Details

sample192.0ms

Algorithm

intervals

Results

62.0ms	256×	body	80	valid
38.0ms	66×	body	10240	exit
23.0ms	301×	body	80	nan

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	115	9
5	274	9
6	837	9
7	3217	9
done	5001	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite54.0ms

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:

25.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
17.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sqrt (atan2 b b))

series174.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
45.0ms	(pow (sqrt (atan2 b b)) (- b a))
46.0ms	(sqrt (atan2 b b))

simplify4.2s

Counts

72 → 72

Iterations

Useful iterations: 4 (2.6s)

Iter	Nodes	Cost
0	117	962
1	246	836
2	485	757
3	1266	728
4	4144	699
done	5000	699

prune261.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize15.0ms

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))

rewrite179.0ms

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:

62.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
93.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series247.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
66.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
19.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))

simplify3.7s

Counts

183 → 183

Iterations

Useful iterations: done (3.7s)

Iter	Nodes	Cost
0	209	4894
1	434	3381
2	1247	3082
3	4701	2989
done	5000	2988

prune613.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
done	9	20

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.1s	1783×	body	10240	exit
1.4s	7987×	body	80	valid
1.1s	9775×	body	80	nan
15.0ms	4×	body	5120	valid
3.0ms	2×	body	2560	valid
2.0ms	2×	body	640	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	320	valid