Details

sample76.0ms

Algorithm

intervals

Results

25.0ms	76×	body	1280	valid
16.0ms	74×	body	640	valid
13.0ms	276×	body	80	valid
3.0ms	22×	body	320	valid
2.0ms	18×	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

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: 0.5b

Counts

2 → 1

localize16.0ms

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))

rewrite35.0ms

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

series347.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
118.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
57.0ms	(/ (cos th) (sqrt 2.0))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (41.0ms)

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

prune466.0ms

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: 0.0b

Counts

181 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
0.3b	(/ (pow a1 2) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite47.0ms

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

series355.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
65.0ms	(/ (pow a1 2) (sqrt 2.0))
114.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
63.0ms	(/ (cos th) (sqrt 2.0))

simplify86.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (61.0ms)

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

prune515.0ms

Filtered

252 candidates to 142 candidates (56.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	248	4	252
Fresh	5	8	13
Picked	1	0	1
Done	0	0	0
Total	254	12	266

Merged error: 0b

Counts

266 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

194×	`times-frac`
127×	`add-sqr-sqrt`
122×	`add-cube-cbrt` `*-un-lft-identity`
70×	`sqrt-prod`
31×	`associate-/r*`
25×	`add-exp-log` `add-cbrt-cube`
22×	`associate-l`
12×	`associate-/l*`
9×	`pow1`
8×	`div-inv`
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/` `associate-/r/` `-commutative`

Counts

4 → 229

Calls

4 calls:

8.0ms	(/ a1 (/ (sqrt 2.0) a1))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ (sqrt 2.0) a1)
5.0ms	(/ (cos th) (sqrt 2.0))

series476.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ a1 (/ (sqrt 2.0) a1))
311.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
43.0ms	(/ (sqrt 2.0) a1)
64.0ms	(/ (cos th) (sqrt 2.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	721	1761
1	3520	1580
2	5001	1580

prune479.0ms

Filtered

241 candidates to 146 candidates (60.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	241	12	253

Merged error: 0b

Counts

253 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a2 a2))
0.2b	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite35.0ms

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))

series321.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos th) (* a2 a2))
109.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2.0))
111.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
58.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (42.0ms)

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

prune278.0ms

Filtered

144 candidates to 91 candidates (63.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	144	12	156

Merged error: 0b

Counts

156 → 12

regimes367.0ms

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

sample2.3s

Algorithm

intervals

Results

831.0ms	2517×	body	1280	valid
471.0ms	2069×	body	640	valid
397.0ms	7900×	body	80	valid
169.0ms	1080×	body	320	valid
54.0ms	499×	body	160	valid