Details

sample37.0ms

Algorithm

intervals

Results

20.0ms	98×	body	1280	valid
6.0ms	125×	body	80	valid
3.0ms	19×	body	640	valid
1.0ms	9×	body	320	valid
0.0ms	5×	body	160	valid

simplify5.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
1.1b	(- (atan (+ N 1)) (atan N))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

1.0ms	(atan (+ N 1))
8.0ms	(- (atan (+ N 1)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
12.0ms	(- (atan (+ N 1)) (atan N))

simplify991.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	2000
5	2000
4	719
3	313
2	151
1	77
0	41

prune254.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.7b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite20.0ms

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:

19.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series84.0ms

Counts

2 → 6

Calls

2 calls:

75.0ms	(* (+ N 1) N)
9.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.1s

Counts

36 → 36

Iterations

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

prune290.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))
0.7b	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`

Counts

4 → 53

Calls

4 calls:

6.0ms	(cbrt (+ N 1))
3.0ms	(cbrt (+ N 1))
3.0ms	(cbrt (+ N 1))
0.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(cbrt (+ N 1))
37.0ms	(cbrt (+ N 1))
47.0ms	(cbrt (+ N 1))
3.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt (+ N 1)) N))))

simplify925.0ms

Counts

65 → 65

Iterations

Iter	Nodes
done	2000
4	2000
3	747
2	346
1	167
0	80

prune644.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1))
0.3b	(cbrt (- N 1))
0.7b	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (/ (cbrt (- (* N N) 1)) (cbrt (- N 1))) N))))
15.0b	(cbrt (- (* N N) 1))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

17×	`cbrt-prod`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp` `difference-of-squares`
3×	`pow1/3`
2×	`flip3--` `difference-of-sqr-1` `flip--`
1×	`flip3-+` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 58

Calls

4 calls:

5.0ms	(cbrt (+ N 1))
11.0ms	(cbrt (- N 1))
0.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (/ (cbrt (- (* N N) 1)) (cbrt (- N 1))) N))))
10.0ms	(cbrt (- (* N N) 1))

series263.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(cbrt (+ N 1))
64.0ms	(cbrt (- N 1))
11.0ms	(atan2 1 (+ 1 (* (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (/ (cbrt (- (* N N) 1)) (cbrt (- N 1))) N))))
137.0ms	(cbrt (- (* N N) 1))

simplify1.2s

Counts

70 → 70

Iterations

Iter	Nodes
done	2001
3	2001
2	1172
1	434
0	192

prune1.0s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

regimes61.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	11
1	11
0	6

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s	2854×	body	1280	valid
374.0ms	3996×	body	80	valid
220.0ms	654×	body	640	valid
70.0ms	338×	body	320	valid
51.0ms	158×	body	160	valid