Details

sample71.0ms

Algorithm

intervals

Results

40.0ms	104×	body	1280	valid
10.0ms	116×	body	80	valid
6.0ms	17×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	8×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	12
2	12
1	11
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize30.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
2.2b	(- (atan (+ N 1)) (atan N))

rewrite12.0ms

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:

2.0ms	(atan (+ N 1))
9.0ms	(- (atan (+ N 1)) (atan N))

series25.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
22.0ms	(- (atan (+ N 1)) (atan N))

simplify2.1s

Counts

30 → 30

Iterations

Iter	Nodes
6	5332
5	1658
4	628
3	288
2	151
1	77
0	41

prune181.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* (+ N 1) N))
0.0b	(* (+ N 1) N)
0.6b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`associate-l`
3×	`associate-r` `insert-posit16`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`+-commutative` `sum-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 42

Calls

3 calls:

12.0ms	(+ 1 (* (+ N 1) N))
15.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series69.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(+ 1 (* (+ N 1) N))
49.0ms	(* (+ N 1) N)
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify5.3s

Counts

51 → 51

Iterations

Iter	Nodes
4	8220
3	1536
2	476
1	176
0	72

prune267.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.6b	(atan2 1 (+ 1 (* (+ N 1) N)))
17.5b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
17.5b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 44

Calls

4 calls:

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

series33.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify2.4s

Counts

56 → 56

Iterations

Iter	Nodes
8	5941
7	1332
6	544
5	246
4	152
3	106
2	76
1	52
0	32

prune357.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1 (+ 1 (* (+ N 1) N)))
17.5b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
17.5b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
17.5b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 50

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify2.3s

Counts

62 → 62

Iterations

Iter	Nodes
8	5941
7	1332
6	544
5	246
4	152
3	106
2	76
1	52
0	32

prune458.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.5b

regimes54.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
2	11
1	11
0	6

end0.0ms

sample1.4s

Algorithm

intervals

Results

936.0ms	2856×	body	1280	valid
235.0ms	4043×	body	80	valid
103.0ms	617×	body	640	valid
40.0ms	310×	body	320	valid
16.0ms	174×	body	160	valid