Details

sample42.0ms

Algorithm

intervals

Results

21.0ms	85×	body	1280	valid
8.0ms	136×	body	80	valid
4.0ms	22×	body	640	valid
2.0ms	10×	body	320	valid
0.0ms	3×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
1.8b	(- (atan (+ N 1)) (atan N))

rewrite7.0ms

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))
5.0ms	(- (atan (+ N 1)) (atan N))

series23.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
20.0ms	(- (atan (+ N 1)) (atan N))

simplify2.4s

Counts

30 → 30

Iterations

Iter	Nodes
6	5474
5	1652
4	618
3	287
2	149
1	75
0	41

prune187.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.1b	(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)
1.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series50.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify1.7s

Counts

36 → 36

Iterations

Iter	Nodes
4	3175
3	832
2	305
1	119
0	55

prune250.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (+ N 1)) (cbrt (+ N 1)))
0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))
0.3b	(cbrt (+ N 1))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 99

Calls

4 calls:

35.0ms	(* (cbrt (+ N 1)) (cbrt (+ N 1)))
3.0ms	(cbrt (+ N 1))
3.0ms	(cbrt (+ N 1))
3.0ms	(cbrt (+ N 1))

series169.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (cbrt (+ N 1)) (cbrt (+ N 1)))
42.0ms	(cbrt (+ N 1))
35.0ms	(cbrt (+ N 1))
45.0ms	(cbrt (+ N 1))

simplify1.2s

Counts

111 → 111

Iterations

Iter	Nodes
4	3034
3	1278
2	610
1	269
0	123

prune855.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

214×	`cbrt-prod`
95×	`add-sqr-sqrt`
85×	`*-un-lft-identity`
74×	`cbrt-div`
41×	`add-cube-cbrt`
36×	`swap-sqr`
30×	`associate-r` `associate-l`
27×	`unswap-sqr`
25×	`pow1`
19×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
12×	`frac-times`
10×	`add-exp-log`
6×	`pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 219

Calls

4 calls:

3.0ms	(cbrt (+ N 1))
29.0ms	(* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1))))
29.0ms	(* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1))))
29.0ms	(* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(cbrt (+ N 1))
41.0ms	(* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1))))
42.0ms	(* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1))))
55.0ms	(* (cbrt (cbrt (+ N 1))) (cbrt (cbrt (+ N 1))))

simplify1.4s

Counts

231 → 231

Iterations

Iter	Nodes
4	2883
3	1332
2	641
1	303
0	151

prune2.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes63.0ms

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
2	9
1	9
0	6

end0.0ms

sample2.0s

Algorithm

intervals

Results

923.0ms	2877×	body	1280	valid
551.0ms	587×	body	640	valid
291.0ms	4059×	body	80	valid
57.0ms	320×	body	320	valid
20.0ms	157×	body	160	valid