Details

sample59.0ms

Algorithm

intervals

Results

35.0ms	112×	body	1280	valid
8.0ms	112×	body	80	valid
5.0ms	17×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	8×	body	160	valid

simplify4.0ms

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

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
1.6b	(- (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:

2.0ms	(atan (+ N 1))
7.0ms	(- (atan (+ N 1)) (atan N))

series20.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
17.0ms	(- (atan (+ N 1)) (atan N))

simplify2.4s

Counts

30 → 30

Iterations

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

prune218.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

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)))

rewrite33.0ms

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:

6.0ms	(+ 1 (* (+ N 1) N))
26.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series76.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+ 1 (* (+ N 1) N))
58.0ms	(* (+ N 1) N)
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify5.5s

Counts

51 → 51

Iterations

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

prune290.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (cbrt (* (+ N 1) N)))))
19.0b	(cbrt (* (+ N 1) N))
19.0b	(cbrt (* (+ N 1) N))
19.0b	(cbrt (* (+ N 1) N))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 44

Calls

4 calls:

0.0ms	(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (cbrt (* (+ N 1) N)))))
5.0ms	(cbrt (* (+ N 1) N))
5.0ms	(cbrt (* (+ N 1) N))
5.0ms	(cbrt (* (+ N 1) N))

series162.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1 (+ 1 (* (* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N))) (cbrt (* (+ N 1) N)))))
53.0ms	(cbrt (* (+ N 1) N))
48.0ms	(cbrt (* (+ N 1) N))
56.0ms	(cbrt (* (+ N 1) N))

simplify1.0s

Counts

56 → 56

Iterations

Iter	Nodes
4	2756
3	982
2	424
1	183
0	86

prune406.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

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

series579.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1 (+ 1 (* (* (+ N 1) (* (cbrt N) (cbrt N))) (cbrt N))))
191.0ms	(cbrt N)
191.0ms	(cbrt N)
192.0ms	(cbrt N)

simplify1.3s

Counts

56 → 56

Iterations

Iter	Nodes
5	3479
4	987
3	383
2	157
1	79
0	43

prune360.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.5b

regimes55.0ms

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	11
1	11
0	6

end0.0ms

sample1.2s

Algorithm

intervals

Results

729.0ms	2910×	body	1280	valid
208.0ms	4042×	body	80	valid
130.0ms	609×	body	640	valid
37.0ms	292×	body	320	valid
13.0ms	147×	body	160	valid