Details

sample84.0ms

Algorithm

intervals

Results

29.0ms	80×	body	1280	valid
17.0ms	67×	body	640	valid
15.0ms	251×	body	80	valid
5.0ms	30×	body	320	valid
1.0ms	11×	body	160	valid

simplify17.0ms

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: 0.6b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

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

series348.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
115.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
57.0ms	(/ (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	5002	1136

prune456.0ms

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: 0b

Counts

181 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite135.0ms

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)))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))

series341.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a1 a1))
65.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
98.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
65.0ms	(/ (cos th) (sqrt 2.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

756 → 756

Iterations

Useful iterations: 1 (42.0ms)

Iter	Nodes	Cost
0	1544	9868
1	5002	8666

prune1.7s

Filtered

756 candidates to 352 candidates (46.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	755	1	756
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	756	14	770

Merged error: 0b

Counts

770 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (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:

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

series330.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
65.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
99.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify133.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	1115	6666
1	4569	5845
2	5002	5839

prune726.0ms

Filtered

481 candidates to 189 candidates (39.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	480	1	481
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	481	14	495

Merged error: 0b

Counts

495 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.6b	(/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
0.6b	(/ 1 (/ (sqrt (sqrt 2.0)) (cos th)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

2861×	`times-frac`
1831×	`sqrt-prod`
1332×	`add-sqr-sqrt`
1327×	`add-cube-cbrt` `*-un-lft-identity`
104×	`associate-/l*`
48×	`add-exp-log` `div-inv`
46×	`associate-/r*`
32×	`add-cbrt-cube`
24×	`div-exp`
22×	`associate-l`
12×	`cbrt-undiv`
11×	`associate-/r/`
10×	`pow1`
6×	`prod-exp` `cbrt-unprod`
4×	`rec-exp` `1-exp` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`pow-flip` `associate-r` `associate-l/` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 1242

Calls

4 calls:

14.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
38.0ms	(/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
10.0ms	(/ 1 (/ (sqrt (sqrt 2.0)) (cos th)))
5.0ms	(/ (cos th) (sqrt 2.0))

series345.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
59.0ms	(/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
104.0ms	(/ 1 (/ (sqrt (sqrt 2.0)) (cos th)))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify250.0ms

Algorithm

egg-herbie

Counts

1254 → 1254

Iterations

Useful iterations: 1 (63.0ms)

Iter	Nodes	Cost
0	3016	23114
1	5002	20809

prune1.8s

Filtered

1254 candidates to 409 candidates (32.6%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	1254	0	1254
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	1254	14	1268

Merged error: 0b

Counts

1268 → 14

regimes405.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b 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

sample2.6s

Algorithm

intervals

Results

942.0ms	2507×	body	1280	valid
546.0ms	2108×	body	640	valid
494.0ms	7898×	body	80	valid
199.0ms	1051×	body	320	valid
71.0ms	535×	body	160	valid