Details

sample67.0ms

Algorithm

intervals

Results

24.0ms	56×	body	10240	exit
14.0ms	256×	body	80	valid
14.0ms	306×	body	80	nan

simplify4.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	110	9
5	262	9
6	738	9
7	2638	9
done	5000	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

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))

rewrite10.0ms

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

Counts

3 → 48

Calls

3 calls:

4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series92.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
20.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify1.8s

Counts

57 → 57

Iterations

Useful iterations: 3 (164.0ms)

Iter	Nodes	Cost
0	75	614
1	148	575
2	344	536
3	812	527
4	2393	527
done	5001	527

prune135.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
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×	`pow1/2` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 162

Calls

4 calls:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
26.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series86.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
36.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
9.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify3.1s

Counts

174 → 174

Iterations

Useful iterations: 3 (1.8s)

Iter	Nodes	Cost
0	144	3870
1	293	2920
2	1048	2760
3	4813	2711
done	5000	2711

prune370.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite9.0ms

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

Counts

3 → 48

Calls

3 calls:

4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series86.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sqrt (atan2 b b))

simplify1.7s

Counts

57 → 57

Iterations

Useful iterations: 3 (163.0ms)

Iter	Nodes	Cost
0	75	614
1	148	575
2	344	536
3	812	527
4	2393	527
done	5001	527

prune130.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

101×	`unpow-prod-down`
76×	`add-sqr-sqrt`
69×	`sqrt-prod`
35×	`unswap-sqr`
24×	`add-exp-log`
21×	`*-un-lft-identity` `sqr-pow`
19×	`add-cube-cbrt`
18×	`pow-exp`
17×	`associate-r`
15×	`associate-l` `prod-exp`
12×	`pow-to-exp`
9×	`pow1`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow`
4×	`unpow-prod-up` `pow1/2` `add-log-exp`
2×	`sub-neg` `rem-sqrt-square` `pow-sub`
1×	`associate-l/` `-commutative` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 151

Calls

4 calls:

4.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
36.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series621.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
575.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify700.0ms

Counts

163 → 163

Iterations

Useful iterations: done (695.0ms)

Iter	Nodes	Cost
0	194	4482
1	445	4317
2	1516	4034
done	5000	4022

prune409.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes72.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	9	11
1	12	9
done	12	9

end0.0ms

sample1.9s

Algorithm

intervals

Results

702.0ms	1811×	body	10240	exit
420.0ms	9846×	body	80	nan
414.0ms	7989×	body	80	valid
5.0ms	2×	body	5120	valid
1.0ms	2×	body	1280	valid
1.0ms	1×	body	2560	valid
1.0ms	2×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid