Details

sample99.0ms

Algorithm

intervals

Results

36.0ms	72×	body	10240	exit
23.0ms	330×	body	80	nan
22.0ms	256×	body	80	valid

simplify52.0ms

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	315	5
5	1609	5
6	5001	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

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))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `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 → 48

Calls

3 calls:

4.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series98.0ms

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))
11.0ms	(sqrt (atan2 b b))

simplify48.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1345	292
3	5001	290

prune130.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-up`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 26

Calls

2 calls:

4.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
2.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series80.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
23.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	145	236
1	453	212
2	1900	202
3	5001	199

prune74.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (pow (atan2 b b) (- b a)) 3/2)
0.0b	(sin (cbrt (pow (pow (atan2 b b) (- b a)) 3/2)))
0.0b	(pow (atan2 b b) (- b a))
0.0b	(cbrt (pow (pow (atan2 b b) (- b a)) 3/2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

27×	`unpow-prod-down`
14×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`cbrt-prod`
12×	`add-cube-cbrt`
8×	`pow-unpow`
7×	`add-exp-log`
6×	`unpow-prod-up`
5×	`pow1` `pow-exp` `sqr-pow`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-to-exp` `sub-neg`
2×	`pow-pow`
1×	`pow1/3` `distribute-lft-out--` `pow-sub` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

3.0ms	(pow (pow (atan2 b b) (- b a)) 3/2)
7.0ms	(sin (cbrt (pow (pow (atan2 b b) (- b a)) 3/2)))
3.0ms	(pow (atan2 b b) (- b a))
3.0ms	(cbrt (pow (pow (atan2 b b) (- b a)) 3/2))

series159.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (pow (atan2 b b) (- b a)) 3/2)
67.0ms	(sin (cbrt (pow (pow (atan2 b b) (- b a)) 3/2)))
17.0ms	(pow (atan2 b b) (- b a))
32.0ms	(cbrt (pow (pow (atan2 b b) (- b a)) 3/2))

simplify91.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	261	631
1	756	592
2	3155	576
3	5001	551

prune219.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (atan2 b b) (- b a))
0.0b	(cbrt (pow (pow (pow (atan2 b b) (- b a)) (sqrt 3/2)) (sqrt 3/2)))
0.0b	(pow (pow (atan2 b b) (- b a)) (sqrt 3/2))
0.0b	(pow (pow (pow (atan2 b b) (- b a)) (sqrt 3/2)) (sqrt 3/2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

65×	`unpow-prod-down`
21×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
17×	`cbrt-prod` `pow-unpow`
14×	`pow-exp`
10×	`add-exp-log`
9×	`sqr-pow`
8×	`unpow-prod-up`
6×	`pow-to-exp` `sqrt-prod`
5×	`pow1`
4×	`sub-neg` `add-cbrt-cube` `add-log-exp`
3×	`pow-pow`
1×	`pow1/3` `distribute-lft-out--` `pow-sub` `difference-of-squares`

Counts

4 → 109

Calls

4 calls:

3.0ms	(pow (atan2 b b) (- b a))
6.0ms	(cbrt (pow (pow (pow (atan2 b b) (- b a)) (sqrt 3/2)) (sqrt 3/2)))
3.0ms	(pow (pow (atan2 b b) (- b a)) (sqrt 3/2))
10.0ms	(pow (pow (pow (atan2 b b) (- b a)) (sqrt 3/2)) (sqrt 3/2))

series450.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (atan2 b b) (- b a))
210.0ms	(cbrt (pow (pow (pow (atan2 b b) (- b a)) (sqrt 3/2)) (sqrt 3/2)))
73.0ms	(pow (pow (atan2 b b) (- b a)) (sqrt 3/2))
145.0ms	(pow (pow (pow (atan2 b b) (- b a)) (sqrt 3/2)) (sqrt 3/2))

simplify128.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	363	1171
1	1065	1113
2	4412	1058
3	5001	1015

prune311.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

808.0ms	1735×	body	10240	exit
705.0ms	7992×	body	80	valid
669.0ms	9800×	body	80	nan
9.0ms	3×	body	5120	valid
4.0ms	3×	body	2560	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid