Details

sample524.0ms

Algorithm

intervals

Results

235.0ms	256×	body	80	valid
61.0ms	58×	body	10240	exit
40.0ms	327×	body	80	nan

simplify736.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.0b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

21.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sqrt (atan2 b b))

series191.0ms

Counts

3 → 9

Calls

3 calls:

92.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
41.0ms	(pow (sqrt (atan2 b b)) (- b a))
58.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts: 57 → 57

prune229.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`pow1/2` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

17.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
65.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series158.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
60.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
26.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify821.0ms

Counts: 174 → 174

prune744.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (* (pow 1 (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
9×	`unpow-prod-down`
8×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow-pow` `sqrt-pow1`
4×	`unpow-prod-up` `add-exp-log`
3×	`pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 50

Calls

3 calls:

38.0ms	(sin (* (pow 1 (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
12.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
2.0ms	(sqrt (atan2 b b))

series8.6m

Counts

3 → 9

Calls

3 calls:

8.6m	(sin (* (pow 1 (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
64.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
21.0ms	(sqrt (atan2 b b))

simplify983.0ms

Counts: 59 → 59

prune185.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
6.0ms	(sqrt (atan2 b b))

series45.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts: 64 → 64

prune289.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify719.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.8s	1777×	body	10240	exit
802.0ms	9788×	body	80	nan
724.0ms	7988×	body	80	valid
12.0ms	4×	body	5120	valid
4.0ms	1×	body	2560	valid
1.0ms	5×	body	160	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid

Details

sample524.0ms

simplify736.0ms

prune8.0ms

localize30.0ms

rewrite49.0ms

series191.0ms

simplify2.2s

prune229.0ms

localize15.0ms

rewrite100.0ms

series158.0ms

simplify821.0ms

prune744.0ms

localize23.0ms

rewrite55.0ms

series8.6m

simplify983.0ms

prune185.0ms

localize22.0ms

rewrite11.0ms

series45.0ms

simplify1.5s

prune289.0ms

regimes46.0ms

bsearch0.0ms

simplify719.0ms

end0.0ms

sample3.9s

end1.2m