Details

sample28.0ms

Algorithm

intervals

Results

13.0ms	95×	body	1280	valid
4.0ms	125×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4
done	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.2b	(- (atan (+ N 1.0)) (atan N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
5.0ms	(- (atan (+ N 1.0)) (atan N))

series13.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify76.0ms

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142
done	5001	142

prune50.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize6.0ms

Local error

Found 1 expressions with local error:

0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 7

Calls

1 calls:

0.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify310.0ms

Counts

10 → 10

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	65
1	50	53
2	113	53
3	224	53
4	687	53
5	4299	53
6	5001	53
done	5001	53

prune19.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
14.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
16.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series38.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
4.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify106.0ms

Counts

94 → 94

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	110	649
1	391	565
2	2248	539
3	5001	520
done	5001	520

prune139.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
14.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

54×	`sqrt-pow1`
45×	`pow1`
30×	`pow1/2` `pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`pow-prod-down`
6×	`associate-l` `pow-sqr`
4×	`add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-r` `*-commutative`

Counts

4 → 85

Calls

4 calls:

46.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (* (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify84.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	193	630
1	469	496
2	1361	484
3	5001	484
done	5001	484

prune148.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes31.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4
done	12	4

end0.0ms

sample747.0ms

Algorithm

intervals

Results

373.0ms	2823×	body	1280	valid
125.0ms	4078×	body	80	valid
69.0ms	639×	body	640	valid
31.0ms	312×	body	320	valid
12.0ms	148×	body	160	valid