Details

sample173.0ms

Algorithm

intervals

Results

65.0ms	256×	body	80	valid
50.0ms	68×	body	10240	exit
34.0ms	319×	body	80	nan

simplify3.7s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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))

rewrite41.0ms

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	(pow (sqrt (atan2 b b)) (- b a))
21.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series180.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(pow (sqrt (atan2 b b)) (- b a))
128.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
27.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts

57 → 57

Iterations

Useful iterations: 3 (234.0ms)

Iter	Nodes	Cost
0	75	614
1	147	571
2	337	536
3	843	527
4	2738	527
done	5000	527

prune165.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 1 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

1 → 7

Calls

1 calls:

12.0ms

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

series78.0ms

Counts

1 → 3

Calls

1 calls:

78.0ms

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

simplify4.3s

Counts

10 → 10

Iterations

Useful iterations: 4 (304.0ms)

Iter	Nodes	Cost
0	31	160
1	65	160
2	159	140
3	394	119
4	710	116
5	1404	116
6	4860	116
done	5001	116

prune35.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(* (cos 1) (log (sqrt (atan2 b b))))
2.0b	(log (sqrt (atan2 b b)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`log-prod`
16×	`pow1` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`add-exp-log` `sqrt-prod`
11×	`associate-r` `add-cbrt-cube`
8×	`distribute-rgt-in` `distribute-lft-in`
6×	`log-pow`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`sub-neg` `associate-r/` `-commutative`
1×	`rem-sqrt-square` `flip3--` `rem-log-exp` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 89

Calls

4 calls:

40.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))
14.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
2.0ms	(log (sqrt (atan2 b b)))

series440.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
12.0ms	(sqrt (atan2 b b))
169.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
75.0ms	(log (sqrt (atan2 b b)))

simplify1.8s

Counts

101 → 101

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	119	1237
1	240	1183
2	842	1012
3	3049	1012
done	5000	1012

prune213.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

Details

sample173.0ms

simplify3.7s

prune5.0ms

localize23.0ms

rewrite41.0ms

series180.0ms

simplify2.2s

prune165.0ms

localize16.0ms

rewrite13.0ms

series78.0ms

simplify4.3s

prune35.0ms

localize16.0ms

rewrite60.0ms

series440.0ms

simplify1.8s

prune213.0ms

regimes1.0ms