Details

sample69.0ms

Algorithm

intervals

Results

39.0ms	85×	body	1280	valid
11.0ms	148×	body	80	valid
4.0ms	14×	body	640	valid
2.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify6.0ms

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: 12.6b

localize12.0ms

Local error

Found 1 expressions with local error:

1.2b	(- (atan (+ N 1)) (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` `insert-posit16` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 16

Calls

1 calls:

6.0ms

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

series15.0ms

Counts

1 → 3

Calls

1 calls:

15.0ms

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

simplify1.7s

Counts

19 → 19

Iterations

Iter	Nodes
done	5000
5	1968
4	692
3	307
2	147
1	73
0	36

prune65.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.5b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite35.0ms

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:

34.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series70.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify3.3s

Counts

36 → 36

Iterations

Iter	Nodes
done	5008
4	2728
3	706
2	266
1	121
0	55

prune155.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (+ 1 N) (* N N))
0.5b	(atan2 1 (+ (+ 1 N) (* N N)))

rewrite31.0ms

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:

30.0ms	(+ (+ 1 N) (* N N))
0.0ms	(atan2 1 (+ (+ 1 N) (* N N)))

series24.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(+ (+ 1 N) (* N N))
3.0ms	(atan2 1 (+ (+ 1 N) (* N N)))

simplify1.9s

Counts

28 → 28

Iterations

Iter	Nodes
done	5003
3	1964
2	380
1	120
0	46

prune86.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.7b	(cbrt N)
0.7b	(cbrt N)
0.7b	(cbrt N)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 77

Calls

4 calls:

15.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
2.0ms	(cbrt N)

series1.0s

Counts

4 → 12

Calls

4 calls:

294.0ms	(* (cbrt N) (cbrt N))
244.0ms	(cbrt N)
256.0ms	(cbrt N)
227.0ms	(cbrt N)

simplify2.8s

Counts

89 → 89

Iterations

Iter	Nodes
done	5002
4	3832
3	1045
2	380
1	138
0	63

prune331.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes44.0ms

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

sample1.8s

Algorithm

intervals

Results

851.0ms	2867×	body	1280	valid
443.0ms	613×	body	640	valid
304.0ms	4022×	body	80	valid
55.0ms	339×	body	320	valid
18.0ms	159×	body	160	valid