Details

sample68.0ms

Algorithm

intervals

Results

22.0ms	57×	body	10240	exit
13.0ms	305×	body	80	nan
13.0ms	256×	body	80	valid

simplify2.2s

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	115	9
5	268	9
6	834	9
7	3197	9
done	5001	9

prune2.0ms

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))

rewrite18.0ms

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:

9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series101.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
27.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(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

prune126.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite77.0ms

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:

26.0ms	(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)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series159.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
45.0ms	(* (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))

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

prune293.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

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:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
15.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
13.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms	(sqrt (atan2 b b))

series239.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
81.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
113.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
11.0ms	(sqrt (atan2 b b))

simplify1.4s

Counts

74 → 74

Iterations

Useful iterations: done (1.4s)

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

prune190.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series46.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.3s

Counts

64 → 64

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	18	384
1	23	328
2	26	320
3	30	320
4	36	320
5	46	320
6	67	320
7	145	320
8	432	320
9	1822	320
done	5000	320

prune211.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

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	12	14
1	13	14
done	13	14

end0.0ms

sample2.1s

Algorithm

intervals

Results

725.0ms	1805×	body	10240	exit
425.0ms	7991×	body	80	valid
422.0ms	9659×	body	80	nan
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