Details

sample76.0ms

Algorithm

intervals

Results

43.0ms	95×	body	1280	valid
10.0ms	125×	body	80	valid
7.0ms	19×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	6×	body	160	valid

simplify21.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

21.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize11.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (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`

Counts

2 → 24

Calls

2 calls:

Slowest

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

series15.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

13.0ms	(- (atan (+ N 1)) (atan N))
1.0ms	(atan (+ N 1))

simplify191.0ms

Counts

12 → 30

Calls

12 calls:

Slowest

33.0ms	(/ (exp (atan (+ N 1))) (exp (atan N)))
26.0ms	(- (+ N 1) N)
20.0ms	(- (atan (+ N 1)) (atan N))
20.0ms	(- (atan (+ N 1)) (atan N))
17.0ms	(- (atan (+ N 1)) (atan N))

prune177.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

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

15.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series76.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

74.0ms	(* (+ N 1) N)
2.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify728.0ms

Counts

17 → 36

Calls

17 calls:

Slowest

297.0ms	(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
97.0ms	(* (+ (pow N 3) (pow 1 3)) N)
88.0ms	(* (- (* N N) (* 1 1)) N)
51.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
36.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune319.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize36.0ms

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)))

rewrite24.0ms

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

17.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
3.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
2.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series43.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

21.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
13.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
4.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.3s

Counts

82 → 98

Calls

82 calls:

Slowest

130.0ms	(* (* (* (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))))))
126.0ms	(* (* (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)))))))
60.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))
55.0ms	(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
54.0ms	(atan2 1 (+ N (+ (pow N 2) 1)))

prune895.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.4b

localize37.0ms

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

Slowest

40.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))))
2.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
2.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
2.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

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

simplify3.1s

Counts

87 → 101

Calls

87 calls:

Slowest

386.0ms	(* (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (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 (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))))
355.0ms	(* (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (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 (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))))
85.0ms	(* (atan2 1 (+ 1 (* (+ N 1) N))) (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))
72.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (* (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))))
66.0ms	(* (atan2 1 (+ 1 (* (+ N 1) N))) (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))

prune778.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.4b

regimes69.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s	2860×	body	1280	valid
278.0ms	4053×	body	80	valid
111.0ms	617×	body	640	valid
41.0ms	303×	body	320	valid
16.0ms	167×	body	160	valid