Details

sample100.0ms

Algorithm

intervals

Results

31.0ms	83×	body	1280	valid
22.0ms	73×	body	640	valid
13.0ms	225×	body	80	valid
6.0ms	33×	body	320	valid
2.0ms	18×	body	160	valid

simplify14.0ms

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

prune10.0ms

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

rewrite38.0ms

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

series319.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
105.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
58.0ms	(/ (cos th) (sqrt 2.0))
55.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (38.0ms)

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

prune730.0ms

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: 0b

Counts

181 → 12

localize14.0ms

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

rewrite50.0ms

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)))
6.0ms	(/ (pow a2 2) (sqrt 2.0))
10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))

series323.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
55.0ms	(/ (pow a2 2) (sqrt 2.0))
106.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
55.0ms	(/ (cos th) (sqrt 2.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (57.0ms)

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

prune813.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	253	11	264

Merged error: 0b

Counts

264 → 11

localize15.0ms

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))
0.4b	(/ a2 (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite34.0ms

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

series308.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (* a2 (cos th)) (/ a2 (sqrt 2.0)))
106.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
51.0ms	(/ a2 (sqrt 2.0))
59.0ms	(/ (cos th) (sqrt 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (57.0ms)

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

prune609.0ms

Filtered

177 candidates to 109 candidates (61.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	177	11	188

Merged error: 0b

Counts

188 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a2 (sqrt (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.4b	(* (/ a2 (sqrt (sqrt 2.0))) (/ a2 (sqrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

239×	`add-sqr-sqrt`
233×	`times-frac`
226×	`sqrt-prod`
142×	`add-cube-cbrt` `*-un-lft-identity`
53×	`associate-l`
49×	`swap-sqr`
32×	`add-exp-log` `associate-r` `add-cbrt-cube`
19×	`unswap-sqr`
16×	`pow1`
15×	`associate-/r*`
10×	`prod-exp` `cbrt-unprod`
8×	`cbrt-undiv` `div-exp`
7×	`div-inv`
6×	`associate-/l*`
4×	`pow-prod-down` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow2` `frac-times` `pow-plus` `associate-*r/` `pow-sqr` `pow-prod-up`

Counts

4 → 286

Calls

4 calls:

5.0ms	(/ a2 (sqrt (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
28.0ms	(* (/ a2 (sqrt (sqrt 2.0))) (/ a2 (sqrt (sqrt 2.0))))
5.0ms	(/ (cos th) (sqrt 2.0))

series321.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ a2 (sqrt (sqrt 2.0)))
101.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
62.0ms	(* (/ a2 (sqrt (sqrt 2.0))) (/ a2 (sqrt (sqrt 2.0))))
56.0ms	(/ (cos th) (sqrt 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

298 → 298

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	873	3089
1	4139	2759
2	5001	2731

prune874.0ms

Filtered

298 candidates to 157 candidates (52.7%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	298	0	298
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	298	11	309

Merged error: 0b

Counts

309 → 11

regimes777.0ms

Accuracy

0% (0.5b 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

sample2.7s

Algorithm

intervals

Results

948.0ms	2502×	body	1280	valid
512.0ms	1973×	body	640	valid
476.0ms	8004×	body	80	valid
190.0ms	1010×	body	320	valid
67.0ms	539×	body	160	valid

Details

sample100.0ms

simplify14.0ms

prune10.0ms

localize12.0ms

rewrite38.0ms

series319.0ms

simplify54.0ms

prune730.0ms

localize14.0ms

rewrite50.0ms

series323.0ms

simplify75.0ms

prune813.0ms

localize15.0ms

rewrite34.0ms

series308.0ms

simplify70.0ms

prune609.0ms

localize14.0ms

rewrite65.0ms

series321.0ms

simplify100.0ms

prune874.0ms

regimes777.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

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