Details

sample141.0ms

Algorithm

intervals

Results

46.0ms	45×	body	10240	exit
33.0ms	331×	body	80	nan
30.0ms	256×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	438
4	117
3	45
2	22
1	13
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

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))

rewrite15.0ms

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` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

8.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series138.0ms

Counts

3 → 9

Calls

3 calls:

84.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
41.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts

57 → 57

Iterations

Iter	Nodes
done	5002
3	4103
2	655
1	188
0	75

prune306.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

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))

rewrite24.0ms

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×	`pow1/2` `add-exp-log`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

10.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
8.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series136.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
44.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
21.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify751.0ms

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	801
1	219
0	82

prune490.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-up`
3×	`add-sqr-sqrt` `pow1` `unpow-prod-down` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 26

Calls

2 calls:

8.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
3.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series122.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
36.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify1.9s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
3	2470
2	529
1	162
0	66

prune169.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize75.0ms

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))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series67.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(sqrt (atan2 b b))
17.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
8	1052
7	320
6	141
5	72
4	38
3	30
2	26
1	23
0	18

prune374.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes98.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.5s	1746×	body	10240	exit
1.1s	9649×	body	80	nan
1.1s	7986×	body	80	valid
5.0ms	1×	body	5120	valid
3.0ms	4×	body	640	valid
2.0ms	4×	body	320	valid
2.0ms	1×	body	1280	valid
1.0ms	4×	body	160	valid