Details

sample119.0ms

Algorithm

intervals

Results

34.0ms	255×	body	80	valid
32.0ms	58×	body	10240	exit
24.0ms	360×	body	80	nan
0.0ms	1×	body	320	valid

simplify719.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite30.0ms

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:

12.0ms	(pow (sqrt (atan2 b b)) (- b a))
14.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series180.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(pow (sqrt (atan2 b b)) (- b a))
113.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
27.0ms	(sqrt (atan2 b b))

simplify2.3s

Counts

57 → 57

Iterations

Iter	Nodes
done	5002
3	4131
2	653
1	188
0	75

prune283.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.2b	(sin (* (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))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
27.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series181.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
118.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
16.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify414.0ms

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
2	944
1	265
0	104

prune388.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (* (- b a) 1/2))
0.3b	(sin (pow (atan2 b b) (* (- b a) 1/2)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `unpow-prod-down` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
2×	`add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 22

Calls

2 calls:

6.0ms	(pow (atan2 b b) (* (- b a) 1/2))
15.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))

series113.0ms

Counts

2 → 6

Calls

2 calls:

27.0ms	(pow (atan2 b b) (* (- b a) 1/2))
86.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))

simplify1.8s

Counts

28 → 28

Iterations

Iter	Nodes
done	5001
3	2968
2	484
1	139
0	57

prune171.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (* (pow (* (cbrt (atan2 b b)) (cbrt (atan2 b b))) (* 1/2 (- b a))) (pow (cbrt (atan2 b b)) (* 1/2 (- b a)))))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

39.0ms	(sin (* (pow (* (cbrt (atan2 b b)) (cbrt (atan2 b b))) (* 1/2 (- b a))) (pow (cbrt (atan2 b b)) (* 1/2 (- b a)))))
1.0ms	(cbrt (atan2 b b))
1.0ms	(cbrt (atan2 b b))
1.0ms	(cbrt (atan2 b b))

series692.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(sin (* (pow (* (cbrt (atan2 b b)) (cbrt (atan2 b b))) (* 1/2 (- b a))) (pow (cbrt (atan2 b b)) (* 1/2 (- b a)))))
145.0ms	(cbrt (atan2 b b))
132.0ms	(cbrt (atan2 b b))
148.0ms	(cbrt (atan2 b b))

simplify1.2s

Counts

52 → 52

Iterations

Iter	Nodes
done	5000
3	1857
2	447
1	145
0	63

prune243.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes81.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.4s	1790×	body	10240	exit
1.0s	7991×	body	80	valid
998.0ms	9657×	body	80	nan
3.0ms	1×	body	2560	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	640	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid