Details

sample53.0ms

Algorithm

intervals

Results

24.0ms	87×	body	1280	valid
9.0ms	135×	body	80	valid
4.0ms	20×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	6×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize15.0ms

Local error

Found 1 expressions with local error:

1.4b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

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:

7.0ms

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

series14.0ms

Counts

1 → 3

Calls

1 calls:

14.0ms

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

simplify57.0ms

Counts: 18 → 18

prune48.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b	(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)))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify197.0ms

Counts: 10 → 10

prune30.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
15.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
25.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (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))))

series44.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
7.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (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))))

simplify55.0ms

Counts: 94 → 94

prune201.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
15.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.5b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.5b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `sqrt-prod`
6×	`add-exp-log` `cbrt-prod` `associate-r` `add-cbrt-cube`
4×	`add-log-exp`
3×	`associate-l`
2×	`pow1/3` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 57

Calls

4 calls:

11.0ms	(* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (fabs (cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
16.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
160.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
156.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify68.0ms

Counts: 69 → 69

prune178.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.2s

Algorithm

intervals

Results

579.0ms	2828×	body	1280	valid
282.0ms	4027×	body	80	valid
87.0ms	618×	body	640	valid
36.0ms	340×	body	320	valid
15.0ms	187×	body	160	valid