Details

sample87.0ms

Algorithm

intervals

Results

27.0ms	84×	body	1280	valid
18.0ms	272×	body	80	valid
17.0ms	78×	body	640	valid
6.0ms	33×	body	320	valid
2.0ms	14×	body	160	valid

simplify16.0ms

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

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.8b	(/ (cos th) (sqrt 2.0))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite35.0ms

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

series356.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
115.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
64.0ms	(/ (cos th) (sqrt 2.0))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (42.0ms)

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

prune457.0ms

Filtered

180 candidates to 116 candidates (64.4%)

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: 0.0b

Counts

181 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
0.3b	(/ (pow a2 2) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
121×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
77×	`sqrt-prod`
53×	`associate-r`
41×	`unpow-prod-down`
33×	`add-exp-log`
25×	`associate-l` `add-cbrt-cube`
15×	`unpow2` `sqr-pow`
12×	`associate-/r*` `unswap-sqr`
11×	`pow1` `associate-/l*`
10×	`prod-exp`
9×	`div-exp`
8×	`cbrt-unprod`
5×	`cbrt-undiv`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative`
1×	`associate-r/` `associate-l/`

Counts

4 → 240

Calls

4 calls:

20.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
6.0ms	(/ (pow a2 2) (sqrt 2.0))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))

series355.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
65.0ms	(/ (pow a2 2) (sqrt 2.0))
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
64.0ms	(/ (cos th) (sqrt 2.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	693	1786
1	3017	1552
2	5001	1540

prune512.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	252	12	264

Merged error: 0.0b

Counts

264 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a2 (/ (sqrt 2.0) a2))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b	(/ (sqrt 2.0) a2)
0.8b	(/ (cos th) (sqrt 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
127×	`add-sqr-sqrt`
122×	`add-cube-cbrt` `*-un-lft-identity`
70×	`sqrt-prod`
31×	`associate-/r*`
25×	`add-exp-log` `add-cbrt-cube`
22×	`associate-l`
12×	`associate-/l*`
9×	`pow1`
8×	`div-inv`
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/` `associate-/r/` `-commutative`

Counts

4 → 229

Calls

4 calls:

8.0ms	(/ a2 (/ (sqrt 2.0) a2))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms	(/ (sqrt 2.0) a2)
5.0ms	(/ (cos th) (sqrt 2.0))

series291.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ a2 (/ (sqrt 2.0) a2))
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
49.0ms	(/ (sqrt 2.0) a2)
64.0ms	(/ (cos th) (sqrt 2.0))

simplify93.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	721	1761
1	3520	1580
2	5001	1580

prune493.0ms

Filtered

241 candidates to 146 candidates (60.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	242	11	253

Merged error: 0.0b

Counts

253 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.3b	(/ (pow a1 2) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

142×	`times-frac`
121×	`add-sqr-sqrt`
94×	`add-cube-cbrt` `*-un-lft-identity`
77×	`sqrt-prod`
53×	`associate-r`
41×	`unpow-prod-down`
33×	`add-exp-log`
25×	`associate-l` `add-cbrt-cube`
15×	`unpow2` `sqr-pow`
12×	`associate-/r*` `unswap-sqr`
11×	`pow1` `associate-/l*`
10×	`prod-exp`
9×	`div-exp`
8×	`cbrt-unprod`
5×	`cbrt-undiv`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative`
1×	`associate-r/` `associate-l/`

Counts

4 → 240

Calls

4 calls:

16.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
6.0ms	(/ (pow a1 2) (sqrt 2.0))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms	(/ (cos th) (sqrt 2.0))

series545.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
62.0ms	(/ (pow a1 2) (sqrt 2.0))
311.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	694	1786
1	3024	1552
2	5001	1540

prune458.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	253	10	263

Merged error: 0b

Counts

263 → 10

regimes317.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	11
1	16	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

828.0ms	2502×	body	1280	valid
464.0ms	2059×	body	640	valid
431.0ms	8035×	body	80	valid
168.0ms	1042×	body	320	valid
61.0ms	536×	body	160	valid