Details

sample43.0ms

Algorithm

intervals

Results

22.0ms	91×	body	1280	valid
7.0ms	130×	body	80	valid
5.0ms	22×	body	640	valid
1.0ms	8×	body	160	valid
1.0ms	5×	body	320	valid

simplify18.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

18.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize22.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (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))

series22.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

19.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify297.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

63.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
48.0ms	(- (+ N 1) N)
48.0ms	(+ 1 (* (+ N 1) N))
27.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))
23.0ms	(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))

prune279.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.9b

localize13.0ms

Local error

Found 1 expressions with local error:

0.9b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

1 → 8

Calls

1 calls:

Slowest

1.0ms

(atan2 1 (+ 1 (* (+ N 1) N)))

series5.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

4.0ms

(atan2 1 (+ 1 (* (+ N 1) N)))

simplify128.0ms

Counts

3 → 11

Calls

3 calls:

Slowest

57.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
39.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
31.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune86.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

localize26.0ms

Local error

Found 2 expressions with local error:

0.9b	(atan2 1 (+ N (+ (* N N) 1)))
0.0b	(+ N (+ (* N N) 1))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
4×	`*-un-lft-identity`
3×	`sum-log`
2×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `distribute-lft-out`

Counts

2 → 23

Calls

2 calls:

Slowest

27.0ms	(+ N (+ (* N N) 1))
0.0ms	(atan2 1 (+ N (+ (* N N) 1)))

series31.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

26.0ms	(+ N (+ (* N N) 1))
4.0ms	(atan2 1 (+ N (+ (* N N) 1)))

simplify911.0ms

Counts

9 → 29

Calls

9 calls:

Slowest

444.0ms	(* (exp N) (* (exp (* N N)) (exp 1)))
180.0ms	(* (exp N) (exp (+ (* N N) 1)))
53.0ms	(+ N (+ (pow N 2) 1))
50.0ms	(+ N (+ (pow N 2) 1))
46.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune212.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize33.0ms

Local error

Found 4 expressions with local error:

14.3b	(sqrt (atan2 1 (+ N (+ (* N N) 1))))
14.3b	(sqrt (atan2 1 (+ N (+ (* N N) 1))))
0.9b	(atan2 1 (+ N (+ (* N N) 1)))
0.9b	(atan2 1 (+ N (+ (* N N) 1)))

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

24.0ms	(sqrt (atan2 1 (+ N (+ (* N N) 1))))
15.0ms	(sqrt (atan2 1 (+ N (+ (* N N) 1))))
4.0ms	(atan2 1 (+ N (+ (* N N) 1)))
4.0ms	(atan2 1 (+ N (+ (* N N) 1)))

simplify908.0ms

Counts

22 → 56

Calls

22 calls:

Slowest

58.0ms	(sqrt (* (cbrt (atan2 1 (+ N (+ (* N N) 1)))) (cbrt (atan2 1 (+ N (+ (* N N) 1))))))
56.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
55.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
55.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
54.0ms	(sqrt (atan2 1 (+ N (+ (* N N) 1))))

prune431.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.9b

regimes47.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.0s	2849×	body	1280	valid
388.0ms	4051×	body	80	valid
160.0ms	632×	body	640	valid
108.0ms	312×	body	320	valid
22.0ms	156×	body	160	valid