Details

sample58.0ms

Algorithm

intervals

Results

27.0ms	89×	body	1280	valid
9.0ms	130×	body	80	valid
5.0ms	22×	body	640	valid
2.0ms	9×	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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize29.0ms

Local error

Found 1 expressions with local error:

1.5b	(- (atan (+ N 1.0)) (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` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 15

Calls

1 calls:

8.0ms

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

series22.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify1.6s

Counts

18 → 18

Iterations

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

prune63.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ 1.0 N))
0.3b	(atan2 1.0 (+ (* N (+ 1.0 N)) 1))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `add-cube-cbrt`
3×	`associate-l`
2×	`associate-*r/` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

19.0ms	(* N (+ 1.0 N))
0.0ms	(atan2 1.0 (+ (* N (+ 1.0 N)) 1))

series66.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(* N (+ 1.0 N))
4.0ms	(atan2 1.0 (+ (* N (+ 1.0 N)) 1))

simplify414.0ms

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
2	758
1	156
0	56

prune152.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* N (+ N 1.0))) (cbrt (* N (+ N 1.0))))
14.6b	(cbrt (* N (+ N 1.0)))
14.6b	(cbrt (* N (+ N 1.0)))
14.6b	(cbrt (* N (+ N 1.0)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/`
18×	`cbrt-div`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`flip3-+` `pow1/3` `flip-+`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `swap-sqr` `associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

15.0ms	(* (cbrt (* N (+ N 1.0))) (cbrt (* N (+ N 1.0))))
6.0ms	(cbrt (* N (+ N 1.0)))
5.0ms	(cbrt (* N (+ N 1.0)))
9.0ms	(cbrt (* N (+ N 1.0)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(* (cbrt (* N (+ N 1.0))) (cbrt (* N (+ N 1.0))))
131.0ms	(cbrt (* N (+ N 1.0)))
157.0ms	(cbrt (* N (+ N 1.0)))
134.0ms	(cbrt (* N (+ N 1.0)))

simplify589.0ms

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1635
1	388
0	152

prune417.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* N (+ N 1.0))) (* (cbrt N) (cbrt (+ 1.0 N))))
0.5b	(cbrt N)
14.6b	(cbrt (* N (+ N 1.0)))
14.6b	(cbrt (* N (+ N 1.0)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-*r/`
16×	`cbrt-div`
9×	`pow1` `add-exp-log`
8×	`flip3-+` `flip-+`
6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `pow1/3` `add-cube-cbrt`
5×	`add-cbrt-cube` `pow-prod-down`
4×	`frac-times` `associate-l` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
2×	`associate-*l/`
1×	`associate-r` `*-commutative`

Counts

4 → 61

Calls

4 calls:

37.0ms	(* (cbrt (* N (+ N 1.0))) (* (cbrt N) (cbrt (+ 1.0 N))))
1.0ms	(cbrt N)
5.0ms	(cbrt (* N (+ N 1.0)))
6.0ms	(cbrt (* N (+ N 1.0)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (cbrt (* N (+ N 1.0))) (* (cbrt N) (cbrt (+ 1.0 N))))
200.0ms	(cbrt N)
105.0ms	(cbrt (* N (+ N 1.0)))
107.0ms	(cbrt (* N (+ N 1.0)))

simplify613.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1802
1	457
0	180

prune386.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes93.0ms

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

sample1.3s

Algorithm

intervals

Results

858.0ms	2873×	body	1280	valid
160.0ms	4029×	body	80	valid
101.0ms	344×	body	320	valid
80.0ms	589×	body	640	valid
13.0ms	165×	body	160	valid