Details

sample34.0ms

Algorithm

intervals

Results

16.0ms	95×	body	1280	valid
5.0ms	132×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	9×	body	320	valid

simplify25.0ms

Counts: 1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.1b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
6.0ms	(- (atan (+ N 1.0)) (atan N))

series14.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(atan (+ N 1.0))
13.0ms	(- (atan (+ N 1.0)) (atan N))

simplify1.2s

Counts: 28 → 28

prune75.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.5b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite22.0ms

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:

21.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series52.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify683.0ms

Counts: 34 → 34

prune65.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(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))))

rewrite18.0ms

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))))

series49.0ms

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

simplify4.5s

Counts: 94 → 94

prune151.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ N 1.0))
0.0b	(* (sqrt (+ N 1.0)) N)
0.1b	(* (sqrt (+ N 1.0)) (* (sqrt (+ N 1.0)) N))
0.2b	(atan2 1.0 (+ 1 (* (sqrt (+ N 1.0)) (* (sqrt (+ N 1.0)) N))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity` `sqrt-div`
15×	`add-sqr-sqrt`
14×	`associate-l`
13×	`sqrt-prod`
12×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `associate-*l/`
8×	`flip3-+` `flip-+`
4×	`frac-times` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`distribute-lft-out`
2×	`associate-r/` `-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 78

Calls

4 calls:

7.0ms	(sqrt (+ N 1.0))
25.0ms	(* (sqrt (+ N 1.0)) N)
58.0ms	(* (sqrt (+ N 1.0)) (* (sqrt (+ N 1.0)) N))
0.0ms	(atan2 1.0 (+ 1 (* (sqrt (+ N 1.0)) (* (sqrt (+ N 1.0)) N))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (+ N 1.0))
76.0ms	(* (sqrt (+ N 1.0)) N)
46.0ms	(* (sqrt (+ N 1.0)) (* (sqrt (+ N 1.0)) N))
4.0ms	(atan2 1.0 (+ 1 (* (sqrt (+ N 1.0)) (* (sqrt (+ N 1.0)) N))))

simplify1.4s

Counts: 90 → 90

prune187.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0.4b

regimes37.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify25.0ms

end0.0ms

sample1.1s

Algorithm

intervals

Results

557.0ms	2892×	body	1280	valid
290.0ms	4054×	body	80	valid
82.0ms	592×	body	640	valid
33.0ms	309×	body	320	valid
14.0ms	153×	body	160	valid