Details

sample77.0ms

Algorithm

intervals

Results

26.0ms	58×	body	10240	exit
18.0ms	321×	body	80	nan
14.0ms	255×	body	80	valid
3.0ms	1×	body	5120	valid

simplify2.3s

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	254	9
6	734	9
7	2636	9
done	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.3b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite14.0ms

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` `log1p-expm1-u` `add-log-exp`
2×	`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 → 63

Calls

3 calls:

5.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series96.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow (sqrt (atan2 b b)) (- b a))
66.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify2.4s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	117	962
1	252	836
2	532	757
3	1271	728
4	3912	699
done	5000	699

prune167.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

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))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`unpow-prod-down`
48×	`unpow-prod-up`
46×	`add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
16×	`add-exp-log`
14×	`sqr-pow`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 171

Calls

4 calls:

44.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
9.0ms	(sin (* (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))

series148.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
89.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.1s

Counts

183 → 183

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	209	4894
1	449	3381
2	1502	3082
done	5001	2999

prune458.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
0.3b	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)))
1.0b	(sqrt (atan2 b b))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

66×	`unpow-prod-up`
62×	`unpow-prod-down`
54×	`add-sqr-sqrt` `prod-diff`
53×	`add-cube-cbrt` `*-un-lft-identity`
35×	`cube-prod`
33×	`distribute-rgt-in` `distribute-lft-in`
30×	`sqrt-prod`
8×	`pow1`
7×	`add-exp-log`
6×	`sub-neg` `pow-pow`
5×	`sqrt-pow1` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `pow1/2`
1×	`cube-mult` `rem-sqrt-square` `unpow3` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 165

Calls

4 calls:

7.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
16.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
41.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)))
1.0ms	(sqrt (atan2 b b))

series174.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
55.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)
78.0ms	(sin (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) 3)))
10.0ms	(sqrt (atan2 b b))

simplify717.0ms

Counts

177 → 177

Iterations

Useful iterations: done (711.0ms)

Iter	Nodes	Cost
0	250	4547
1	598	3749
2	1531	3351
done	5001	3125

prune361.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)) 3)
0.1b	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
0.3b	(sin (cbrt (pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)) 3)))
1.0b	(sqrt (atan2 b b))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

130×	`unpow-prod-down`
56×	`cbrt-prod`
42×	`add-sqr-sqrt`
41×	`add-cube-cbrt` `*-un-lft-identity`
33×	`unpow-prod-up`
31×	`cube-prod`
30×	`sqrt-prod`
27×	`prod-diff`
7×	`add-exp-log` `sqr-pow`
6×	`pow1` `pow-unpow`
5×	`pow-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `sub-neg` `pow-pow`
1×	`cube-mult` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `unpow3` `rem-cube-cbrt`

Counts

4 → 148

Calls

4 calls:

23.0ms	(pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)) 3)
9.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
55.0ms	(sin (cbrt (pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)) 3)))
1.0ms	(sqrt (atan2 b b))

series225.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)) 3)
60.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)
85.0ms	(sin (cbrt (pow (cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 6)) 3)))
16.0ms	(sqrt (atan2 b b))

simplify2.7s

Counts

160 → 160

Iterations

Useful iterations: 3 (799.0ms)

Iter	Nodes	Cost
0	270	3906
1	689	3058
2	1349	2779
3	4647	2673
done	5000	2673

prune386.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes49.0ms

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: 0 (0.0ms)

Iter	Nodes	Cost
0	13	15
1	14	15
done	14	15

end0.0ms

sample2.1s

Algorithm

intervals

Results

793.0ms	1866×	body	10240	exit
454.0ms	10105×	body	80	nan
451.0ms	7995×	body	80	valid
6.0ms	2×	body	5120	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid