Details

sample113.0ms

Algorithm

intervals

Results

38.0ms	77×	body	1280	valid
24.0ms	79×	body	640	valid
18.0ms	250×	body	80	valid
8.0ms	33×	body	320	valid
3.0ms	21×	body	160	valid

simplify17.0ms

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

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: 0.5b

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))

rewrite34.0ms

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))

series53.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
17.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
6.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (39.0ms)

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

prune340.0ms

Filtered

180 candidates to 116 candidates (35.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	169	11	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	170	11	181

Merged error: 0.0b

Counts

181 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* (cos th) (* a2 a2))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
16.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	501	987
1	2125	864
2	5002	850

prune224.0ms

Filtered

144 candidates to 91 candidates (36.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	144	11	155

Merged error: 0b

Counts

155 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

256×	`sqrt-prod`
254×	`times-frac`
125×	`add-sqr-sqrt`
120×	`add-cube-cbrt` `*-un-lft-identity`
41×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
22×	`associate-l`
17×	`associate-/l*`
14×	`div-inv`
13×	`cbrt-undiv` `div-exp`
12×	`prod-exp` `cbrt-unprod`
9×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 277

Calls

4 calls:

10.0ms	(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0)))
15.0ms	(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))

series61.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0)))
16.0ms	(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
10.0ms	(/ (cos th) (sqrt 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	914	3480
1	4149	2999
2	5002	2994

prune512.0ms

Filtered

289 candidates to 140 candidates (51.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	289	11	300

Merged error: 0b

Counts

300 → 11

localize18.0ms

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))

rewrite140.0ms

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:

50.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
6.0ms	(/ (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))

series35.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
8.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify112.0ms

Algorithm

egg-herbie

Counts

756 → 756

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1544	9868
1	5001	8666

prune1.6s

Filtered

756 candidates to 353 candidates (53.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	756	0	756
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	756	11	767

Merged error: 0b

Counts

767 → 11

regimes611.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	11
1	16	11

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	2528×	body	1280	valid
652.0ms	2080×	body	640	valid
629.0ms	7943×	body	80	valid
256.0ms	1060×	body	320	valid
84.0ms	534×	body	160	valid

Details

sample113.0ms

simplify17.0ms

prune11.0ms

localize12.0ms

rewrite34.0ms

series53.0ms

simplify51.0ms

prune340.0ms

localize13.0ms

rewrite32.0ms

series49.0ms

simplify51.0ms

prune224.0ms

localize16.0ms

rewrite52.0ms

series61.0ms

simplify102.0ms

prune512.0ms

localize18.0ms

rewrite140.0ms

series35.0ms

simplify112.0ms

prune1.6s

regimes611.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling