Details

sample56.0ms

Algorithm

intervals

Results

28.0ms	84×	body	1280	valid
11.0ms	141×	body	80	valid
5.0ms	16×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	4×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.6b

localize12.0ms

Local error

Found 1 expressions with local error:

0.8b	(- (atan (+ N 1)) (atan N))

rewrite5.0ms

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` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 16

Calls

1 calls:

5.0ms

(- (atan (+ N 1)) (atan N))

series26.0ms

Counts

1 → 3

Calls

1 calls:

26.0ms

(- (atan (+ N 1)) (atan N))

simplify1.3s

Counts

19 → 19

Iterations

Iter	Nodes
done	2000
6	2000
5	1968
4	692
3	307
2	147
1	73
0	36

prune81.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.2b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite25.0ms

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:

24.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series63.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.2s

Counts

36 → 36

Iterations

Iter	Nodes
done	2002
4	2002
3	706
2	266
1	121
0	55

prune124.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.6b	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
15.7b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.7b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite12.0ms

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×	`insert-posit16` `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 → 86

Calls

4 calls:

0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
8.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
5.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
19.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
done	2004
5	2004
4	1111
3	489
2	247
1	128
0	65

prune315.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
15.7b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.7b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.7b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-pow1`
51×	`pow1`
36×	`pow1/2`
34×	`pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`pow-sqr`
7×	`pow-prod-down`
6×	`pow-plus` `associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-l` `*-commutative`

Counts

4 → 95

Calls

4 calls:

44.0ms	(* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

series50.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
18.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify1.2s

Counts

107 → 107

Iterations

Iter	Nodes
done	2003
5	2003
4	1189
3	845
2	402
1	188
0	87

prune621.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes88.0ms

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
done	11
1	11
0	6

end0.0ms

sample1.6s

Algorithm

intervals

Results

874.0ms	2859×	body	1280	valid
344.0ms	4076×	body	80	valid
190.0ms	623×	body	640	valid
54.0ms	300×	body	320	valid
47.0ms	142×	body	160	valid