Details

sample43.0ms

Algorithm

intervals

Results

22.0ms	95×	body	1280	valid
6.0ms	125×	body	80	valid
4.0ms	19×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	6×	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: 15.8b

localize21.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (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

21.0ms	(- (atan (+ N 1)) (atan N))
2.0ms	(atan (+ N 1))

simplify199.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

38.0ms	(- (+ N 1) N)
34.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
21.0ms	(- (sqrt (atan (+ N 1))) (sqrt (atan N)))
15.0ms	(+ 1 (* (+ N 1) N))
14.0ms	(- (atan (+ N 1)) (atan N))

prune254.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite28.0ms

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

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

series77.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

69.0ms	(* (+ N 1) N)
8.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify814.0ms

Counts

17 → 36

Calls

17 calls:

Slowest

332.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
130.0ms	(* (+ (pow N 3) (pow 1 3)) N)
76.0ms	(* (- (* N N) (* 1 1)) N)
53.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
50.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune286.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 4 expressions with local error:

15.4b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.4b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.6b	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
0.4b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite14.0ms

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:

Slowest

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

series32.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
3.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.2s

Counts

82 → 98

Calls

82 calls:

Slowest

201.0ms	(* (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))
121.0ms	(* (* (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (* (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))))
59.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
57.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
55.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))

prune694.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

15.4b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.4b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
15.4b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
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)))))

rewrite55.0ms

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:

Slowest

51.0ms	(* (* (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))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

20.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
17.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
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)))))

simplify3.1s

Counts

94 → 107

Calls

94 calls:

Slowest

326.0ms	(* (* (* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))) (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))) (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))
301.0ms	(* (* (* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))) (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))
118.0ms	(* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
116.0ms	(* (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
111.0ms	(* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (atan2 1 (+ 1 (* (+ N 1) N))))

prune843.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.4b

regimes70.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

695.0ms	2860×	body	1280	valid
499.0ms	4053×	body	80	valid
135.0ms	617×	body	640	valid
47.0ms	167×	body	160	valid
41.0ms	303×	body	320	valid