Details

sample38.0ms

Algorithm

intervals

Results

17.0ms	89×	body	1280	valid
5.0ms	130×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	6×	body	160	valid

simplify7.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	292
1	9	292
2	10	292
done	10	292

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize9.0ms

Local error

Found 1 expressions with local error:

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

Counts

1 → 15

Calls

1 calls:

5.0ms

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

series24.0ms

Counts

1 → 3

Calls

1 calls:

24.0ms

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

simplify2.9s

Counts

18 → 18

Iterations

Useful iterations: 4 (257.0ms)

Iter	Nodes	Cost
0	36	7214
1	73	6843
2	149	6843
3	326	6803
4	966	6762
5	3570	6762
done	5001	6762

prune72.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.3b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) 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/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

33.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series65.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* (+ N 1.0) N)
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify801.0ms

Counts

34 → 34

Iterations

Useful iterations: done (797.0ms)

Iter	Nodes	Cost
0	55	8106
1	127	6708
2	695	6468
done	5002	6388

prune146.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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` `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 → 73

Calls

4 calls:

21.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series1.1s

Counts

4 → 12

Calls

4 calls:

340.0ms	(* (cbrt N) (cbrt N))
291.0ms	(cbrt N)
274.0ms	(cbrt N)
231.0ms	(cbrt N)

simplify1.4s

Counts

85 → 85

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	61	17134
1	138	14621
2	727	14346
done	5000	13666

prune322.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
0.3b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
0.5b	(cbrt N)
28.8b	(cbrt (* N N))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 50

Calls

4 calls:

47.0ms	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
0.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
1.0ms	(cbrt N)
6.0ms	(cbrt (* N N))

series581.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))
8.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (* N N))) (cbrt N))))
236.0ms	(cbrt N)
256.0ms	(cbrt (* N N))

simplify924.0ms

Counts

62 → 62

Iterations

Useful iterations: done (920.0ms)

Iter	Nodes	Cost
0	102	20058
1	252	17926
2	1237	17567
done	5001	17087

prune287.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.2b

regimes123.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	263
1	12	263
done	12	263

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	2873×	body	1280	valid
214.0ms	4029×	body	80	valid
131.0ms	589×	body	640	valid
89.0ms	344×	body	320	valid
15.0ms	165×	body	160	valid