Details

sample70.0ms

Algorithm

intervals

Results

24.0ms	69×	body	10240	exit
14.0ms	312×	body	80	nan
13.0ms	256×	body	80	valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	321	5
5	1627	5
6	5001	5
done	5001	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite26.0ms

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:

16.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
8.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series96.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify78.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2702	425
3	5002	408
done	5002	408

prune149.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

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))

rewrite95.0ms

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:

26.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
58.0ms	(* (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))

series162.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(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)))
14.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify60.0ms

Counts

183 → 183

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	451	2193
1	1880	1915
2	5002	1883
done	5002	1883

prune420.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b	(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-diff`
12×	`sqrt-prod`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`unpow-prod-down`
7×	`pow1`
5×	`pow-pow` `sqrt-pow1`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg`
1×	`pow-to-exp` `rem-sqrt-square` `pow-unpow` `pow-exp` `sqrt-pow2` `sqr-pow`

Counts

3 → 74

Calls

3 calls:

9.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
32.0ms	(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms	(sqrt (atan2 b b))

series7.3m

Counts

3 → 9

Calls

3 calls:

43.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
7.3m	(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
11.0ms	(sqrt (atan2 b b))

simplify43.0ms

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	404	929
1	1367	771
2	5002	725
done	5002	725

prune187.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (* (pow 1 (- b a)) (* (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))))
0.0b	(* (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

312×	`sqrt-prod`
152×	`add-sqr-sqrt`
96×	`unpow-prod-up`
84×	`unpow-prod-down`
74×	`add-cube-cbrt` `*-un-lft-identity`
72×	`prod-diff`
50×	`swap-sqr`
48×	`distribute-rgt-in` `distribute-lft-in`
38×	`associate-r` `associate-l`
36×	`unswap-sqr`
16×	`sqr-pow`
13×	`pow1`
12×	`sub-neg`
8×	`sqrt-pow1` `pow1/2`
6×	`add-exp-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr` `pow-prod-up`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 226

Calls

4 calls:

97.0ms	(sin (* (pow 1 (- b a)) (* (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))))
104.0ms	(* (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series2.7m

Calls

3 calls:

33.0ms	(* (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))) (sqrt (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))