Details

sample95.0ms

Algorithm

intervals

Results

37.0ms	92×	body	1280	valid
16.0ms	64×	body	640	valid
16.0ms	253×	body	80	valid
7.0ms	36×	body	320	valid
2.0ms	14×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune8.0ms

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: 0.4b

Counts

2 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (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))

rewrite40.0ms

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:

15.0ms	(* (/ (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))

series357.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
114.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
66.0ms	(/ (cos th) (sqrt 2.0))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (43.0ms)

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

prune451.0ms

Filtered

180 candidates to 116 candidates (64.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	170	10	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	172	10	182

Merged error: 0.0b

Counts

182 → 10

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

rewrite73.0ms

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)) (* a2 a2))
21.0ms	(/ (/ (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))

series531.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
62.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
295.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
66.0ms	(/ (cos th) (sqrt 2.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

481 → 481

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	1115	6666
1	4568	5845
2	5001	5839

prune715.0ms

Filtered

481 candidates to 187 candidates (38.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	481	0	481
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	481	10	491

Merged error: 0.0b

Counts

491 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (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))

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

series341.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
62.0ms	(/ (pow a1 2) (sqrt 2.0))
56.0ms	(/ (cos th) (sqrt 2.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	694	1786
1	3024	1552
2	5001	1540

prune495.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	252	10	262

Merged error: 0.0b

Counts

262 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* a1 (/ a1 (sqrt 2.0)))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.5b	(/ a1 (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 165

Calls

4 calls:

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

series300.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* a1 (/ a1 (sqrt 2.0)))
120.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
58.0ms	(/ a1 (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	503	1082
1	2105	979
2	5001	954

prune336.0ms

Filtered

177 candidates to 109 candidates (61.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	177	10	187

Merged error: 0.0b

Counts

187 → 10

regimes300.0ms

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	18	15
1	18	15

end0.0ms

sample2.7s

Algorithm

intervals

Results

951.0ms	2465×	body	1280	valid
548.0ms	2077×	body	640	valid
501.0ms	8047×	body	80	valid
209.0ms	1060×	body	320	valid
80.0ms	568×	body	160	valid