Details

sample583.0ms

Algorithm

intervals

Results

231.0ms	304×	body	80	nan
163.0ms	63×	body	10240	exit
95.0ms	256×	body	80	valid

simplify9.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	438	9
6	4540	9
done	5001	9

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

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))

rewrite40.0ms

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:

10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
15.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sqrt (atan2 b b))

series138.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
32.0ms	(pow (sqrt (atan2 b b)) (- b a))
21.0ms	(sqrt (atan2 b b))

simplify2.9s

Counts

57 → 57

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	75	614
1	188	571
2	654	536
3	4069	527
done	5001	527

prune226.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 1 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

1 → 7

Calls

1 calls:

15.0ms

(sin (pow (atan2 b b) (* 1/2 (- b a))))

series93.0ms

Counts

1 → 3

Calls

1 calls:

93.0ms

(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify1.9s

Counts

10 → 10

Iterations

Useful iterations: 4 (309.0ms)

Iter	Nodes	Cost
0	31	160
1	65	160
2	159	140
3	425	119
4	955	116
5	2592	116
done	5000	116

prune54.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize30.0ms

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
20×	`add-sqr-sqrt`
18×	`unpow-prod-down` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

16.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
17.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series125.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
48.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
17.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify515.0ms

Counts

104 → 104

Iterations

Useful iterations: done (513.0ms)

Iter	Nodes	Cost
0	80	1180
1	214	1056
2	782	1032
done	5000	1018

prune368.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	9	10
done	9	10

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.3s	1890×	body	10240	exit
1.5s	7988×	body	80	valid
1.1s	9830×	body	80	nan
5.0ms	3×	body	2560	valid
3.0ms	3×	body	1280	valid
2.0ms	2×	body	640	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid