Details

sample76.0ms

Algorithm

intervals

Results

25.0ms	61×	body	10240	exit
17.0ms	322×	body	80	nan
14.0ms	256×	body	80	valid

simplify2.2s

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	115	9
5	268	9
6	834	9
7	3197	9
done	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

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:

9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series107.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify1.6s

Counts

57 → 57

Iterations

Useful iterations: 3 (180.0ms)

Iter	Nodes	Cost
0	75	614
1	147	571
2	337	536
3	836	527
4	2732	527
done	5001	527

prune122.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite23.0ms

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×	`add-exp-log` `pow1/2`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
8.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
3.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series86.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
31.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts

104 → 104

Iterations

Useful iterations: 3 (190.0ms)

Iter	Nodes	Cost
0	80	1180
1	160	1056
2	351	1032
3	896	1018
4	2657	1018
done	5000	1018

prune268.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

87×	`sqrt-prod`
78×	`add-sqr-sqrt` `unpow-prod-down`
25×	`unswap-sqr`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`swap-sqr`
16×	`add-exp-log`
14×	`sqr-pow`
13×	`associate-r` `associate-l`
9×	`prod-exp`
7×	`pow1`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
4×	`div-sub` `pow-sub` `add-log-exp`
3×	`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 → 134

Calls

4 calls:

41.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (/ (- b a) 2)) (pow (sqrt (sqrt (atan2 b b))) (/ (- b a) 2)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series80.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (/ (- b a) 2)) (pow (sqrt (sqrt (atan2 b b))) (/ (- b a) 2)))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

146 → 146

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	123	3844
1	241	2725
2	843	2566
3	3328	2405
done	5000	2264

prune319.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

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	(sqrt (atan2 b b))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series43.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.3s

Counts

64 → 64

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	18	384
1	23	328
2	26	320
3	30	320
4	36	320
5	46	320
6	67	320
7	145	320
8	432	320
9	1822	320
done	5000	320

prune217.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes39.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	34
1	14	34
done	14	34

end0.0ms

sample2.2s

Algorithm

intervals

Results

770.0ms	1844×	body	10240	exit
447.0ms	9923×	body	80	nan
441.0ms	7988×	body	80	valid
8.0ms	3×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	5×	body	160	valid
1.0ms	3×	body	320	valid