Details

sample93.0ms

Algorithm

intervals

Results

27.0ms	77×	body	1280	valid
17.0ms	69×	body	640	valid
16.0ms	280×	body	80	valid
6.0ms	35×	body	320	valid
2.0ms	14×	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

prune17.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.7b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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))

series337.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
115.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
52.0ms	(/ (cos th) (sqrt 2.0))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	517	1294
1	2057	1166
2	5001	1146

prune717.0ms

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	1	0	1
Picked	1	0	1
Done	0	0	0
Total	168	14	182

Merged error: 0b

Counts

182 → 14

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l` `sqrt-prod`
25×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`

Counts

4 → 165

Calls

4 calls:

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

series332.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
103.0ms	(* (/ (cos th) (sqrt 2.0)) a1)
58.0ms	(/ (cos th) (sqrt 2.0))
55.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	457	1216
1	1837	1113
2	5001	1093

prune655.0ms

Filtered

177 candidates to 117 candidates (66.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	178	13	191

Merged error: 0b

Counts

191 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

56×	`times-frac`
53×	`add-sqr-sqrt`
48×	`add-cube-cbrt` `*-un-lft-identity`
34×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
23×	`associate-l`
14×	`pow1`
12×	`associate-/r*`
11×	`prod-exp` `cbrt-unprod`
6×	`pow-prod-down` `associate-/l*`
5×	`cbrt-undiv` `div-exp`
4×	`associate-r` `add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`associate-*r/`

Counts

4 → 144

Calls

4 calls:

7.0ms	(* (* (cos th) (/ a1 (sqrt 2.0))) a1)
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ a1 (sqrt 2.0))
8.0ms	(/ (cos th) (sqrt 2.0))

series347.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(* (* (cos th) (/ a1 (sqrt 2.0))) a1)
115.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
60.0ms	(/ a1 (sqrt 2.0))
54.0ms	(/ (cos th) (sqrt 2.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	526	1050
1	2323	935
2	5001	915

prune551.0ms

Filtered

156 candidates to 97 candidates (62.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	156	13	169

Merged error: 0b

Counts

169 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite138.0ms

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:

48.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
16.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series336.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
62.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
95.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify117.0ms

Algorithm

egg-herbie

Counts

756 → 756

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1546	9871
1	5002	8669

prune2.1s

Filtered

756 candidates to 351 candidates (46.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	755	1	756
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	757	12	769

Merged error: 0b

Counts

769 → 12

regimes750.0ms

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

sample2.7s

Algorithm

intervals

Results

911.0ms	2557×	body	1280	valid
539.0ms	2176×	body	640	valid
458.0ms	8015×	body	80	valid
198.0ms	1105×	body	320	valid
63.0ms	521×	body	160	valid

Details

sample93.0ms

simplify14.0ms

prune17.0ms

localize11.0ms

rewrite33.0ms

series337.0ms

simplify52.0ms

prune717.0ms

localize12.0ms

rewrite35.0ms

series332.0ms

simplify52.0ms

prune655.0ms

localize12.0ms

rewrite33.0ms

series347.0ms

simplify60.0ms

prune551.0ms

localize15.0ms

rewrite138.0ms

series336.0ms

simplify117.0ms

prune2.1s

regimes750.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

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