Details

sample70.0ms

Algorithm

intervals

Results

36.0ms	92×	body	1280	valid
11.0ms	126×	body	80	valid
7.0ms	22×	body	640	valid
2.0ms	8×	body	320	valid
1.0ms	8×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	12
2	12
1	11
0	6

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1))
2.3b	(- (atan (+ N 1)) (atan N))

rewrite15.0ms

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))
12.0ms	(- (atan (+ N 1)) (atan N))

series24.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
21.0ms	(- (atan (+ N 1)) (atan N))

simplify1.8s

Counts

30 → 30

Iterations

Iter	Nodes
done	5000
5	2018
4	719
3	313
2	151
1	77
0	41

prune126.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1) N)
0.3b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite38.0ms

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:

36.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series73.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.6s

Counts

36 → 36

Iterations

Iter	Nodes
done	5008
4	2728
3	706
2	266
1	121
0	55

prune116.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1))
0.3b	(atan2 1 (+ 1 (* N (+ N 1))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 34

Calls

2 calls:

22.0ms	(* N (+ N 1))
0.0ms	(atan2 1 (+ 1 (* N (+ N 1))))

series56.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(* N (+ N 1))
4.0ms	(atan2 1 (+ 1 (* N (+ N 1))))

simplify1.5s

Counts

40 → 40

Iterations

Iter	Nodes
done	5733
3	2512
2	504
1	149
0	56

prune102.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 163

Calls

4 calls:

109.0ms	(* (cbrt (* N (+ N 1))) (cbrt (* N (+ N 1))))
20.0ms	(cbrt (* N (+ N 1)))
16.0ms	(cbrt (* N (+ N 1)))
18.0ms	(cbrt (* N (+ N 1)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cbrt (* N (+ N 1))) (cbrt (* N (+ N 1))))
48.0ms	(cbrt (* N (+ N 1)))
51.0ms	(cbrt (* N (+ N 1)))
52.0ms	(cbrt (* N (+ N 1)))

simplify2.0s

Counts

175 → 175

Iterations

Iter	Nodes
done	5000
3	4005
2	1284
1	464
0	196

prune587.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes29.0ms

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
done	11
1	11
0	6

end0.0ms

sample1.5s

Algorithm

intervals

Results

976.0ms	2732×	body	1280	valid
246.0ms	4134×	body	80	valid
114.0ms	648×	body	640	valid
42.0ms	318×	body	320	valid
16.0ms	168×	body	160	valid