Details

sample390.0ms

Algorithm

intervals

Results

36.0ms	305×	body	80	nan
26.0ms	57×	body	10240	exit
14.0ms	256×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	115	9
5	268	9
6	834	9
7	3197	9
done	5001	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

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` `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:

15.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series113.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms	(pow (sqrt (atan2 b b)) (- b a))
19.0ms	(sqrt (atan2 b b))

simplify1.6s

Counts

57 → 57

Iterations

Useful iterations: 3 (181.0ms)

Iter	Nodes	Cost
0	75	614
1	147	571
2	337	536
3	836	527
4	2732	527
done	5001	527

prune127.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (atan2 b b) (/ (- b a) 2)))
0.0b	(pow (atan2 b b) (/ (- b a) 2))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow-unpow`
18×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `unpow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `div-sub` `pow-exp` `div-inv` `pow-sub` `sqr-pow`

Counts

2 → 41

Calls

2 calls:

8.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))
7.0ms	(pow (atan2 b b) (/ (- b a) 2))

series88.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))
25.0ms	(pow (atan2 b b) (/ (- b a) 2))

simplify3.3s

Counts

47 → 47

Iterations

Useful iterations: 4 (2.1s)

Iter	Nodes	Cost
0	99	639
1	229	599
2	555	573
3	1502	523
4	4892	522
done	5000	522

prune130.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 136

Calls

4 calls:

27.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
44.0ms	(* (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))

series160.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
42.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts

148 → 148

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	141	3640
1	281	2623
2	957	2461
3	3812	2409
done	5001	2400

prune294.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
0.8b	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqrt-prod`
10×	`add-sqr-sqrt`
9×	`pow1` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
6×	`add-exp-log`
5×	`pow-pow` `sqrt-pow1`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
3×	`log-prod` `pow1/2`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `rem-log-exp` `pow-exp` `log-pow` `sqrt-pow2` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
16.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
12.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms	(sqrt (atan2 b b))

series250.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
80.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
118.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
14.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

74 → 74

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	118	1160
1	252	1077
2	565	956
3	1815	922
done	5001	816

prune188.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	13	14
done	13	14

end0.0ms

sample2.1s

Algorithm

intervals

Results

751.0ms	1805×	body	10240	exit
442.0ms	9659×	body	80	nan
431.0ms	7991×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	3×	body	1280	valid
1.0ms	1×	body	2560	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	640	valid