Details

sample44.0ms

Algorithm

intervals

Results

25.0ms	94×	body	1280	valid
7.0ms	134×	body	80	valid
4.0ms	16×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

Calls

1 calls:

Slowest

11.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.5b	(- (atan (+ N 1)) (atan N))
0.0b	(atan (+ N 1))

rewrite6.0ms

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`

Calls

2 calls:

Slowest

4.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

series27.0ms

Calls

2 calls:

Slowest

25.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

simplify207.0ms

Calls

12 calls:

Slowest

36.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
26.0ms	(+ (sqrt (atan (+ N 1))) (sqrt (atan N)))
24.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))
21.0ms	(- (+ N 1) N)
20.0ms	(- (atan (+ N 1)) (atan N))

prune258.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

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`

Calls

2 calls:

Slowest

17.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series57.0ms

Calls

2 calls:

Slowest

54.0ms	(* (+ N 1) N)
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify776.0ms

Calls

17 calls:

Slowest

357.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
116.0ms	(* (+ (pow N 3) (pow 1 3)) N)
60.0ms	(* (- (* N N) (* 1 1)) N)
42.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
33.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune322.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize36.0ms

Local error

Found 4 expressions with local error:

15.8b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.8b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.7b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.7b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite5.0ms

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`

Calls

4 calls:

Slowest

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

series57.0ms

Calls

4 calls:

Slowest

26.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
24.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
3.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify844.0ms

Calls

22 calls:

Slowest

59.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
58.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
56.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
56.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
54.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune559.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize44.0ms

Local error

Found 4 expressions with local error:

15.8b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.8b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.8b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.7b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite3.0ms

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`

Calls

4 calls:

Slowest

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

series51.0ms

Calls

4 calls:

Slowest

18.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify884.0ms

Calls

27 calls:

Slowest

56.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
55.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
55.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
53.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
51.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune804.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.6b

regimes39.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 0.4b

bsearch2.0ms

end0.0ms

sample1.9s

Algorithm

intervals

Results

878.0ms	2826×	body	1280	valid
528.0ms	612×	body	640	valid
278.0ms	4057×	body	80	valid
96.0ms	321×	body	320	valid
22.0ms	184×	body	160	valid