Details

sample51.0ms

Algorithm

intervals

Results

21.0ms	77×	body	1280	valid
9.0ms	142×	body	80	valid
5.0ms	23×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	6×	body	160	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

Local error

Found 1 expressions with local error:

1.4b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

5.0ms

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

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify1.9s

Counts

18 → 18

Iterations

Iter	Nodes
done	5001
5	3570
4	966
3	326
2	149
1	73
0	36

prune53.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

0.2b	(atan2 1.0 (+ (* N (+ 1.0 N)) 1))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 7

Calls

1 calls:

0.0ms

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

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify1.2s

Counts

10 → 10

Iterations

Iter	Nodes
done	5001
5	2310
4	760
3	251
2	90
1	38
0	20

prune42.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (+ (* N (+ N 1.0)) 1))
0.7b	(* (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))) (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))))
12.5b	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
12.5b	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ (* N (+ N 1.0)) 1))
11.0ms	(* (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))) (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))))
2.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
2.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ (* N (+ N 1.0)) 1))
7.0ms	(* (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))) (sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1))))
30.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
18.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))

simplify8.2s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
3	4350
2	522
1	136
0	64

prune244.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
0.2b	(pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3)
12.5b	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
12.5b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
15×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
9×	`pow1` `unpow-prod-down` `cube-prod`
6×	`sqrt-pow1`
5×	`pow-pow` `add-cbrt-cube` `add-exp-log`
4×	`pow1/2` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `sqrt-pow2` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
4.0ms	(pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3)
1.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
170.0ms	(pow (sqrt (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))) 3)
16.0ms	(sqrt (atan2 1.0 (+ (* N (+ N 1.0)) 1)))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify1.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5002
2	1085
1	269
0	97

prune245.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

regimes47.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	7

end0.0ms

sample1.1s

Algorithm

intervals

Results

645.0ms	2900×	body	1280	valid
146.0ms	3994×	body	80	valid
88.0ms	638×	body	640	valid
34.0ms	323×	body	320	valid
11.0ms	145×	body	160	valid