Details

sample92.0ms

Algorithm

intervals

Results

36.0ms	82×	body	1280	valid
18.0ms	67×	body	640	valid
15.0ms	246×	body	80	valid
5.0ms	25×	body	320	valid
2.0ms	13×	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: 0.5b

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))

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)) (* 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))

series370.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
118.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
69.0ms	(/ (cos th) (sqrt 2.0))
67.0ms	(/ (cos th) (sqrt 2.0))

simplify62.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (41.0ms)

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

prune466.0ms

Filtered

180 candidates to 116 candidates (64.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	166	14	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	14	181

Merged error: 0.0b

Counts

181 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite71.0ms

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:

13.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
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))

series562.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
100.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
281.0ms	(/ (cos th) (sqrt 2.0))

simplify127.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	1115	6666
1	4568	5845
2	5002	5838

prune729.0ms

Filtered

481 candidates to 188 candidates (39.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	481	0	481
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	481	14	495

Merged error: 0.0b

Counts

495 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

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:

19.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
6.0ms	(/ (pow a2 2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series366.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
115.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
67.0ms	(/ (pow a2 2) (sqrt 2.0))
60.0ms	(/ (cos th) (sqrt 2.0))

simplify89.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (67.0ms)

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

prune527.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	3	9	12
Picked	1	0	1
Done	0	1	1
Total	252	14	266

Merged error: 0b

Counts

266 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a2 (cos th)) (/ a2 (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.5b	(/ a2 (sqrt 2.0))
0.8b	(/ (cos th) (sqrt 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

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

series342.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* a2 (cos th)) (/ a2 (sqrt 2.0)))
114.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
61.0ms	(/ a2 (sqrt 2.0))
64.0ms	(/ (cos th) (sqrt 2.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	593	1186
1	2964	1063
2	5001	1037

prune361.0ms

Filtered

177 candidates to 109 candidates (61.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	172	5	177
Fresh	5	7	12
Picked	1	0	1
Done	0	1	1
Total	178	13	191

Merged error: 0b

Counts

191 → 13

regimes371.0ms

Accuracy

0% (0.5b 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 (0.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample2.7s

Algorithm

intervals

Results

976.0ms	2541×	body	1280	valid
569.0ms	2128×	body	640	valid
527.0ms	8197×	body	80	valid
193.0ms	976×	body	320	valid
73.0ms	530×	body	160	valid

Details

sample92.0ms

simplify16.0ms

prune6.0ms

localize12.0ms

rewrite34.0ms

series370.0ms

simplify62.0ms

prune466.0ms

localize15.0ms

rewrite71.0ms

series562.0ms

simplify127.0ms

prune729.0ms

localize14.0ms

rewrite49.0ms

series366.0ms

simplify89.0ms

prune527.0ms

localize13.0ms

rewrite33.0ms

series342.0ms

simplify80.0ms

prune361.0ms

regimes371.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.7s

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