Details

sample83.0ms

Algorithm

intervals

Results

32.0ms	67×	body	10240	exit
18.0ms	361×	body	80	nan
14.0ms	256×	body	80	valid

simplify51.0ms

Algorithm

egg-herbie

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 54

Calls

2 calls:

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

series27.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(pow (sqrt (atan2 b b)) (- b a))
9.0ms	(sqrt (atan2 b b))

simplify65.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	224	417
1	632	348
2	2275	345
3	5001	329

prune116.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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))

rewrite83.0ms

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:

9.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
61.0ms	(* (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))

series84.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
36.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
13.0ms	(sqrt (atan2 b b))
9.0ms	(sqrt (atan2 b b))

simplify68.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	461	2468
1	2032	2166
2	5002	2132

prune486.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 65

Calls

2 calls:

10.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
1.0ms	(sqrt (atan2 b b))

series37.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))
9.0ms	(sqrt (atan2 b b))

simplify43.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	764
1	1154	628
2	5001	583

prune128.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-prod`
31×	`unpow-prod-down`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
17×	`add-cube-cbrt`
16×	`pow-unpow`
9×	`pow1`
7×	`add-exp-log`
6×	`pow-pow` `sqrt-pow1`
5×	`pow-exp`
4×	`expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `sqr-pow`
2×	`rem-sqrt-square` `distribute-lft-out--` `difference-of-squares`
1×	`sqrt-pow2`

Counts

4 → 101

Calls

4 calls:

14.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
8.0ms	(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series733.0ms

Counts

4 → 12

Calls

4 calls:

514.0ms	(pow (pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a))) (sqrt (- b a)))
200.0ms	(pow (sqrt (sqrt (atan2 b b))) (sqrt (- b a)))
9.0ms	(sqrt (atan2 b b))
9.0ms	(sqrt (atan2 b b))

simplify43.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	388	1144
1	1316	1068
2	5001	989

prune354.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes175.0ms

Accuracy

0% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

778.0ms	1922×	body	10240	exit
454.0ms	9906×	body	80	nan
441.0ms	7983×	body	80	valid
6.0ms	2×	body	5120	valid
4.0ms	3×	body	2560	valid
2.0ms	3×	body	1280	valid
2.0ms	4×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid