Details

sample106.0ms

Algorithm

intervals

Results

42.0ms	87×	body	1280	valid
18.0ms	242×	body	80	valid
17.0ms	56×	body	640	valid
4.0ms	21×	body	320	valid
4.0ms	23×	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

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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))

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:

10.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
4.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series46.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
16.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (38.0ms)

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

prune353.0ms

Filtered

116 candidates to 180 candidates (-55.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	169	11	180
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	171	11	182

Merged error: 0.0b

Counts

182 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
12.0ms	(* (/ (cos th) (sqrt 2.0)) a2)
5.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	443	1207
1	1805	1104
2	5001	1084

prune297.0ms

Filtered

117 candidates to 177 candidates (-51.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	178	10	188

Merged error: 0b

Counts

188 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
0.2b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(/ (pow a2 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:

17.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
6.0ms	(/ (pow a2 2) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series42.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (cos th) (/ (pow a2 2) (sqrt 2.0)))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
6.0ms	(/ (pow a2 2) (sqrt 2.0))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	693	1831
1	3202	1552
2	5001	1537

prune402.0ms

Filtered

142 candidates to 252 candidates (-77.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

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

Merged error: 0b

Counts

262 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a1 a1))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
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) (* a1 a1))
8.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms	(/ (cos th) (sqrt 2.0))

series49.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (cos th) (* a1 a1))
15.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2.0))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
9.0ms	(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	501	987
1	2139	864
2	5001	850

prune189.0ms

Filtered

91 candidates to 144 candidates (-58.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	3	4	7
Picked	0	1	1
Done	0	2	2
Total	145	9	154

Merged error: 0b

Counts

154 → 9

regimes586.0ms

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

sample3.1s

Algorithm

intervals

Results

1.1s	2491×	body	1280	valid
627.0ms	2050×	body	640	valid
577.0ms	8173×	body	80	valid
218.0ms	1005×	body	320	valid
78.0ms	526×	body	160	valid

Details

sample106.0ms

simplify14.0ms

prune15.0ms

localize12.0ms

rewrite35.0ms

series46.0ms

simplify52.0ms

prune353.0ms

localize14.0ms

rewrite33.0ms

series38.0ms

simplify54.0ms

prune297.0ms

localize13.0ms

rewrite50.0ms

series42.0ms

simplify78.0ms

prune402.0ms

localize13.0ms

rewrite33.0ms

series49.0ms

simplify52.0ms

prune189.0ms

regimes586.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling