Details

sample416.0ms

Algorithm

intervals

Results

81.0ms	56×	body	5120	exit
24.0ms	256×	body	80	valid
18.0ms	310×	body	80	nan

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 0.2b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.2b	(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))
4.0ms	(sqrt (atan2 b b))

series108.0ms

Counts

3 → 9

Calls

3 calls:

69.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(pow (sqrt (atan2 b b)) (- b a))
17.0ms	(sqrt (atan2 b b))

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	148	325
1	425	298
2	1341	292
3	5001	290

prune114.0ms

Filtered

57 candidates to 36 candidates (63.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	54	3	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	3	58

Merged error: 0.1b

Counts

58 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
20×	`add-sqr-sqrt`
18×	`unpow-prod-down` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series76.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
29.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify51.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	160	630
1	454	596
2	1640	588
3	5002	584

prune232.0ms

Filtered

104 candidates to 62 candidates (59.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	102	5	107

Merged error: 0.1b

Counts

107 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
4.6b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

30×	`log-prod`
24×	`sqrt-prod`
18×	`unpow-prod-down`
17×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity` `exp-sum`
6×	`pow1` `add-exp-log`
4×	`unpow-prod-up` `exp-prod` `add-cbrt-cube` `add-log-exp`
3×	`rem-log-exp`
2×	`sub-neg` `rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `log-pow` `pow-sub` `sqr-pow`
1×	`pow-to-exp` `exp-diff` `pow-exp` `rem-exp-log`

Counts

4 → 81

Calls

4 calls:

5.0ms	(exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
5.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series129.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
82.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify47.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (38.0ms)

Iter	Nodes	Cost
0	205	685
1	440	620
2	1399	610
3	5001	602

prune241.0ms

Filtered

93 candidates to 58 candidates (62.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	92	6	98

Merged error: 0.1b

Counts

98 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`sqrt-prod`
16×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`pow1`
9×	`unpow-prod-down`
7×	`sqrt-pow1`
5×	`add-exp-log` `pow-unpow` `pow-pow` `pow1/2`
4×	`add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square`
2×	`unpow-prod-up`
1×	`pow-to-exp` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series60.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	160	409
1	454	388
2	1640	384
3	5002	382

prune232.0ms

Filtered

84 candidates to 51 candidates (60.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	87	3	90

Merged error: 0.0b

Counts

90 → 3

regimes70.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	20
1	20	20

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.9s	1839×	body	5120	exit
646.0ms	7989×	body	80	valid
568.0ms	9644×	body	80	nan
10.0ms	3×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	1280	valid

Details

sample416.0ms

simplify59.0ms

prune4.0ms

localize11.0ms

rewrite14.0ms

series108.0ms

simplify43.0ms

prune114.0ms

localize11.0ms

rewrite17.0ms

series76.0ms

simplify51.0ms

prune232.0ms

localize14.0ms

rewrite15.0ms

series129.0ms

simplify47.0ms

prune241.0ms

localize16.0ms

rewrite12.0ms

series60.0ms

simplify50.0ms

prune232.0ms

regimes70.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.5s

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