Details

sample309.0ms

Algorithm

intervals

Results

79.0ms	256×	body	80	valid
75.0ms	61×	body	10240	exit
40.0ms	305×	body	80	nan

simplify1.9s

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

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))

rewrite44.0ms

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

series161.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
41.0ms	(pow (sqrt (atan2 b b)) (- b a))
32.0ms	(sqrt (atan2 b b))

simplify1.4s

Counts

75 → 75

Iterations

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

prune809.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
93×	`sqrt-prod`
87×	`unpow-prod-down`
59×	`unpow-prod-up`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
17×	`add-exp-log`
15×	`sqr-pow`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`expm1-log1p-u` `pow1/2` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqrt-pow2` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 210

Calls

4 calls:

12.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
55.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series123.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
50.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
19.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify1.6s

Counts

222 → 222

Iterations

Iter	Nodes
done	2000
3	2000
2	1791
1	582
0	216

prune2.9s

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))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series48.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts

76 → 76

Iterations

Iter	Nodes
done	2012
10	2012
9	1279
8	389
7	163
6	90
5	60
4	41
3	33
2	29
1	26
0	21

prune1.3s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize63.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

14.0ms	(pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series115.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a))
20.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))

simplify1.0s

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
3	2000
2	820
1	375
0	139

prune1.7s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	13
1	13
0	12

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.5s	9866×	body	80	nan
2.4s	1832×	body	10240	exit
1.3s	7992×	body	80	valid
7.0ms	3×	body	2560	valid
3.0ms	1×	body	5120	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid