Details

sample57.0ms

Algorithm

intervals

Results

29.0ms	101×	body	1280	valid
8.0ms	121×	body	80	valid
4.0ms	17×	body	640	valid
2.0ms	10×	body	320	valid
1.0ms	7×	body	160	valid

simplify26.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize16.0ms

Local error

Found 1 expressions with local error:

1.8b	(- (atan (+ N 1.0)) (atan N))

rewrite12.0ms

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:

11.0ms

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

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

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

simplify1.1s

Counts: 18 → 18

prune68.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

29.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series94.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* (+ N 1.0) N)
6.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify835.0ms

Counts: 34 → 34

prune113.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

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)))))
16.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite25.0ms

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)))
18.0ms	(* (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))))

series65.0ms

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)))))
23.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
35.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify5.7s

Counts: 94 → 94

prune195.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

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 (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1)))
16.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.9b	(sqrt (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-prod`
29×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `associate-r`
9×	`unpow-prod-down` `sqrt-pow1`
8×	`unswap-sqr`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
5×	`pow1/2` `sqr-pow`
4×	`rem-sqrt-square` `add-log-exp`
3×	`pow-prod-down`
2×	`pow-prod-up`
1×	`sqrt-unprod` `prod-exp` `pow-sqr` `*-commutative` `cbrt-unprod`

Counts

4 → 80

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
22.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1)))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
3.0ms	(sqrt (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1))

series58.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
7.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1)))
31.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
17.0ms	(sqrt (pow (atan2 1.0 (+ 1 (* (+ N 1.0) N))) 1))

simplify1.6s

Counts: 92 → 92

prune182.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.4b

regimes25.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify24.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

548.0ms	4047×	body	80	valid
529.0ms	2816×	body	1280	valid
134.0ms	644×	body	640	valid
77.0ms	326×	body	320	valid
13.0ms	167×	body	160	valid