854×	body	1280	valid
526.0ms	654×	body	640	valid
215.0ms	3996×	body	80	valid
52.0ms	338×	body	320	valid
17.0ms	158×	body	160	valid