Details

sample310.0ms

Algorithm

intervals

Results

100.0ms	256×	body	80	valid
55.0ms	54×	body	10240	exit
34.0ms	305×	body	80	nan

simplify12.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	444	9
6	4596	9
done	5001	9

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 2 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`unpow-prod-down` `sqrt-prod`
5×	`pow1` `pow-unpow`
3×	`add-exp-log` `pow-pow`
2×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `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 → 54

Calls

2 calls:

16.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sqrt (atan2 b b))

series80.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(pow (sqrt (atan2 b b)) (- b a))
33.0ms	(sqrt (atan2 b b))

simplify1.6s

Counts

60 → 60

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	100	800
1	284	678
2	1021	619
done	5000	602

prune349.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 118

Calls

4 calls:

20.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
18.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series181.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
77.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
21.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify1.4s

Counts

130 → 130

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	120	1876
1	340	1594
2	1216	1474
done	5000	1438

prune772.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize58.0ms

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))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))
5.0ms	(sqrt (atan2 b b))

series76.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt (atan2 b b))
18.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

72 → 72

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	20	424
1	25	368
2	28	360
3	32	360
4	40	360
5	74	360
6	154	360
7	324	360
8	1026	360
done	5000	360

prune604.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (sqrt (atan2 b b)) (- b a)) 3)
0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3))
1.0b	(sqrt (atan2 b b))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

72×	`unpow-prod-down`
55×	`unpow-prod-up` `add-sqr-sqrt`
54×	`*-un-lft-identity`
52×	`add-cube-cbrt`
48×	`cbrt-prod`
45×	`prod-diff`
42×	`cube-prod`
18×	`sqrt-prod`
8×	`pow-unpow`
7×	`pow1` `add-exp-log` `sqr-pow`
5×	`sub-neg` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-pow` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-sub`
2×	`cube-div` `cube-mult` `sqrt-pow1` `pow1/2` `unpow3`
1×	`rem-sqrt-square` `cbrt-div` `pow1/3` `sqrt-pow2` `rem-cbrt-cube` `distribute-lft-out--` `rem-cube-cbrt` `difference-of-squares`

Counts

4 → 178

Calls

4 calls:

20.0ms	(pow (pow (sqrt (atan2 b b)) (- b a)) 3)
14.0ms	(pow (sqrt (atan2 b b)) (- b a))
28.0ms	(cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3))
2.0ms	(sqrt (atan2 b b))

series169.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(pow (pow (sqrt (atan2 b b)) (- b a)) 3)
43.0ms	(pow (sqrt (atan2 b b)) (- b a))
37.0ms	(cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3))
19.0ms	(sqrt (atan2 b b))

simplify3.4s

Counts

190 → 190

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	193	3943
1	592	3047
2	3046	2724
done	5000	2663

prune820.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes178.0ms

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

sample6.7s

Algorithm

intervals

Results

2.4s	1842×	body	10240	exit
1.9s	7988×	body	80	valid
1.4s	9724×	body	80	nan
16.0ms	3×	body	5120	valid
9.0ms	4×	body	2560	valid
3.0ms	3×	body	1280	valid
1.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid