Details

sample112.0ms

Algorithm

intervals

Results

36.0ms	52×	body	10240	exit
23.0ms	324×	body	80	nan
21.0ms	256×	body	80	valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

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))

rewrite16.0ms

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))

series129.0ms

Counts

3 → 9

Calls

3 calls:

82.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
34.0ms	(pow (sqrt (atan2 b b)) (- b a))
13.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts

57 → 57

Iterations

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

prune330.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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))

rewrite39.0ms

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:

14.0ms	(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))

series153.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
55.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
20.0ms	(sqrt (atan2 b b))
23.0ms	(sqrt (atan2 b b))

simplify769.0ms

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	801
1	219
0	82

prune619.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`cbrt-prod`
29×	`sqrt-prod`
19×	`*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
11×	`swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
6×	`pow1/3` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

25.0ms	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series176.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))
12.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

107 → 107

Iterations

Iter	Nodes
done	5002
3	2332
2	401
1	116
0	63

prune607.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize71.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
31×	`unpow-prod-down`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`pow-unpow`
9×	`pow1`
7×	`add-exp-log`
6×	`pow-pow` `sqrt-pow1`
5×	`pow-exp`
4×	`add-cbrt-cube` `pow1/2` `add-log-exp`
3×	`pow-to-exp` `sqr-pow`
2×	`rem-sqrt-square` `distribute-lft-out--` `difference-of-squares`
1×	`sqrt-pow2`

Counts

4 → 93

Calls

4 calls:

14.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
13.0ms	(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series901.0ms

Counts

4 → 12

Calls

4 calls:

591.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
286.0ms	(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify1.6s

Counts

105 → 105

Iterations

Iter	Nodes
done	5001
2	1947
1	487
0	157

prune675.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes131.0ms

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	12
1	12
0	11

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.7s	9879×	body	80	nan
1.7s	1829×	body	10240	exit
1.4s	7989×	body	80	valid
12.0ms	2×	body	5120	valid
4.0ms	2×	body	2560	valid
2.0ms	2×	body	1280	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid