Details

sample5.1s

Algorithm

intervals

Results

3.1s	63×	body	10240	exit
230.0ms	346×	body	80	nan
103.0ms	255×	body	80	valid
1.0ms	1×	body	640	valid

simplify53.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	438	9
6	4540	9
done	5001	9

prune250.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize166.0ms

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))

rewrite453.0ms

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:

318.0ms	(pow (sqrt (atan2 b b)) (- b a))
22.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(sqrt (atan2 b b))

series1.2s

Counts

3 → 9

Calls

3 calls:

199.0ms	(pow (sqrt (atan2 b b)) (- b a))
645.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
341.0ms	(sqrt (atan2 b b))

simplify13.8s

Counts

57 → 57

Iterations

Useful iterations: 3 (6.7s)

Iter	Nodes	Cost
0	75	614
1	188	571
2	654	536
3	4107	527
done	5002	527

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize538.0ms

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`cbrt-prod`
29×	`sqrt-prod`
19×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
11×	`swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
6×	`add-exp-log` `pow1/3`
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:

3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))
75.0ms	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

series1.0s

Counts

4 → 12

Calls

4 calls:

202.0ms	(sqrt (atan2 b b))
61.0ms	(sqrt (atan2 b b))
30.0ms	(sqrt (atan2 b b))
730.0ms	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

simplify14.1s

Counts

107 → 107

Iterations

Useful iterations: done (14.0s)

Iter	Nodes	Cost
0	63	1225
1	116	1069
2	406	1021
3	2648	941
done	5000	860

prune2.1s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite656.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`pow-unpow`
17×	`add-cube-cbrt`
15×	`times-frac`
9×	`sqrt-prod`
8×	`pow1`
6×	`unpow-prod-down`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-pow` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `div-sub` `pow-exp` `sqrt-pow2` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

31.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
536.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
7.0ms	(sqrt (atan2 b b))
5.0ms	(sqrt (atan2 b b))

series792.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
580.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
33.0ms	(sqrt (atan2 b b))
87.0ms	(sqrt (atan2 b b))

simplify20.6s

Counts

85 → 85

Iterations

Useful iterations: 3 (13.2s)

Iter	Nodes	Cost
0	113	1090
1	289	919
2	896	842
3	4531	794
done	5001	794

prune1.8s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes304.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

simplify51.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	26
1	12	26
done	12	26

end15.0ms

sample46.6s

Algorithm

intervals

Results

24.0s	1897×	body	10240	exit
12.2s	10216×	body	80	nan
8.5s	7991×	body	80	valid
65.0ms	1×	body	2560	valid
18.0ms	3×	body	640	valid
1.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	320	valid