Details

sample125.0ms

Algorithm

intervals

Results

42.0ms	54×	body	10240	exit
28.0ms	294×	body	80	nan
25.0ms	255×	body	80	valid
1.0ms	1×	body	320	valid

simplify10.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	438	9
6	4540	9
done	5001	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite20.0ms

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:

7.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series159.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(pow (sqrt (atan2 b b)) (- b a))
117.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms	(sqrt (atan2 b b))

simplify2.7s

Counts

57 → 57

Iterations

Useful iterations: 3 (954.0ms)

Iter	Nodes	Cost
0	75	614
1	188	571
2	654	536
3	4107	527
done	5002	527

prune242.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.3b	(sin (* (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))

rewrite131.0ms

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:

68.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
44.0ms	(sin (* (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))

series280.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
159.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
21.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify1.7s

Counts

148 → 148

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	141	3640
1	315	2631
2	1431	2461
done	5000	2419

prune458.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b)))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

81×	`sqrt-prod`
72×	`cbrt-prod`
70×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
18×	`swap-sqr`
16×	`unswap-sqr`
14×	`pow1`
12×	`associate-r` `associate-l`
6×	`add-exp-log` `pow1/3`
4×	`add-cbrt-cube` `add-log-exp`
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 → 115

Calls

4 calls:

36.0ms	(* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b)))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series226.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (cbrt (sqrt (sqrt (atan2 b b)))) (cbrt (sqrt (sqrt (atan2 b b)))))
18.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))

simplify1.1s

Counts

127 → 127

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	82	1876
1	141	1682
2	673	1626
done	5000	1568

prune581.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(sin (* (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)) (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (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))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 46

Calls

4 calls:

180.0ms	(sin (* (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)) (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series327.0ms

Counts

4 → 12

Calls

4 calls:

284.0ms	(sin (* (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)) (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)))))
18.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify994.0ms

Counts

58 → 58

Iterations

Useful iterations: done (991.0ms)

Iter	Nodes	Cost
0	60	716
1	127	674
2	354	604
3	1518	518
done	5000	513

prune346.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.2b

regimes83.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	9	20
done	9	20

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.2s	1832×	body	10240	exit
1.1s	10000×	body	80	nan
923.0ms	7992×	body	80	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid