Details

sample108.0ms

Algorithm

intervals

Results

35.0ms	80×	body	1280	valid
21.0ms	57×	body	640	valid
19.0ms	259×	body	80	valid
8.0ms	38×	body	320	valid
3.0ms	18×	body	160	valid

simplify15.0ms

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

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite37.0ms

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))

series42.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (41.0ms)

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

prune335.0ms

Filtered

180 candidates to 116 candidates (35.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	168	12	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	12	181

Merged error: 0b

Counts

181 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a1 a1))
0.2b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

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

series46.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos th) (* a1 a1))
14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
16.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	501	987
1	2139	864
2	5002	850

prune214.0ms

Filtered

144 candidates to 91 candidates (36.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	141	3	144
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	147	9	156

Merged error: 0b

Counts

156 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) a1)
0.2b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
44×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1`
10×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-*l/`

Counts

4 → 131

Calls

4 calls:

4.0ms	(* (cos th) a1)
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
7.0ms	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series44.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (cos th) a1)
14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
17.0ms	(/ (* (* (cos th) a1) a1) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	517	953
1	2497	843
2	5001	830

prune210.0ms

Filtered

143 candidates to 92 candidates (35.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	143	9	152

Merged error: 0b

Counts

152 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 744

Calls

4 calls:

48.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series33.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
8.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

simplify116.0ms

Algorithm

egg-herbie

Counts

756 → 756

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1544	9868
1	5001	8666

prune1.5s

Filtered

756 candidates to 353 candidates (53.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	756	0	756
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	756	9	765

Merged error: 0b

Counts

765 → 9

regimes504.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	11
1	17	11

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.1s	2475×	body	1280	valid
632.0ms	2089×	body	640	valid
583.0ms	8097×	body	80	valid
220.0ms	1020×	body	320	valid
78.0ms	531×	body	160	valid

Details

sample108.0ms

simplify15.0ms

prune9.0ms

localize12.0ms

rewrite37.0ms

series42.0ms

simplify55.0ms

prune335.0ms

localize13.0ms

rewrite31.0ms

series46.0ms

simplify52.0ms

prune214.0ms

localize13.0ms

rewrite29.0ms

series44.0ms

simplify62.0ms

prune210.0ms

localize15.0ms

rewrite136.0ms

series33.0ms

simplify116.0ms

prune1.5s

regimes504.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling