Details

sample251.0ms

Algorithm

intervals

Results

49.0ms	54×	body	10240	exit
31.0ms	305×	body	80	nan
28.0ms	256×	body	80	valid

simplify12.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 2 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt` `unpow-prod-down` `sqrt-prod`
5×	`pow1` `pow-unpow`
3×	`add-exp-log` `pow-pow`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

2 → 41

Calls

2 calls:

12.0ms	(pow (sqrt (atan2 b b)) (- b a))
5.0ms	(sqrt (atan2 b b))

series78.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(pow (sqrt (atan2 b b)) (- b a))
32.0ms	(sqrt (atan2 b b))

simplify3.1s

Counts

47 → 47

Iterations

Useful iterations: 2 (135.0ms)

Iter	Nodes	Cost
0	60	472
1	160	429
2	599	412
3	3935	412
done	5002	412

prune268.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

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))

rewrite45.0ms

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:

18.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
18.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series166.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
56.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
21.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify718.0ms

Counts

104 → 104

Iterations

Useful iterations: done (713.0ms)

Iter	Nodes	Cost
0	80	1180
1	214	1056
2	782	1032
done	5000	1018

prune732.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

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))

rewrite12.0ms

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:

2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series88.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify2.7s

Counts

64 → 64

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	18	384
1	23	328
2	26	320
3	30	320
4	38	320
5	72	320
6	141	320
7	319	320
8	1061	320
done	5000	320

prune535.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 2 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`add-cube-cbrt` `unpow-prod-down` `sqrt-prod`
5×	`pow1` `pow-unpow`
3×	`add-exp-log` `pow-pow`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

2 → 41

Calls

2 calls:

20.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series61.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(pow (sqrt (atan2 b b)) (- b a))
21.0ms	(sqrt (atan2 b b))

simplify3.4s

Counts

47 → 47

Iterations

Useful iterations: 2 (146.0ms)

Iter	Nodes	Cost
0	60	472
1	160	429
2	599	412
3	3935	412
done	5002	412

prune291.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes202.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	43
1	14	43
done	14	43

end0.0ms

sample6.9s

Algorithm

intervals

Results

2.5s	1842×	body	10240	exit
2.1s	9724×	body	80	nan
1.2s	7988×	body	80	valid
23.0ms	3×	body	5120	valid
15.0ms	4×	body	2560	valid
3.0ms	3×	body	1280	valid
1.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid