Details

sample34.0ms

Algorithm

intervals

Results

16.0ms	97×	body	1280	valid
5.0ms	125×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	6×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize7.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (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:

6.0ms

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

series13.0ms

Counts

1 → 3

Calls

1 calls:

13.0ms

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

simplify70.0ms

Counts: 18 → 18

prune34.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* (+ N 1.0) N))
0.0b	(* (+ N 1.0) N)
0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
4×	`associate-l`
3×	`associate-r`
2×	`flip3-+` `associate-*l/` `flip-+`
1×	`+-commutative` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 39

Calls

3 calls:

7.0ms	(+ 1 (* (+ N 1.0) N))
22.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series75.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ 1 (* (+ N 1.0) N))
50.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify110.0ms

Counts: 48 → 48

prune88.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(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)))))
16.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite19.0ms

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)))
13.0ms	(* (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))))

series43.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
4.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
18.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
18.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify106.0ms

Counts: 94 → 94

prune142.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
1.1b	(pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 5)
16.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `sqrt-prod`
7×	`pow1`
6×	`cbrt-prod`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `pow1/3` `pow-exp` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
5.0ms	(pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 5)
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
201.0ms	(pow (cbrt (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))) 5)
22.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify164.0ms

Counts: 69 → 69

prune172.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.4b

regimes21.0ms

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

sample1.4s

Algorithm

intervals

Results

913.0ms	2867×	body	1280	valid
195.0ms	4065×	body	80	valid
95.0ms	595×	body	640	valid
37.0ms	327×	body	320	valid
12.0ms	146×	body	160	valid