Details

sample131.0ms

Algorithm

intervals

Results

39.0ms	52×	body	10240	exit
36.0ms	324×	body	80	nan
24.0ms	256×	body	80	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	444
4	117
3	45
2	22
1	13
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite25.0ms

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` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 63

Calls

3 calls:

14.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series169.0ms

Counts

3 → 9

Calls

3 calls:

105.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
43.0ms	(pow (sqrt (atan2 b b)) (- b a))
20.0ms	(sqrt (atan2 b b))

simplify773.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1098
1	315
0	117

prune374.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

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))

rewrite43.0ms

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×	`pow1/2` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

16.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
17.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series116.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
36.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
15.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))

simplify696.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1255
1	345
0	122

prune608.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (fabs (cbrt (atan2 b b))) (- b a))
0.1b	(pow (sqrt (cbrt (atan2 b b))) (- b a))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`add-cube-cbrt`
22×	`unpow-prod-up`
18×	`prod-diff`
12×	`unpow-prod-down`
10×	`pow-unpow`
9×	`cbrt-prod`
7×	`pow1`
6×	`add-exp-log` `sqrt-prod`
5×	`pow-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`pow-to-exp` `sub-neg` `sqrt-pow1` `pow-exp` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`
1×	`pow1/2` `sqrt-pow2`

Counts

4 → 102

Calls

4 calls:

6.0ms	(pow (fabs (cbrt (atan2 b b))) (- b a))
12.0ms	(pow (sqrt (cbrt (atan2 b b))) (- b a))
1.0ms	(cbrt (atan2 b b))
1.0ms	(cbrt (atan2 b b))

series453.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(pow (fabs (cbrt (atan2 b b))) (- b a))
50.0ms	(pow (sqrt (cbrt (atan2 b b))) (- b a))
190.0ms	(cbrt (atan2 b b))
169.0ms	(cbrt (atan2 b b))

simplify1.6s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1933
1	495
0	166

prune590.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
0.1b	(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
31×	`unpow-prod-down`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`pow-unpow`
9×	`pow1`
7×	`add-exp-log`
6×	`pow-pow` `sqrt-pow1`
5×	`pow-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/2` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `sqr-pow`
2×	`rem-sqrt-square` `distribute-lft-out--` `difference-of-squares`
1×	`sqrt-pow2`

Counts

4 → 101

Calls

4 calls:

11.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
13.0ms	(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series910.0ms

Counts

4 → 12

Calls

4 calls:

567.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
315.0ms	(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
11.0ms	(sqrt (atan2 b b))
17.0ms	(sqrt (atan2 b b))

simplify991.0ms

Counts

113 → 113

Iterations

Iter	Nodes
done	5002
2	1992
1	502
0	163

prune728.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes100.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.9s	1829×	body	10240	exit
1.6s	9879×	body	80	nan
1.5s	7989×	body	80	valid
7.0ms	2×	body	5120	valid
5.0ms	2×	body	2560	valid
2.0ms	2×	body	1280	valid
2.0ms	4×	body	160	valid
1.0ms	1×	body	320	valid