Details

sample316.0ms

Algorithm

intervals

Results

26.0ms	57×	body	10240	exit
16.0ms	256×	body	80	valid
11.0ms	336×	body	80	nan

simplify58.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

localize11.0ms

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))

rewrite14.0ms

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:

3.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series112.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(pow (sqrt (atan2 b b)) (- b a))
30.0ms	(sqrt (atan2 b b))

simplify51.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (41.0ms)

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

prune106.0ms

Filtered

57 candidates to 36 candidates (63.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 0.0b

Counts

58 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.0b	(sin (* (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))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`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 → 136

Calls

4 calls:

17.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
3.0ms	(sin (* (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))

series146.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
89.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify53.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	280	1645
1	1169	1507
2	5001	1483

prune244.0ms

Filtered

148 candidates to 71 candidates (48.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	147	5	152

Merged error: 0.0b

Counts

152 → 5

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)))

rewrite7.0ms

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:

3.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
3.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series81.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
23.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify59.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (55.0ms)

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

prune60.0ms

Filtered

32 candidates to 21 candidates (65.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	31	1	32
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Merged error: 0.0b

Counts

37 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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:

4.0ms	(pow (pow (atan2 b b) (- b a)) 3/2)
4.0ms	(cbrt (pow (pow (atan2 b b) (- b a)) 3/2))
5.0ms	(sin (cbrt (pow (pow (atan2 b b) (- b a)) 3/2)))
7.0ms	(pow (atan2 b b) (- b a))

series155.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (pow (atan2 b b) (- b a)) 3/2)
28.0ms	(cbrt (pow (pow (atan2 b b) (- b a)) 3/2))
70.0ms	(sin (cbrt (pow (pow (atan2 b b) (- b a)) 3/2)))
18.0ms	(pow (atan2 b b) (- b a))

simplify94.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	261	631
1	756	592
2	3154	576
3	5001	551

prune170.0ms

Filtered

87 candidates to 57 candidates (65.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	86	1	87
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	88	3	91

Merged error: 0.0b

Counts

91 → 3

regimes41.0ms

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

sample1.9s

Algorithm

intervals

Results

774.0ms	1790×	body	10240	exit
426.0ms	7992×	body	80	valid
357.0ms	9874×	body	80	nan
7.0ms	2×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid