Details

sample72.0ms

Algorithm

intervals

Results

41.0ms	87×	body	1280	valid
11.0ms	133×	body	80	valid
5.0ms	17×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	9×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
2.2b	(- (atan (+ N 1)) (atan N))

rewrite7.0ms

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:

2.0ms	(atan (+ N 1))
5.0ms	(- (atan (+ N 1)) (atan N))

series18.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
15.0ms	(- (atan (+ N 1)) (atan N))

simplify2.3s

Counts

30 → 30

Iterations

Iter	Nodes
6	5332
5	1658
4	628
3	288
2	151
1	77
0	41

prune255.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

1 → 8

Calls

1 calls:

0.0ms

(atan2 1 (+ 1 (* (+ N 1) N)))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(atan2 1 (+ 1 (* (+ N 1) N)))

simplify5.6s

Counts

11 → 11

Iterations

Iter	Nodes
10	7563
9	1652
8	551
7	255
6	153
5	108
4	86
3	63
2	46
1	33
0	19

prune69.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ N 1) (* N N))
0.3b	(atan2 1 (+ (+ N 1) (* N N)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
3×	`sum-log`
2×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

2 → 22

Calls

2 calls:

18.0ms	(+ (+ N 1) (* N N))
0.0ms	(atan2 1 (+ (+ N 1) (* N N)))

series20.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ (+ N 1) (* N N))
3.0ms	(atan2 1 (+ (+ N 1) (* N N)))

simplify3.9s

Counts

28 → 28

Iterations

Iter	Nodes
4	8809
3	1970
2	468
1	123
0	46

prune155.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1 (* (* (cbrt (+ (+ N 1) (* N N))) (cbrt (+ (+ N 1) (* N N)))) (cbrt (+ (+ N 1) (* N N)))))
14.2b	(cbrt (+ (+ N 1) (* N N)))
14.2b	(cbrt (+ (+ N 1) (* N N)))
14.2b	(cbrt (+ (+ N 1) (* N N)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 50

Calls

4 calls:

0.0ms	(atan2 1 (* (* (cbrt (+ (+ N 1) (* N N))) (cbrt (+ (+ N 1) (* N N)))) (cbrt (+ (+ N 1) (* N N)))))
10.0ms	(cbrt (+ (+ N 1) (* N N)))
9.0ms	(cbrt (+ (+ N 1) (* N N)))
10.0ms	(cbrt (+ (+ N 1) (* N N)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1 (* (* (cbrt (+ (+ N 1) (* N N))) (cbrt (+ (+ N 1) (* N N)))) (cbrt (+ (+ N 1) (* N N)))))
39.0ms	(cbrt (+ (+ N 1) (* N N)))
40.0ms	(cbrt (+ (+ N 1) (* N N)))
41.0ms	(cbrt (+ (+ N 1) (* N N)))

simplify1.3s

Counts

62 → 62

Iterations

Iter	Nodes
4	2823
3	1014
2	374
1	152
0	70

prune434.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes30.0ms

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
2	10
1	10
0	6

end0.0ms

sample1.2s

Algorithm

intervals

Results

742.0ms	2890×	body	1280	valid
210.0ms	3977×	body	80	valid
139.0ms	653×	body	640	valid
43.0ms	327×	body	320	valid
14.0ms	153×	body	160	valid