Details

sample128.0ms

Algorithm

intervals

Results

60.0ms	64×	body	10240	exit
26.0ms	380×	body	80	nan
20.0ms	256×	body	80	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

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))

rewrite31.0ms

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:

9.0ms	(pow (sqrt (atan2 b b)) (- b a))
19.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series122.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(pow (sqrt (atan2 b b)) (- b a))
81.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
12.0ms	(sqrt (atan2 b b))

simplify3.7s

Counts

57 → 57

Iterations

Useful iterations: 3 (436.0ms)

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

prune285.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `unpow-prod-down` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
2×	`add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 22

Calls

2 calls:

3.0ms	(pow (atan2 b b) (* (- b a) 1/2))
17.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))

series114.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(pow (atan2 b b) (* (- b a) 1/2))
80.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))

simplify6.7s

Counts

28 → 28

Iterations

Useful iterations: done (6.7s)

Iter	Nodes	Cost
0	57	15191
1	134	14605
2	323	14175
3	1067	14015
4	4525	13955
done	5004	13832

prune168.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `rem-cbrt-cube` `sin-mult`

Counts

4 → 50

Calls

4 calls:

57.0ms	(cbrt (* (* (sin (pow (sqrt (atan2 b b)) (- b a))) (sin (pow (sqrt (atan2 b b)) (- b a)))) (sin (pow (sqrt (atan2 b b)) (- b a)))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series117.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(cbrt (* (* (sin (pow (sqrt (atan2 b b)) (- b a))) (sin (pow (sqrt (atan2 b b)) (- b a)))) (sin (pow (sqrt (atan2 b b)) (- b a)))))
12.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify30.0ms

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	49	19472