Details

sample50.0ms

Algorithm

intervals

Results

30.0ms	87×	body	1280	valid
8.0ms	137×	body	80	valid
2.0ms	12×	body	640	valid
2.0ms	14×	body	320	valid
1.0ms	6×	body	160	valid

simplify4.0ms

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: 13.9b

localize11.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (atan (+ N 1)) (atan N))

rewrite9.0ms

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:

9.0ms

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

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

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

simplify2.0s

Counts

19 → 19

Iterations

Iter	Nodes
done	5002
5	2767
4	896
3	342
2	148
1	73
0	36

prune77.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

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:

30.0ms	(* (+ N 1) N)
1.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series85.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify3.4s

Counts

36 → 36

Iterations

Iter	Nodes
done	5005
4	4011
3	930
2	299
1	121
0	55

prune132.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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)))
9.0ms	(* (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))))

series36.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
3.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
15.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify3.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5063
5	3816
4	1087
3	515
2	252
1	128
0	65

prune292.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 1 expressions with local error:

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

series5.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

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

simplify2.4s

Counts

11 → 11

Iterations

Iter	Nodes
done	5043
9	4358
8	1736
7	958
6	527
5	298
4	126
3	80
2	55
1	34
0	19

prune29.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes49.0ms

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	10
1	10
0	6

end0.0ms

sample1.9s

Algorithm

intervals

Results

1.2s	2934×	body	1280	valid
233.0ms	4006×	body	80	valid
192.0ms	596×	body	640	valid
95.0ms	293×	body	320	valid
21.0ms	171×	body	160	valid