Details

sample52.0ms

Algorithm

intervals

Results

23.0ms	85×	body	1280	valid
9.0ms	148×	body	80	valid
3.0ms	14×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify20.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize13.0ms

Local error

Found 1 expressions with local error:

1.2b	(- (atan (+ N 1.0)) (atan N))

rewrite11.0ms

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` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 30

Calls

1 calls:

9.0ms

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

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

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

simplify5.1s

Counts

33 → 33

Iterations

Iter	Nodes
done	5000
4	2267
3	779
2	279
1	137
0	63

prune234.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize18.0ms

Local error

Found 1 expressions with local error:

0.5b	(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` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

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

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

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

simplify10.5s

Counts

13 → 13

Iterations

Iter	Nodes
done	5010
10	3647
9	1229
8	744
7	431
6	130
5	94
4	82
3	62
2	38
1	26
0	19

prune158.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize25.0ms

Local error

Found 3 expressions with local error:

0.5b	(atan2 1.0 (fma N (+ 1.0 N) 1))
0.5b	(log1p (atan2 1.0 (fma N (+ 1.0 N) 1)))
0.6b	(expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`expm1-log1p-u`
3×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef`

Counts

3 → 34

Calls

3 calls:

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

series468.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(atan2 1.0 (fma N (+ 1.0 N) 1))
184.0ms	(log1p (atan2 1.0 (fma N (+ 1.0 N) 1)))
271.0ms	(expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1))))

simplify4.3s

Counts

43 → 43

Iterations

Iter	Nodes
done	5000
9	2703
8	901
7	418
6	250
5	176
4	135
3	102
2	74
1	59
0	42

prune294.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize93.0ms

Local error

Found 4 expressions with local error:

0.6b	(expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1))))
13.2b	(cbrt (expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1)))))
13.2b	(cbrt (expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1)))))
13.2b	(cbrt (expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`expm1-log1p` `expm1-udef`

Counts

4 → 54

Calls

4 calls:

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

series1.5s

Counts

4 → 12

Calls

4 calls:

215.0ms	(expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1))))
418.0ms	(cbrt (expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1)))))
421.0ms	(cbrt (expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1)))))
413.0ms	(cbrt (expm1 (log1p (atan2 1.0 (fma N (+ 1.0 N) 1)))))

simplify5.5s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
5	2771
4	720
3	221
2	100
1	52
0	36

prune504.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes189.0ms

Accuracy

0% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 0.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	11
1	11
0	8

end0.0ms

sample1.4s

Algorithm

intervals

Results

925.0ms	2867×	body	1280	valid
150.0ms	4022×	body	80	valid
113.0ms	613×	body	640	valid
37.0ms	339×	body	320	valid
12.0ms	159×	body	160	valid