Details

sample42.0ms

Algorithm

intervals

Results

25.0ms	108×	body	1280	valid
4.0ms	116×	body	80	valid
3.0ms	24×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	4×	body	160	valid

simplify14.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize7.0ms

Local error

Found 1 expressions with local error:

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

rewrite7.0ms

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))

series16.0ms

Counts

1 → 3

Calls

1 calls:

16.0ms

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

simplify950.0ms

Counts: 18 → 18

prune46.0ms

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)))

rewrite23.0ms

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:

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

series56.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(* (+ N 1.0) N)
4.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify564.0ms

Counts: 34 → 34

prune59.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.4b	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod` `*-un-lft-identity`
22×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
9×	`swap-sqr`
8×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 88

Calls

4 calls:

4.0ms	(cbrt (+ N 1.0))
4.0ms	(cbrt (+ N 1.0))
42.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

series297.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ N 1.0))
93.0ms	(cbrt (+ N 1.0))
108.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
4.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))) (* (cbrt (+ N 1.0)) N))))

simplify1.7s

Counts: 100 → 100

prune260.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.4b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.5b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
19.0b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
19.0b	(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))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(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)))))
27.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
23.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify4.6s

Counts: 94 → 94

prune141.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes17.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify24.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

598.0ms	2872×	body	1280	valid
453.0ms	625×	body	640	valid
197.0ms	4058×	body	80	valid
34.0ms	290×	body	320	valid
13.0ms	155×	body	160	valid