Details

sample40.0ms

Algorithm

intervals

Results

21.0ms	105×	body	1280	valid
5.0ms	120×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	2×	body	160	valid

simplify20.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

20.0ms

(- (atan (+ N 1)) (atan N))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize37.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

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:

Slowest

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

series25.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

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

simplify198.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

34.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
19.0ms	(- (atan (+ N 1)) (atan N))
19.0ms	(- (atan (+ N 1)) (atan N))
19.0ms	(- (atan (+ N 1)) (atan N))
18.0ms	(- (atan (+ N 1)) (atan N))

prune209.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 2 expressions with local error:

0.7b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite14.0ms

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:

Slowest

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

series65.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

62.0ms	(* (+ N 1) N)
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify771.0ms

Counts

17 → 36

Calls

17 calls:

Slowest

347.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
80.0ms	(* (+ (pow N 3) (pow 1 3)) N)
62.0ms	(* (- (* N N) (* 1 1)) N)
55.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
54.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune289.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

18.2b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
18.2b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.7b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.7b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite3.0ms

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:

Slowest

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

23.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify741.0ms

Counts

22 → 56

Calls

22 calls:

Slowest

59.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
57.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
57.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
54.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
50.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))

prune519.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

localize45.0ms

Local error

Found 4 expressions with local error:

18.2b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
18.2b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
18.2b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.7b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite6.0ms

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:

Slowest

3.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
2.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
1.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

19.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify921.0ms

Counts

27 → 62

Calls

27 calls:

Slowest

61.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
59.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
58.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
57.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
57.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))

prune798.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.6b

regimes53.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.4s	2827×	body	1280	valid
298.0ms	4033×	body	80	valid
147.0ms	629×	body	640	valid
64.0ms	351×	body	320	valid
20.0ms	160×	body	160	valid