Details

sample120.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

42.0ms	94×	body	1280	valid
22.0ms	71×	body	640	valid
20.0ms	259×	body	80	valid
11.0ms	34×	body	320	valid
3.0ms	20×	body	160	valid

simplify15.0ms

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

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

localize12.0ms

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))
0.6b	(/ (cos th) (sqrt 2.0))
0.6b	(/ (cos th) (sqrt 2.0))

rewrite37.0ms

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))
4.0ms	(/ (cos th) (sqrt 2.0))
7.0ms	(/ (cos th) (sqrt 2.0))

series43.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 2 (38.0ms)

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

prune341.0ms

Filtered

116 candidates to 180 candidates (-55.2%)

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: 0b

Counts

181 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
0.6b	(/ (cos th) (sqrt (sqrt 2.0)))
0.6b	(/ (cos th) (sqrt 2.0))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

1149×	`sqrt-prod`
1137×	`times-frac`
626×	`add-sqr-sqrt`
592×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-l`
37×	`associate-/l*`
34×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r*`
23×	`div-inv`
13×	`unswap-sqr`
11×	`cbrt-undiv` `div-exp`
9×	`pow1` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 744

Calls

4 calls:

45.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
6.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))
17.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (* a2 a2))
8.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms	(/ (cos th) (sqrt 2.0))
6.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify114.0ms

Algorithm

egg-herbie

Counts

756 → 756

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1544	9868
1	5001	8669

prune1.5s

Filtered

352 candidates to 756 candidates (-114.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	755	1	756
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	757	13	770

Merged error: 0b

Counts

770 → 13

localize15.0ms

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))
0.6b	(/ (cos th) (sqrt 2.0))

rewrite45.0ms

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:

15.0ms	(* (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))

series47.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (cos th) (/ (pow a1 2) (sqrt 2.0)))
6.0ms	(/ (pow a1 2) (sqrt 2.0))
19.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	694	1831
1	3211	1552
2	5001	1537

prune587.0ms

Filtered

142 candidates to 252 candidates (-77.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	249	3	252
Fresh	4	7	11
Picked	1	0	1
Done	0	1	1
Total	254	11	265

Merged error: 0b

Counts

265 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ a1 (cbrt (sqrt 2.0)))
0.2b	(* (/ a1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ a1 (cbrt (sqrt 2.0))))
0.3b	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
0.6b	(/ (cos th) (sqrt 2.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
102×	`add-sqr-sqrt`
75×	`add-cube-cbrt` `*-un-lft-identity`
46×	`cbrt-prod`
45×	`sqrt-prod`
41×	`add-exp-log`
33×	`add-cbrt-cube`
32×	`associate-r`
29×	`associate-l`
15×	`associate-/r*`
14×	`prod-exp` `cbrt-unprod`
11×	`pow1` `cbrt-undiv` `div-exp` `unswap-sqr`
6×	`associate-/l*`
5×	`div-inv`
4×	`pow-prod-down` `add-log-exp`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 205

Calls

4 calls:

4.0ms	(/ a1 (cbrt (sqrt 2.0)))
20.0ms	(* (/ a1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ a1 (cbrt (sqrt 2.0))))
9.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
5.0ms	(/ (cos th) (sqrt 2.0))

series57.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ a1 (cbrt (sqrt 2.0)))
6.0ms	(* (/ a1 (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (/ a1 (cbrt (sqrt 2.0))))
15.0ms	(* (/ (cos th) (sqrt 2.0)) (* a2 a2))
6.0ms	(/ (cos th) (sqrt 2.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	757	1995
1	3678	1801
2	5001	1715

prune514.0ms

Filtered

145 candidates to 217 candidates (-49.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	217	11	228

Merged error: 0b

Counts

228 → 11

regimes649.0ms

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	20	18
1	20	18

end0.0ms

sample3.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 100%

Results

1.2s	2576×	body	1280	valid
668.0ms	2141×	body	640	valid
596.0ms	7934×	body	80	valid
237.0ms	1055×	body	320	valid
83.0ms	524×	body	160	valid

Details

sample120.0ms

simplify15.0ms

prune9.0ms

localize12.0ms

rewrite37.0ms

series43.0ms

simplify55.0ms

prune341.0ms

localize15.0ms

rewrite140.0ms

series35.0ms

simplify114.0ms

prune1.5s

localize15.0ms

rewrite45.0ms

series47.0ms

simplify79.0ms

prune587.0ms

localize16.0ms

rewrite47.0ms

series57.0ms

simplify90.0ms

prune514.0ms

regimes649.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling