Details

sample93.0ms

Algorithm

intervals

Results

33.0ms	63×	body	10240	exit
20.0ms	304×	body	80	nan
18.0ms	256×	body	80	valid

simplify9.5s

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	117	9
5	444	9
6	4596	9
done	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

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))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`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 → 63

Calls

3 calls:

22.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series170.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
44.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify740.0ms

Counts

72 → 72

Iterations

Useful iterations: done (737.0ms)

Iter	Nodes	Cost
0	117	962
1	315	839
2	1095	762
done	5001	737

prune262.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 1 expressions with local error:

0.0b	(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

35.0ms

(sin (pow (atan2 b b) (* 1/2 (- b a))))

series86.0ms

Counts

1 → 3

Calls

1 calls:

86.0ms

(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify2.9s

Counts

12 → 12

Iterations

Useful iterations: 4 (514.0ms)

Iter	Nodes	Cost
0	33	182
1	68	181
2	166	161
3	469	139
4	1271	135
5	3184	135
done	5000	135

prune83.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize28.0ms

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:

19.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
19.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series134.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
56.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
19.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))

simplify1.0s

Counts

130 → 130

Iterations

Useful iterations: done (1.0s)

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

prune423.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes48.0ms

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	8	10
1	9	10
done	9	10

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.2s	1890×	body	10240	exit
1.4s	7988×	body	80	valid
1.4s	9830×	body	80	nan
7.0ms	3×	body	2560	valid
3.0ms	3×	body	1280	valid
2.0ms	2×	body	640	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid