Details

sample45.0ms

Algorithm

intervals

Results

23.0ms	95×	body	1280	valid
6.0ms	127×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	6×	body	160	valid

simplify32.0ms

Counts: 1 → 1

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize24.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (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))

series14.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

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

simplify2.3s

Counts: 30 → 30

prune181.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 2 expressions with local error:

0.1b	(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b	(* (+ N 1) N)

rewrite23.0ms

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

22.0ms	(* (+ N 1) N)
0.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

series64.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

60.0ms	(* (+ N 1) N)
4.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))

simplify839.0ms

Counts: 36 → 36

prune327.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

16.1b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.1b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.6b	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
0.1b	(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite12.0ms

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

8.0ms	(* (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)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

15.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
6.0ms	(atan2 1 (+ 1 (* (+ N 1) N)))
3.0ms	(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))

simplify2.8s

Counts: 98 → 98

prune742.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

16.1b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.1b	(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
16.1b	(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)))))))

rewrite45.0ms

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)))))))
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))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

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

simplify3.6s

Counts: 101 → 101

prune863.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s	2820×	body	1280	valid
274.0ms	4113×	body	80	valid
137.0ms	589×	body	640	valid
55.0ms	313×	body	320	valid
21.0ms	165×	body	160	valid