Details

sample316.0ms

Algorithm

intervals

Results

24.0ms	56×	body	10240	exit
16.0ms	256×	body	80	valid
15.0ms	325×	body	80	nan

simplify2.8s

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	110	9
5	254	9
6	734	9
7	2642	9
done	5000	9

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

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))

rewrite16.0ms

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:

6.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series105.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

72 → 72

Iterations

Useful iterations: 4 (1.6s)

Iter	Nodes	Cost
0	117	962
1	252	836
2	532	757
3	1278	728
4	3946	699
done	5000	699

prune154.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
93×	`sqrt-prod`
87×	`unpow-prod-down`
59×	`unpow-prod-up`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
17×	`add-exp-log`
15×	`sqr-pow`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 206

Calls

4 calls:

5.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
40.0ms	(* (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))

series87.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
14.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify849.0ms

Counts

218 → 218

Iterations

Useful iterations: done (843.0ms)

Iter	Nodes	Cost
0	210	5420
1	458	3874
2	1529	3547
done	5000	3504

prune482.0ms

Pruning

4 alts after pruning (4 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))) (- b a))
0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt` `sqrt-prod`
24×	`associate-l`
22×	`unpow-prod-up`
21×	`unpow-prod-down`
18×	`prod-diff`
10×	`add-exp-log`
9×	`pow1`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `unswap-sqr`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `prod-exp` `sqr-pow`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `pow-sub`
1×	`associate-l/` `-commutative` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 121

Calls

4 calls:

8.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
18.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series135.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
87.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a)))))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.7s

Counts

133 → 133

Iterations

Useful iterations: 3 (888.0ms)

Iter	Nodes	Cost
0	163	2396
1	361	1893
2	920	1732
3	3244	1670
done	5000	1670

prune417.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

0.0ms	(cbrt (atan2 b b))
0.0ms	(cbrt (atan2 b b))
0.0ms	(cbrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series335.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (atan2 b b))
108.0ms	(cbrt (atan2 b b))
107.0ms	(cbrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify1.8s

Counts

66 → 66

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	31	424
1	41	398
2	71	360
3	125	351
4	336	351
5	1512	351
done	5001	351

prune268.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes120.0ms

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	11	22
1	12	22
done	12	22

end0.0ms

sample2.2s

Algorithm

intervals

Results

739.0ms	1753×	body	10240	exit
593.0ms	9664×	body	80	nan
458.0ms	7986×	body	80	valid
6.0ms	2×	body	5120	valid
1.0ms	3×	body	640	valid
1.0ms	6×	body	160	valid
1.0ms	1×	body	1280	valid
0.0ms	2×	body	320	valid