Details

sample93.0ms

Algorithm

intervals

Results

35.0ms	96×	body	1280	valid
18.0ms	72×	body	640	valid
18.0ms	251×	body	80	valid
5.0ms	26×	body	320	valid
1.0ms	9×	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

localize11.0ms

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))
0.7b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite39.0ms

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))
9.0ms	(/ (cos th) (sqrt 2.0))

series349.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
118.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
56.0ms	(/ (cos th) (sqrt 2.0))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (40.0ms)

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

prune472.0ms

Filtered

180 candidates to 116 candidates (64.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	167	13	180
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	168	13	181

Merged error: 0.0b

Counts

181 → 13

localize13.0ms

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))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite47.0ms

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 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))

series348.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
109.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
64.0ms	(/ (pow a2 2) (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify85.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (60.0ms)

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

prune721.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	249	3	252
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	253	12	265

Merged error: 0b

Counts

265 → 12

localize12.0ms

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))
0.3b	(/ a2 (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite37.0ms

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)))
12.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
4.0ms	(/ a2 (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series328.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (* a2 (cos th)) (/ a2 (sqrt 2.0)))
109.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
52.0ms	(/ a2 (sqrt 2.0))
62.0ms	(/ (cos th) (sqrt 2.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (59.0ms)

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

prune374.0ms

Filtered

177 candidates to 109 candidates (61.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	177	12	189

Merged error: 0b

Counts

189 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.3b	(/ (pow a1 2) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite51.0ms

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)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
10.0ms	(/ (pow a1 2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series347.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
112.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
63.0ms	(/ (pow a1 2) (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	694	1831
1	3211	1552
2	5001	1537

prune495.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	2	7	9
Picked	0	1	1
Done	0	2	2
Total	253	11	264

Merged error: 0b

Counts

264 → 11

regimes335.0ms

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	17	11
1	17	11

end0.0ms

sample2.6s

Algorithm

intervals

Results

912.0ms	2495×	body	1280	valid
555.0ms	2190×	body	640	valid
487.0ms	8034×	body	80	valid
193.0ms	1050×	body	320	valid
63.0ms	488×	body	160	valid

Details

sample93.0ms

simplify16.0ms

prune6.0ms

localize11.0ms

rewrite39.0ms

series349.0ms

simplify54.0ms

prune472.0ms

localize13.0ms

rewrite47.0ms

series348.0ms

simplify85.0ms

prune721.0ms

localize12.0ms

rewrite37.0ms

series328.0ms

simplify72.0ms

prune374.0ms

localize13.0ms

rewrite51.0ms

series347.0ms

simplify78.0ms

prune495.0ms

regimes335.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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