Details

sample79.0ms

Algorithm

intervals

Results

22.0ms	67×	body	1280	valid
21.0ms	82×	body	640	valid
14.0ms	263×	body	80	valid
5.0ms	29×	body	320	valid
1.0ms	13×	body	160	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	26	7
1	57	6
2	87	6
3	114	6
4	132	6
5	151	6
6	171	6
7	173	6
8	173	6

prune8.0ms

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)) (* 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))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
92×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity`
58×	`sqrt-prod`
50×	`associate-l`
38×	`unswap-sqr`
36×	`associate-r`
32×	`add-exp-log` `add-cbrt-cube`
24×	`associate-l/` `associate-/r`
14×	`pow1`
12×	`swap-sqr` `prod-exp` `cbrt-unprod` `associate-/l*`
10×	`*-commutative`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 250

Calls

4 calls:

18.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
18.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
8.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))

series368.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
116.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
64.0ms	(/ (cos th) (sqrt 2.0))
67.0ms	(/ (cos th) (sqrt 2.0))

simplify106.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	754	1862
1	4173	1710
2	5001	1700

prune464.0ms

Filtered

262 candidates to 158 candidates (39.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	254	8	262
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	255	9	264

Merged error: 0b

Counts

264 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.5b	(/ (* (cos th) (fabs a2)) (sqrt 2.0))
0.7b	(/ (cos th) (sqrt 2.0))
21.7b	(sqrt (* a2 a2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
118×	`times-frac`
92×	`add-cube-cbrt` `*-un-lft-identity`
83×	`sqrt-prod`
49×	`associate-l`
42×	`associate-r`
28×	`unswap-sqr`
23×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r` `associate-/l`
17×	`pow1`
14×	`*-commutative`
12×	`associate-*l/`
10×	`swap-sqr`
7×	`prod-exp` `cbrt-unprod`
6×	`sqrt-pow1`
5×	`cbrt-undiv` `rem-sqrt-square` `div-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `div-inv`
1×	`pow2` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 267

Calls

4 calls:

22.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
9.0ms	(/ (* (cos th) (fabs a2)) (sqrt 2.0))
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(sqrt (* a2 a2))

series263.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
73.0ms	(/ (* (cos th) (fabs a2)) (sqrt 2.0))
65.0ms	(/ (cos th) (sqrt 2.0))
8.0ms	(sqrt (* a2 a2))

simplify104.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	788	2055
1	3667	1953
2	5001	1948

prune622.0ms

Filtered

279 candidates to 170 candidates (39.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	278	1	279
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	280	8	288

Merged error: 0b

Counts

288 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
0.3b	(* (/ (fabs a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt 2.0))
21.7b	(sqrt (* a2 a2))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

1352×	`add-sqr-sqrt`
1194×	`cbrt-prod`
1150×	`associate-/r*`
735×	`frac-times`
641×	`sqrt-prod`
572×	`*-un-lft-identity`
571×	`add-cube-cbrt`
332×	`associate-l`
324×	`times-frac`
300×	`unswap-sqr`
239×	`swap-sqr`
223×	`associate-r`
205×	`associate-/l*`
75×	`add-cbrt-cube`
69×	`clear-num`
68×	`frac-2neg`
61×	`associate-*l/`
39×	`add-exp-log`
36×	`cbrt-unprod`
31×	`*-commutative`
30×	`cbrt-undiv`
19×	`pow1`
15×	`associate-*r/`
14×	`prod-exp`
10×	`div-exp`
6×	`sqrt-pow1`
5×	`rem-sqrt-square` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`un-div-inv`
1×	`pow2` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up`

Counts

4 → 1233

Calls

4 calls:

18.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
102.0ms	(* (/ (fabs a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))
5.0ms	(/ (cos th) (sqrt 2.0))
5.0ms	(sqrt (* a2 a2))

series298.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (/ (cos th) (sqrt 2.0)) (* a1 a1))
100.0ms	(* (/ (fabs a2) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ (cos th) (cbrt (sqrt 2.0))))
68.0ms	(/ (cos th) (sqrt 2.0))
9.0ms	(sqrt (* a2 a2))

simplify252.0ms

Algorithm

egg-herbie

Counts

1245 → 1245

Iterations

Useful iterations: 1 (75.0ms)

Iter	Nodes	Cost
0	3772	22064
1	5001	21398

prune2.7s

Filtered

1245 candidates to 541 candidates (56.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1242	3	1245
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	1246	7	1253

Merged error: 0b

Counts

1253 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.4b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
68×	`add-sqr-sqrt`
52×	`add-cube-cbrt` `*-un-lft-identity`
39×	`sqrt-prod`
24×	`associate-r` `associate-l`
12×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
8×	`*-commutative` `unswap-sqr`
6×	`associate-/r*`
5×	`pow1`
3×	`expm1-log1p-u` `fma-udef` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `div-inv`

Counts

3 → 138

Calls

3 calls:

1.0ms	(fma a1 a1 (* a2 a2))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
10.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

series396.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma a1 a1 (* a2 a2))
117.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
238.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt 2.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	391	1439
1	1666	1325
2	5001	1292

prune243.0ms

Filtered

147 candidates to 93 candidates (36.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	149	5	154

Merged error: 0b

Counts

154 → 5

regimes179.0ms

Accuracy

0% (0.4b 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	11	6
1	11	6

end0.0ms

sample2.4s

Algorithm

intervals

Results

860.0ms	2509×	body	1280	valid
485.0ms	2099×	body	640	valid
437.0ms	8111×	body	80	valid
166.0ms	1003×	body	320	valid
61.0ms	528×	body	160	valid