Details

sample128.0ms

Algorithm

intervals

Results

44.0ms	67×	body	10240	exit
30.0ms	340×	body	80	nan
25.0ms	256×	body	80	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	438
4	117
3	45
2	22
1	13
0	7

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `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 → 48

Calls

3 calls:

10.0ms	(pow (sqrt (atan2 b b)) (- b a))
14.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series157.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(pow (sqrt (atan2 b b)) (- b a))
110.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
20.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts

57 → 57

Iterations

Iter	Nodes
done	5002
3	4131
2	653
1	188
0	75

prune217.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.0b	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
0.0b	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
1.0b	(sqrt (atan2 b b))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`log-pow` `add-cube-cbrt`
12×	`exp-prod` `unpow-prod-down`
9×	`sqrt-prod`
8×	`pow1`
6×	`log-prod`
5×	`pow-unpow` `add-exp-log`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
3×	`pow-pow` `sin-sum`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `rem-log-exp` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

5.0ms	(pow (sqrt (atan2 b b)) (- b a))
35.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
17.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
2.0ms	(sqrt (atan2 b b))

series167.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(pow (sqrt (atan2 b b)) (- b a))
83.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
31.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
12.0ms	(sqrt (atan2 b b))

simplify2.4s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
3	4621
2	761
1	251
0	126

prune513.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-pow`
28×	`sqrt-pow1`
24×	`exp-prod`
18×	`add-sqr-sqrt` `sqrt-prod`
16×	`*-un-lft-identity` `add-cube-cbrt`
12×	`log-prod` `unpow-prod-down`
10×	`pow1`
6×	`add-exp-log`
4×	`unpow-prod-up` `add-cbrt-cube` `pow1/2` `add-log-exp`
2×	`rem-sqrt-square` `sub-neg` `rem-log-exp` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

20.0ms	(log (sqrt (exp (pow (sqrt (atan2 b b)) (- b a)))))
20.0ms	(log (sqrt (exp (pow (sqrt (atan2 b b)) (- b a)))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series296.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(log (sqrt (exp (pow (sqrt (atan2 b b)) (- b a)))))
132.0ms	(log (sqrt (exp (pow (sqrt (atan2 b b)) (- b a)))))
21.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify1.7s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
4	1183
3	451
2	226
1	131
0	87

prune627.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))) (cbrt (sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
16×	`cbrt-prod`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
9×	`sqrt-prod`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 79

Calls

4 calls:

102.0ms	(* (cbrt (sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))) (cbrt (sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series285.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(* (cbrt (sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))) (cbrt (sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))))
19.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify3.7s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
3	3564
2	617
1	176
0	82

prune669.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	11
0	11

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	1884×	body	10240	exit
1.4s	7993×	body	80	valid
1.1s	9640×	body	80	nan
3.0ms	3×	body	1280	valid
1.0ms	1×	body	2560	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid