Details

sample71.0ms

Algorithm

intervals

Results

34.0ms	93×	body	1280	valid
17.0ms	126×	body	80	valid
6.0ms	21×	body	640	valid
3.0ms	12×	body	320	valid
1.0ms	4×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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))

series22.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(atan (+ N 1))
19.0ms	(- (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

prune248.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

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:

26.0ms	(* (+ N 1) N)
1.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series46.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (+ N 1) N)
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.0s

Counts

36 → 36

Iterations

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

prune305.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.6b	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
15.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`pow-prod-up`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 86

Calls

4 calls:

0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
11.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (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))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
5.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
28.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
24.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify2.2s

Counts

98 → 98

Iterations

Iter	Nodes
5	3261
4	872
3	416
2	237
1	123
0	65

prune711.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
15.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.6b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

60×	`sqrt-pow1`
51×	`pow1`
36×	`pow1/2`
34×	`pow-prod-up`
16×	`add-sqr-sqrt`
14×	`sqrt-prod`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
8×	`pow-sqr`
7×	`pow-prod-down`
6×	`pow-plus` `associate-r`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `prod-exp` `cbrt-unprod`
2×	`sqrt-unprod` `swap-sqr` `unswap-sqr`
1×	`associate-l` `*-commutative`

Counts

4 → 95

Calls

4 calls:

37.0ms	(* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (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))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

series57.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
16.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
23.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

simplify1.6s

Counts

107 → 107

Iterations

Iter	Nodes
5	2000
4	1354
3	851
2	427
1	183
0	87

prune791.0ms

Pruning

8 alts after pruning (4 fresh and 4 done)

Merged error: 0.1b

regimes78.0ms

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

sample1.5s

Algorithm

intervals

Results

914.0ms	2859×	body	1280	valid
259.0ms	4083×	body	80	valid
129.0ms	609×	body	640	valid
50.0ms	299×	body	320	valid
17.0ms	150×	body	160	valid