Details

sample232.0ms

Algorithm

intervals

Results

88.0ms	67×	body	10240	exit
82.0ms	323×	body	80	nan
40.0ms	256×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2040
7	2040
6	1114
5	256
4	110
3	45
2	22
1	13
0	7

prune3.0ms

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))

rewrite31.0ms

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` `insert-posit16` `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 → 66

Calls

3 calls:

17.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
9.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series132.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
26.0ms	(pow (sqrt (atan2 b b)) (- b a))
20.0ms	(sqrt (atan2 b b))

simplify1.4s

Counts

75 → 75

Iterations

Iter	Nodes
done	2001
4	2001
3	1724
2	687
1	311
0	120

prune361.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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` `insert-posit16` `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 → 122

Calls

4 calls:

10.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series103.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
34.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
12.0ms	(sqrt (atan2 b b))
15.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts

134 → 134

Iterations

Iter	Nodes
done	2012
4	2012
3	1980
2	766
1	338
0	124

prune954.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite16.0ms

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` `insert-posit16` `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 → 122

Calls

4 calls:

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

series127.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
58.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
19.0ms	(sqrt (atan2 b b))
16.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts

134 → 134

Iterations

Iter	Nodes
done	2012
4	2012
3	1980
2	766
1	338
0	124

prune653.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

31×	`unpow-prod-down`
29×	`sqrt-prod`
28×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
22×	`add-cube-cbrt`
13×	`pow-unpow`
11×	`unpow-prod-up`
9×	`pow1` `prod-diff`
7×	`add-exp-log`
6×	`pow-pow` `sqrt-pow1`
5×	`pow-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/2` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `sqr-pow`
2×	`rem-sqrt-square` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `sqrt-pow2` `pow-sub`

Counts

4 → 114

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
13.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series632.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
557.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
12.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.3s

Counts

126 → 126

Iterations

Iter	Nodes
done	2001
3	2001
2	1393
1	593
0	217

prune732.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes65.0ms

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

sample6.8s

Algorithm

intervals

Results

2.8s	1794×	body	10240	exit
1.8s	7989×	body	80	valid
1.8s	9772×	body	80	nan
5.0ms	2×	body	2560	valid
3.0ms	1×	body	5120	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid