Details

sample62.0ms

Algorithm

intervals

Results

30.0ms	79×	body	1280	valid
9.0ms	134×	body	80	valid
6.0ms	26×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	6×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize71.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.9b	(- (atan (+ N 1.0)) (atan N))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

3.0ms	(atan (+ N 1.0))
13.0ms	(- (atan (+ N 1.0)) (atan N))

series46.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(atan (+ N 1.0))
38.0ms	(- (atan (+ N 1.0)) (atan N))

simplify8.8s

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
6	4826
5	1486
4	575
3	276
2	152
1	78
0	42

prune231.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.9b

localize37.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.9b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cbrt-cube` `associate-l` `add-exp-log` `add-cube-cbrt`
3×	`associate-r`
2×	`associate-*l/` `insert-posit16` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

48.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series76.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(* (+ N 1.0) N)
9.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify3.2s

Counts

36 → 36

Iterations

Iter	Nodes
done	5000
3	1277
2	340
1	128
0	57

prune298.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize83.0ms

Local error

Found 4 expressions with local error:

0.9b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.9b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.0b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.0b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 44

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
3.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
20.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
43.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
46.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify3.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	5004
7	2311
6	986
5	401
4	178
3	118
2	79
1	55
0	34

prune368.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize110.0ms

Local error

Found 4 expressions with local error:

0.9b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.0b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.0b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.0b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 50

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
3.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
3.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
37.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
40.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
36.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify3.2s

Counts

62 → 62

Iterations

Iter	Nodes
done	5004
7	2311
6	986
5	401
4	178
3	118
2	79
1	55
0	34

prune400.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.9b

regimes84.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.8s

Algorithm

intervals

Results

909.0ms	2937×	body	1280	valid
282.0ms	149×	body	160	valid
226.0ms	3972×	body	80	valid
133.0ms	615×	body	640	valid
75.0ms	327×	body	320	valid