Details

sample72.0ms

Algorithm

intervals

Results

24.0ms	57×	body	10240	exit
15.0ms	305×	body	80	nan
14.0ms	256×	body	80	valid

simplify2.5s

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	274	9
6	837	9
7	3217	9
done	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite23.0ms

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:

12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
8.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series105.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms	(pow (sqrt (atan2 b b)) (- b a))
16.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.7s)

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

prune153.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite102.0ms

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:

28.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
62.0ms	(* (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))

series154.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
41.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify2.4s

Counts

183 → 183

Iterations

Useful iterations: done (2.4s)

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

prune397.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
0.0b	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
0.8b	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0b	(sqrt (atan2 b b))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

12.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
22.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
16.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
1.0ms	(sqrt (atan2 b b))

series239.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
81.0ms	(sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))))
113.0ms	(log (sin (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
11.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

100 → 100

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	200	1956
1	418	1708
2	802	1499
3	2450	1388
done	5000	1153

prune231.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a)))))
0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.8b	(log (expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a))))))
1.0b	(sqrt (atan2 b b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
8×	`pow1`
6×	`add-exp-log` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `pow-pow`
2×	`sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `expm1-log1p` `rem-log-exp` `pow-exp` `log-pow` `sqrt-pow2` `distribute-lft-out--` `expm1-udef` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

0.0ms	(expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a)))))
11.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(log (expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a))))))
2.0ms	(sqrt (atan2 b b))

series255.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a)))))
21.0ms	(pow (sqrt (atan2 b b)) (- b a))
125.0ms	(log (expm1 (log1p (sin (pow (sqrt (atan2 b b)) (- b a))))))
11.0ms	(sqrt (atan2 b b))

simplify2.9s

Counts

91 → 91

Iterations

Useful iterations: 4 (1.9s)

Iter	Nodes	Cost
0	139	1295
1	279	1104
2	548	996
3	1435	966
4	4793	932
done	5000	932

prune241.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	14
1	13	14
done	13	14

end0.0ms

sample2.4s

Algorithm

intervals

Results

758.0ms	1805×	body	10240	exit
643.0ms	9659×	body	80	nan
452.0ms	7991×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	3×	body	1280	valid
1.0ms	1×	body	2560	valid
1.0ms	1×	body	640	valid
1.0ms	3×	body	160	valid