Details

sample362.0ms

Algorithm

intervals

Results

60.0ms	57×	body	5120	exit
21.0ms	256×	body	80	valid
18.0ms	309×	body	80	nan

simplify61.0ms

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

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(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))

series100.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
21.0ms	(pow (sqrt (atan2 b b)) (- b a))
16.0ms	(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

prune105.0ms

Filtered

57 candidates to 36 candidates (63.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	2	58

Merged error: 0.0b

Counts

58 → 2

localize14.0ms

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))
2.0ms	(sqrt (atan2 b b))

series72.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify57.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (45.0ms)

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

prune221.0ms

Filtered

104 candidates to 62 candidates (59.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	3	106

Merged error: 0.0b

Counts

106 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.3b	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

42×	`unpow-prod-down`
36×	`cbrt-prod`
33×	`sqrt-prod`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
15×	`cube-prod`
9×	`pow1`
6×	`unpow-prod-up` `sqrt-pow1`
5×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`pow1/2` `add-cbrt-cube` `add-log-exp` `sqr-pow`
3×	`sub-neg`
2×	`rem-sqrt-square` `pow-sub`
1×	`cube-div` `cube-mult` `pow-to-exp` `cbrt-div` `pow1/3` `unpow3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 105

Calls

4 calls:

6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
7.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series76.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
26.0ms	(cbrt (pow (pow (sqrt (sqrt (atan2 b b))) (- b a)) 3))
10.0ms	(sqrt (atan2 b b))
14.0ms	(sqrt (atan2 b b))

simplify97.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	309	860
1	1090	829
2	3922	821
3	5001	821

prune252.0ms

Filtered

117 candidates to 62 candidates (53.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	117	3	120

Merged error: 0.0b

Counts

120 → 3

localize17.0ms

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))

series59.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms	(sqrt (atan2 b b))
11.0ms	(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

prune248.0ms

Filtered

84 candidates to 51 candidates (60.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Merged error: 0.0b

Counts

87 → 3

regimes43.0ms

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	14	22
1	14	22

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.9s	1897×	body	5120	exit
647.0ms	7993×	body	80	valid
597.0ms	9969×	body	80	nan
6.0ms	2×	body	5120	valid
3.0ms	2×	body	2560	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

Details

sample362.0ms

simplify61.0ms

prune4.0ms

localize24.0ms

rewrite14.0ms

series100.0ms

simplify48.0ms

prune105.0ms

localize14.0ms

rewrite17.0ms

series72.0ms

simplify57.0ms

prune221.0ms

localize14.0ms

rewrite19.0ms

series76.0ms

simplify97.0ms

prune252.0ms

localize17.0ms

rewrite12.0ms

series59.0ms

simplify50.0ms

prune248.0ms

regimes43.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.6s

Profiling