Details

sample90.0ms

Algorithm

intervals

Results

33.0ms	88×	body	1280	valid
17.0ms	69×	body	640	valid
15.0ms	260×	body	80	valid
5.0ms	29×	body	320	valid
3.0ms	23×	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

prune7.0ms

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

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

series355.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
119.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
57.0ms	(/ (cos th) (sqrt 2.0))
66.0ms	(/ (cos th) (sqrt 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	504	1284
1	2009	1156
2	5002	1136

prune457.0ms

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

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a2 a2))
0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

44×	`times-frac`
43×	`add-sqr-sqrt`
37×	`add-cube-cbrt` `*-un-lft-identity`
32×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-prod`
25×	`associate-l`
14×	`pow1`
12×	`prod-exp` `associate-/r*` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`associate-*l/`

Counts

4 → 132

Calls

4 calls:

6.0ms	(* (cos th) (* a2 a2))
8.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))

series335.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos th) (* a2 a2))
113.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	501	987
1	2125	864
2	5002	850

prune309.0ms

Filtered

144 candidates to 91 candidates (63.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	146	11	157

Merged error: 0.0b

Counts

157 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

256×	`sqrt-prod`
254×	`times-frac`
125×	`add-sqr-sqrt`
120×	`add-cube-cbrt` `*-un-lft-identity`
41×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
22×	`associate-l`
17×	`associate-/l*`
14×	`div-inv`
13×	`cbrt-undiv` `div-exp`
12×	`prod-exp` `cbrt-unprod`
9×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 277

Calls

4 calls:

9.0ms	(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0)))
15.0ms	(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
5.0ms	(/ (cos th) (sqrt 2.0))

series463.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0)))
121.0ms	(/ (/ (* (cos th) (* a2 a2)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
112.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify102.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	914	3480
1	4149	2999
2	5001	2994

prune695.0ms

Filtered

289 candidates to 139 candidates (48.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	289	0	289
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	289	11	300

Merged error: 0.0b

Counts

300 → 11

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))

rewrite49.0ms

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:

19.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms	(/ (pow a1 2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series342.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
110.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
63.0ms	(/ (pow a1 2) (sqrt 2.0))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (62.0ms)

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

prune466.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	249	3	252
Fresh	4	4	8
Picked	0	1	1
Done	0	2	2
Total	253	10	263

Merged error: 0b

Counts

263 → 10

regimes271.0ms

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	16	11
1	16	11

end0.0ms

sample2.6s

Algorithm

intervals

Results

950.0ms	2527×	body	1280	valid
555.0ms	2150×	body	640	valid
503.0ms	8184×	body	80	valid
191.0ms	1012×	body	320	valid
64.0ms	505×	body	160	valid