Details

sample70.0ms

Algorithm

intervals

Results

45.0ms	97×	body	1280	valid
10.0ms	134×	body	80	valid
4.0ms	15×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
0.9b	(- (atan (+ N 1)) (atan N))

rewrite10.0ms

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))
8.0ms	(- (atan (+ N 1)) (atan N))

series23.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1))
21.0ms	(- (atan (+ N 1)) (atan N))

simplify2.5s

Counts

30 → 30

Iterations

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

prune264.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

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:

5.0ms	(+ 1 (* (+ N 1) N))
14.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series87.0ms

Counts

3 → 9

Calls

3 calls:

16.0ms	(+ 1 (* (+ N 1) N))
68.0ms	(* (+ N 1) N)
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify6.9s

Counts

51 → 51

Iterations

Iter	Nodes
4	8175
3	1538
2	477
1	174
0	72

prune343.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
17.0b	(cbrt (* (+ N 1) N))
17.0b	(cbrt (* (+ N 1) N))
17.0b	(cbrt (* (+ N 1) N))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*l/`
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` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `associate-*r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

24.0ms	(* (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))

series240.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
57.0ms	(cbrt (* (+ N 1) N))
63.0ms	(cbrt (* (+ N 1) N))
51.0ms	(cbrt (* (+ N 1) N))

simplify1.1s

Counts

88 → 88

Iterations

Iter	Nodes
3	2145
2	916
1	325
0	138

prune658.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
0.6b	(cbrt N)
17.0b	(cbrt (* (+ N 1) N))
17.0b	(cbrt (* (+ N 1) N))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

21.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
1.0ms	(cbrt N)
5.0ms	(cbrt (* (+ N 1) N))
5.0ms	(cbrt (* (+ N 1) N))

series365.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (cbrt (* (+ N 1) N)) (cbrt (* (+ N 1) N)))
200.0ms	(cbrt N)
55.0ms	(cbrt (* (+ N 1) N))
50.0ms	(cbrt (* (+ N 1) N))

simplify768.0ms

Counts

88 → 88

Iterations

Iter	Nodes
3	2222
2	958
1	352
0	154

prune754.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes35.0ms

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	9
1	9
0	6

end0.0ms

sample1.3s

Algorithm

intervals

Results

743.0ms	2905×	body	1280	valid
269.0ms	4085×	body	80	valid
99.0ms	577×	body	640	valid
41.0ms	298×	body	320	valid
13.0ms	135×	body	160	valid