Details

analyze767.0ms

Algorithm: search

sample99.0ms

Algorithm

intervals

Results

17.0ms	38×	body	1280	valid
16.0ms	36×	body	1280	invalid
12.0ms	38×	body	640	valid
11.0ms	144×	body	80	valid
11.0ms	35×	body	640	invalid
6.0ms	10×	body	160	valid
6.0ms	26×	body	320	valid
3.0ms	13×	body	320	invalid
2.0ms	11×	body	160	invalid
2.0ms	21×	body	80	invalid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	7
1	50	7
2	77	7
3	96	7
4	112	7
5	127	7
6	141	7
7	141	7

prune11.0ms

Filtered

1 candidates to 1 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: 0.8b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.5b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
32×	`add-exp-log` `add-cbrt-cube`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`div-inv` `add-log-exp`
2×	`frac-2neg` `associate-r` `associate-l/` `clear-num` `-commutative`

Counts

4 → 168

Calls

4 calls:

9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series41.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	504	1284
1	2009	1156
2	5001	1136

prune337.0ms

Filtered

116 candidates to 180 candidates (-55.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	12	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	170	12	182

Merged error: 0.0b

Counts

182 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.4b	(* (/ (cos th) (sqrt 2.0)) a1)
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 165

Calls

4 calls:

9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
8.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
5.0ms	(/ (cos th) (sqrt 2.0))
4.0ms	(/ (cos th) (sqrt 2.0))

series40.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
14.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify50.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	444	1207
1	1802	1104
2	5001	1084

prune290.0ms

Filtered

117 candidates to 177 candidates (-51.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	176	13	189

Merged error: 0b

Counts

189 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
640×	`add-sqr-sqrt`
593×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
37×	`associate-/l*`
24×	`associate-/r*`
23×	`div-inv`
22×	`add-exp-log` `add-cbrt-cube`
13×	`unswap-sqr`
8×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `associate-r` `prod-exp` `clear-num` `cbrt-unprod`
1×	`pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 739

Calls

4 calls:

49.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
15.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt 2.0))

series31.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) a1)
5.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
8.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify158.0ms

Algorithm

egg-herbie

Counts

751 → 751

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1319	9484
1	4967	8360
2	5001	8360

prune1.7s

Filtered

353 candidates to 751 candidates (-112.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	751	0	751
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	751	13	764

Merged error: 0b

Counts

764 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`add-cube-cbrt` `*-un-lft-identity`
37×	`associate-/l*`
25×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
22×	`associate-l`
14×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 469

Calls

4 calls:

9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
15.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))

series36.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify121.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	1115	6666
1	4569	5845
2	5001	5839

prune619.0ms

Filtered

188 candidates to 481 candidates (-155.9%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	480	1	481
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	481	13	494

Merged error: 0b

Counts

494 → 13

regimes763.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	15
1	19	15

end0.0ms

analyze753.0ms

Algorithm: search

sample2.8s

Algorithm

intervals

Results

626.0ms	1362×	body	1280	valid
530.0ms	1169×	body	1280	invalid
361.0ms	1127×	body	640	valid
349.0ms	4648×	body	80	valid
307.0ms	954×	body	640	invalid
130.0ms	573×	body	320	valid
112.0ms	476×	body	320	invalid
45.0ms	290×	body	160	valid
40.0ms	497×	body	80	invalid
36.0ms	235×	body	160	invalid

Details

analyze767.0ms

sample99.0ms

simplify14.0ms

prune11.0ms

localize12.0ms

rewrite36.0ms

series41.0ms

simplify52.0ms

prune337.0ms

localize11.0ms

rewrite32.0ms

series40.0ms

simplify50.0ms

prune290.0ms

localize15.0ms

rewrite138.0ms

series31.0ms

simplify158.0ms

prune1.7s

localize15.0ms

rewrite66.0ms

series36.0ms

simplify121.0ms

prune619.0ms

regimes763.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

analyze753.0ms

sample2.8s

Profiling