Details

sample89.0ms

Algorithm

intervals

Results

34.0ms	58×	body	10240	exit
17.0ms	321×	body	80	nan
16.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify5.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	110	9
5	264	9
6	1186	9
7	4138	9
done	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite10.0ms

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:

4.0ms	(pow (sqrt (atan2 b b)) (- b a))
4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series90.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow (sqrt (atan2 b b)) (- b a))
61.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify6.7s

Counts

57 → 57

Iterations

Useful iterations: 3 (150.0ms)

Iter	Nodes	Cost
0	75	614
1	150	575
2	397	536
3	1196	527
4	4650	527
done	5000	527

prune133.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.3b	(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))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

31.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
9.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series154.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
95.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify857.0ms

Counts

148 → 148

Iterations

Useful iterations: done (849.0ms)

Iter	Nodes	Cost
0	141	3640
1	289	2649
2	1095	2461
done	5000	2444

prune310.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
0.3b	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)))
1.0b	(sqrt (atan2 b b))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

44×	`unpow-prod-down`
30×	`sqrt-prod`
18×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity` `cube-prod`
12×	`unpow-prod-up`
8×	`pow1`
7×	`add-exp-log`
6×	`distribute-rgt-in` `sub-neg` `pow-pow` `distribute-lft-in`
5×	`sqrt-pow1` `pow-exp` `add-cbrt-cube`
4×	`pow-unpow` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow1/2`
1×	`cube-mult` `rem-sqrt-square` `unpow3` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 103

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
8.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
21.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)))
1.0ms	(sqrt (atan2 b b))

series168.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
53.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
74.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)))
10.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

115 → 115

Iterations

Useful iterations: 2 (152.0ms)

Iter	Nodes	Cost
0	144	2185
1	388	1947
2	1437	1783
done	5000	1783

prune264.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
0.0b	(pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)) 3)
0.3b	(sin (cbrt (pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)) 3)))
1.0b	(sqrt (atan2 b b))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

148×	`unpow-prod-down`
94×	`cube-prod`
80×	`cbrt-prod`
57×	`sqrt-prod`
36×	`add-sqr-sqrt`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-up`
12×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
10×	`sqr-pow`
7×	`add-exp-log`
6×	`pow1` `pow-unpow`
5×	`pow-exp` `add-cbrt-cube`
4×	`cube-mult` `unpow3` `add-log-exp`
3×	`pow-to-exp` `pow-pow`
2×	`rem-cube-cbrt`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 177

Calls

4 calls:

9.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
24.0ms	(pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)) 3)
58.0ms	(sin (cbrt (pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)) 3)))
1.0ms	(sqrt (atan2 b b))

series192.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
53.0ms	(pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)) 3)
75.0ms	(sin (cbrt (pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)) 3)))
14.0ms	(sqrt (atan2 b b))

simplify1.4s

Counts

189 → 189

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	200	4954
1	506	3815
2	1369	3549
done	5001	3516

prune331.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes48.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	14	15
done	14	15

end0.0ms

sample2.1s

Algorithm

intervals

Results

826.0ms	1866×	body	10240	exit
477.0ms	10105×	body	80	nan
453.0ms	7995×	body	80	valid
6.0ms	2×	body	5120	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid