Details

sample32.0ms

Algorithm

intervals

Results

15.0ms	91×	body	1280	valid
4.0ms	124×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	5×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.8b

localize6.0ms

Local error

Found 1 expressions with local error:

1.2b	(- (atan (+ N 1.0)) (atan N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `diff-atan` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 15

Calls

1 calls:

5.0ms

(- (atan (+ N 1.0)) (atan N))

series23.0ms

Counts

1 → 3

Calls

1 calls:

23.0ms

(- (atan (+ N 1.0)) (atan N))

simplify69.0ms

Counts: 18 → 18

prune33.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize7.0ms

Local error

Found 1 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 7

Calls

1 calls:

0.0ms

(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify300.0ms

Counts: 10 → 10

prune27.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize9.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 40

Calls

4 calls:

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

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify66.0ms

Counts: 52 → 52

prune107.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 46

Calls

4 calls:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify67.0ms

Counts: 58 → 58

prune129.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

regimes29.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Algorithm

intervals

Results

548.0ms	2857×	body	1280	valid
357.0ms	645×	body	640	valid
202.0ms	4009×	body	80	valid
32.0ms	321×	body	320	valid
13.0ms	168×	body	160	valid