Details

sample149.0ms

Algorithm

intervals

Results

51.0ms	336×	body	80	nan
37.0ms	51×	body	10240	exit
25.0ms	256×	body	80	valid

simplify802.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	438	9
done	5000	9

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite19.0ms

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:

7.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series172.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
53.0ms	(pow (sqrt (atan2 b b)) (- b a))
27.0ms	(sqrt (atan2 b b))

simplify2.0s

Counts

57 → 57

Iterations

Useful iterations: 3 (882.0ms)

Iter	Nodes	Cost
0	75	614
1	188	571
2	655	536
3	4103	527
done	5002	527

prune208.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite21.0ms

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:

16.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
4.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series128.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
42.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify1.6s

Counts

32 → 32

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	66	476
1	162	459
2	529	411
3	2470	371
done	5000	367

prune172.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

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))

rewrite18.0ms

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:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
7.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series105.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
44.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
15.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify439.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (158.0ms)

Iter	Nodes	Cost
0	82	1184
1	219	1056
2	801	1018
done	5000	1018

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* (- b a) 1/4)))
0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b	(pow (atan2 b b) (* (- b a) 1/4))
1.0b	(sqrt (atan2 b b))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`unpow-prod-down`
30×	`sqrt-prod`
18×	`*-un-lft-identity` `add-exp-log`
16×	`add-cube-cbrt`
15×	`associate-l` `unswap-sqr`
12×	`sqr-pow`
9×	`pow1` `prod-exp`
8×	`pow-to-exp` `pow-exp`
7×	`associate-r`
6×	`pow-unpow` `pow-pow` `add-cbrt-cube`
5×	`sqrt-pow1`
4×	`unpow-prod-up` `add-log-exp`
3×	`pow1/2`
2×	`sub-neg` `pow-sub`
1×	`rem-sqrt-square` `associate-l/` `-commutative` `cbrt-unprod` `sqrt-pow2` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 117

Calls

4 calls:

64.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* (- b a) 1/4)))
13.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
6.0ms	(pow (atan2 b b) (* (- b a) 1/4))
2.0ms	(sqrt (atan2 b b))

series205.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (atan2 b b) (* (- b a) 1/4)))
53.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
23.0ms	(pow (atan2 b b) (* (- b a) 1/4))
18.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts

129 → 129

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	153	2480
1	417	2337
2	1967	2230
done	5000	2204

prune574.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	22
1	17	22
done	17	22

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.0s	1752×	body	10240	exit
1.4s	7988×	body	80	valid
1.0s	9700×	body	80	nan
4.0ms	2×	body	2560	valid
3.0ms	1×	body	5120	valid
2.0ms	2×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid