Details

sample547.0ms

Algorithm

intervals

Results

337.0ms	256×	body	80	valid
51.0ms	64×	body	10240	exit
38.0ms	380×	body	80	nan

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	492
1	13	492
2	22	492
3	45	492
4	110	492
5	250	492
6	1161	492
done	5019	492

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

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

Counts

3 → 48

Calls

3 calls:

6.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(sqrt (atan2 b b))

series124.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(pow (sqrt (atan2 b b)) (- b a))
75.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms	(sqrt (atan2 b b))

simplify3.4s

Counts

57 → 57

Iterations

Useful iterations: 3 (438.0ms)

Iter	Nodes	Cost
0	75	26038
1	181	24619
2	395	24579
3	1057	24539
4	3357	24539
done	5002	24539

prune321.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (* 1/2 (- b a)))
0.0b	(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-up`
3×	`add-sqr-sqrt` `pow1` `unpow-prod-down` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 26

Calls

2 calls:

7.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
11.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series168.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
126.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify2.4s

Counts

32 → 32

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	66	18451
1	157	17776
2	397	17074
3	1337	16914
done	5001	16591

prune187.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
2.0b	(log (sqrt (atan2 b b)))
2.0b	(log (sqrt (atan2 b b)))
2.0b	(log (sqrt (atan2 b b)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

2.0ms	(sqrt (atan2 b b))
3.0ms	(log (sqrt (atan2 b b)))
3.0ms	(log (sqrt (atan2 b b)))
3.0ms	(log (sqrt (atan2 b b)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (atan2 b b))
115.0ms	(log (sqrt (atan2 b b)))
115.0ms	(log (sqrt (atan2 b b)))
92.0ms	(log (sqrt (atan2 b b)))

simplify19.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	33	24383